SolidWorks Simulation Tutorial

PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e ® SolidWorks

2012

SolidWorks Simulation

Dassault Systèmes SolidWorks Corporation 175 Wyman Street Waltham, Massachusetts 02451 USA

In the event that you receive a request from any agency of the U.S. government to provide Software with rights beyond those set forth above, you will notify DS SolidWorks of the scope of the request and DS SolidWorks will have five (5) business days to, in its sole discretion, accept or reject such request. Contractor/Manufacturer: Dassault Systèmes SolidWorks Corporation, 175 Wyman Street, Waltham, Massachusetts 02451 US.

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© 1995-2011, Dassault Systèmes SolidWorks Corporation, a Dassault Systèmes S.A. company, 175 Wyman Street, Waltham, MA 02451 USA. All rights reserved. The information and the software discussed in this document are subject to change without notice and are not commitments by Dassault Systèmes SolidWorks Corporation (DS SolidWorks). No material may be reproduced or transmitted in any form or by any means, electronically or manually, for any purpose without the express written permission of DS SolidWorks. The software discussed in this document is furnished under a license and may be used or copied only in accordance with the terms of the license. All warranties given by DS SolidWorks as to the software and documentation are set forth in the license agreement, and nothing stated in, or implied by, this document or its contents shall be considered or deemed a modification or amendment of any terms, including warranties, in the license agreement. Patent Notices

SolidWorks® 3D mechanical CAD software is protected by U.S. Patents 5,815,154; 6,219,049; 6,219,055; 6,611,725; 6,844,877; 6,898,560; 6,906,712; 7,079,990; 7,477,262; 7,558,705; 7,571,079; 7,590,497; 7,643,027; 7,672,822; 7,688,318; 7,694,238; 7,853,940 and foreign patents, (e.g., EP 1,116,190 and JP 3,517,643).

eDrawings® software is protected by U.S. Patent 7,184,044; U.S. Patent 7,502,027; and Canadian Patent 2,318,706. U.S. and foreign patents pending.

Trademarks and Product Names for SolidWorks Products and Services SolidWorks, 3D PartStream.NET, 3D ContentCentral, eDrawings, and the eDrawings logo are registered trademarks and FeatureManager is a jointly owned registered trademarkof DS SolidWorks. CircuitWorks, FloXpress, TolAnalyst, and XchangeWorks are trademarks of DS SolidWorks. FeatureWorks is a registered trademark of Geometric Ltd. SolidWorks 2012, SolidWorks Enterprise PDM, SolidWorks Workgroup PDM, SolidWorks Simulation, SolidWorks Flow Simulation, eDrawings Professional, and SolidWorks Sustainability are product names of DS SolidWorks. Other brand or product names are trademarks or registered trademarks of their respective holders. COMMERCIAL COMPUTER SOFTWARE — PROPRIETARY The Software is a “commercial item” as that term is defined at 48 C.F.R. 2.101 (OCT 1995), consisting of “commercial computer software” and “commercial software documentation” as such terms are used in 48 C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government (a) for acquisition by or on behalf of civilian agencies, consistent with the policy set forth in 48 C.F.R. 12.212; or (b) for acquisition by or on behalf of units 3 of the department of Defense, consistent with the policies set forth in 48 C.F.R. 227.7202-1 (JUN 1995) and 227.7202-4 (JUN 1995).

Document Number: PMT1240-ENG

Copyright Notices for SolidWorks Standard, Premium, Professional, and Education Products Portions of this software © 1986-2011 Siemens Product Lifecycle Management Software Inc. All rights reserved. Portions of this software © 1986-2011 Siemens Industry Software Limited. All rights reserved. Portions of this software © 1998-2011 Geometric Ltd. Portions of this software © 1996-2011 Microsoft Corporation. All rights reserved. Portions of this software incorporate PhysX™™ by NVIDIA 2006-2010. Portions of this software © 2001-2011 Luxology, Inc. All rights reserved, patents pending. Portions of this software © 2007-2011 DriveWorks Ltd. Copyright 1984-2010 Adobe Systems Inc. and its licensors. All rights reserved. Protected by U.S. Patents 5,929,866; 5,943,063; 6,289,364; 6,563,502; 6,639,593; 6,754,382; patents pending. Adobe, the Adobe logo, Acrobat, the Adobe PDF logo, Distiller and Reader are registered trademarks or trademarks of Adobe Systems Inc. in the U.S. and other countries. For more SolidWorks® copyright information, see Help > About SolidWorks. Copyright Notices for SolidWorks Simulation Products Portions of this software © 2008 Solversoft Corporation. PCGLSS © 1992-2010 Computational Applications and System Integration, Inc. All rights reserved. Copyright Notices for Enterprise PDM Product Outside In® Viewer Technology, © 1992-2010 Oracle Portions of this software © 1996-2011 Microsoft Corporation. All rights reserved.

Copyright Notices for eDrawings Products Portions of this software © 2000-2011 Tech Soft 3D. Portions of this software © 1995-1998 Jean-Loup Gailly and Mark Adler. Portions of this software © 1998-2001 3Dconnexion. Portions of this software © 1998-2011 Open Design Alliance. All rights reserved. Portions of this software © 1995-2010 Spatial Corporation. This software is based in part on the work of the Independent JPEG Group.

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Introduction:

About This Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Course Design Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Using this Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Laboratory Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 About the Training Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Windows® XP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Conventions Used in this Book . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Use of Color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 What is SolidWorks Simulation? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 What Is Finite Element Analysis? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Build Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Defeaturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Idealization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Clean-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Build Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Solve Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Analyze Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Errors in FEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Finite Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Element Types Available in SolidWorks Simulation . . . . . . . . . . 10 First Order Solid Tetrahedral Elements . . . . . . . . . . . . . . . . . . . . 11 Second Order Solid Tetrahedral Elements . . . . . . . . . . . . . . . . . . 12 First Order Triangular Shell Elements . . . . . . . . . . . . . . . . . . . . . 13 Second Order Triangular Shell Elements . . . . . . . . . . . . . . . . . . . 14 Beam Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 i

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Choosing Between Solid and Shell Elements. . . . . . . . . . . . . . . . 15 Draft vs. High Solid and Shell Elements . . . . . . . . . . . . . . . . . . . 15 Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Calculations in FEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Interpretation of FEA Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Principal Stresses: P1, P2, and P3. . . . . . . . . . . . . . . . . . . . . . . . . 18 Units of Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Limitations of SolidWorks Simulation . . . . . . . . . . . . . . . . . . . . . . . . 19 Linear Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Small Structural Deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Static Loads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Lesson 1: The Analysis Process

Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 The Analysis Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Stages in the Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Case Study: Stress in a Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 SolidWorks Simulation Interface . . . . . . . . . . . . . . . . . . . . . . . . . 26 SolidWorks Simulation Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Plot Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 New Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Assigning Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Fixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Fixture Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Display/Hide Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 External Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Size and Color of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Preprocessing Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Curvature Based Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Mesh Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Element Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Minimum Number of Elements in a Circle . . . . . . . . . . . . . . . . . 44 Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Mesh Quality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Postprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Result Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Editing Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Nodal vs. Element Stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Show as Tensor Plot Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Modifying Result Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Other Plot Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Other Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

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Multiple Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Creating New Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Copy Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Check Convergence and Accuracy . . . . . . . . . . . . . . . . . . . . . . . . 64 Results Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Comparison With Analytical Results . . . . . . . . . . . . . . . . . . . . . . 66 Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Exercise 1: Bracket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Exercise 2: Compressive Spring Stiffness . . . . . . . . . . . . . . . . . . . . . 81 Exercise 3: Container Handle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Lesson 2: Mesh Controls, Stress Concentrations and Boundary Conditions Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Mesh Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Case Study: The L Bracket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Stages in the Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Run All Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Analysis with Local Mesh Refinement. . . . . . . . . . . . . . . . . . . . . 90 Mesh Controls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Results Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Stress Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Case Study: Analysis of Bracket with a Fillet . . . . . . . . . . . . . . . . . . 97 Case Study: Analysis of a Welded Bracket. . . . . . . . . . . . . . . . . . . . 101 Understanding the Effect of Boundary Conditions. . . . . . . . . . . . . . 102 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Exercise 4: C-bracket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Exercise 5: Bone Wrench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Exercise 6: Foundation Bracket . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Lesson 3: Assembly Analysis with Contacts Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Contact Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Case Study: Pliers with Global Contact . . . . . . . . . . . . . . . . . . . . . . 130 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Stages in the Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Applying Materials to Assemblies . . . . . . . . . . . . . . . . . . . . . . . 131 Component Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Component Contact: Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Component Contact: Default setting. . . . . . . . . . . . . . . . . . . . . . 134

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Component Contact: Hierarchy and Conflicts . . . . . . . . . . . . . . 134 Viewing Assembly Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Handle Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Required Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Pliers with Local Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Local Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Local Contact Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 No Penetration Local Contact Options . . . . . . . . . . . . . . . . . . . . 143 No Penetration Local Contact: Accuracy . . . . . . . . . . . . . . . . . . 144 No Penetration Local Contact: Remarks . . . . . . . . . . . . . . . . . . 144 Contact Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Exercise 7: Two Ring Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Lesson 4: Symmetrical and Free Self-Equilibrated Assemblies Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Shrink Fit Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Case Study: Shrink Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Stages in the Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Defeaturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Rigid Body Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Shrink Fit Contact Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Plot Results in Local Coordinate System . . . . . . . . . . . . . . . . . . 160 Cylindrical Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . 160 Saving All Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 What’s Wrong Feature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 Analysis with Soft Springs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 Soft Springs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Inertial Relief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Exercise 8: Chain Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Exercise 9: Chain Link 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Lesson 5: Assembly Analysis with Connectors Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Connecting Components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Connector Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Case Study: Vise Grip Pliers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Stages in the Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Spring Connector Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

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Spring Connector Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 Pin/Bolt Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Exercise 10: Lift Assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Exercise 11: Analysis with Base (optional) . . . . . . . . . . . . . . . . . . . 216 Exercise 12: Shock Absorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Exercise 13: Spot Welds-Solid Mesh . . . . . . . . . . . . . . . . . . . . . . . . 221

Lesson 6: Compatible/Incompatible Meshes Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Compatible / Incompatible Meshing. . . . . . . . . . . . . . . . . . . . . . . . . 230 Case Study: Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 Compatible Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Incompatible Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 Automatic Switch to Incompatible Mesh . . . . . . . . . . . . . . . . . . 234 Incompatible Bonding Options. . . . . . . . . . . . . . . . . . . . . . . . . . 236 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Lesson 7: Assembly Analysis Mesh Refinement Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Mesh Control in an Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Case Study: Cardan Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Part 1: Draft Quality Coarse Mesh Analysis . . . . . . . . . . . . . . . . . . 241 Remote Load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 Bolt Tight fit and Diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 Bolt Pre-load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Local Contact Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 No Penetration Local Contact Options . . . . . . . . . . . . . . . . . . . . 250 Rotational and Axial Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . 256 Knowledge Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 Part 2: High Quality Mesh Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 261 Required Number of Solid Elements in Thin Features. . . . . . . . 262 Aspect Ratio Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 Jacobian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 Exercise 14: Bolt Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 Exercise 15: Awning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Lesson 8: Analysis of Thin Components Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Thin Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 Case Study: Pulley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

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Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Part 1: Mesh with Solid Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Symmetry Fixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 Part 2: Refined Solid Mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Solid vs. Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Creating Shell Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Part 3: Shell Elements - Mid-plane Surface . . . . . . . . . . . . . . . . . . . 285 Thin vs. Thick Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Shell Mesh Colors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Changing Mesh Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Shell Element Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 Automatic Shell Surface Re-alignment . . . . . . . . . . . . . . . . . . . 292 Applying Symmetry Restraints. . . . . . . . . . . . . . . . . . . . . . . . . . 295 Deformed Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 Results Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Computational Effort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Case Study: Joist Hanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 Exercise 16: Bracket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 Exercise 17: Shell Mesh Using Outer/Inner Faces . . . . . . . . . . . . . . 315 Exercise 18: Spot Welds - Shell mesh . . . . . . . . . . . . . . . . . . . . . . . 319 Exercise 19: Edge Weld Connector . . . . . . . . . . . . . . . . . . . . . . . . . 320 Exercise 20: Container Handle Weld . . . . . . . . . . . . . . . . . . . . . . . . 328

Lesson 9: Mixed Meshing Shells & Solids Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Mixed Meshing Solids and Shells . . . . . . . . . . . . . . . . . . . . . . . . . . 330 Bonding Shells and Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Mixed Mesh: Supported Analysis Types . . . . . . . . . . . . . . . . . . 331 Case Study: Pressure Vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 Analyze the Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 Preparing the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 Steel Identification Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 UNS Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 Other Indices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 Bulk and Shear Moduli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 Bonding Entities with Clearance . . . . . . . . . . . . . . . . . . . . . . . . 339 Shell Face to Shell Face Bonding . . . . . . . . . . . . . . . . . . . . . . . . 339 Shell Edge to Shell Face Bonding . . . . . . . . . . . . . . . . . . . . . . . 339 Shell to Solid Bonded Contact . . . . . . . . . . . . . . . . . . . . . . . . . . 340 Failure Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Meshing Small Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

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Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 Exercise 21: Mixed Mesh Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 351

Lesson 10: Mixed Meshing Solids, Beams & Shells Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 Mixed Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Case Study: Particle Separator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Element Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Beam elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Stages in the Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Beam Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 Beam Joints: Locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 Beam Joint Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 Section Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 Connected and Disconnected Joints . . . . . . . . . . . . . . . . . . . . . . 369 Sphere Diameter Defining Beam Joint . . . . . . . . . . . . . . . . . . . . 369 Render Beam Profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Beam imprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 Cross-section 1st and 2nd Directions . . . . . . . . . . . . . . . . . . . . . 375 Bending Moment and Shear Force Diagrams. . . . . . . . . . . . . . . 377 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 Exercise 22: Beam Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 Slenderness ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 Exercise 23: Cabinet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 Exercise 24: Frame Rigidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 Lesson 11: Design Study Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 Design Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 Case Study: Suspension Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 Stages in the Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 Part 1: Multiple Load Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 Design Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 Design Study Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 Design Study Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 Part 2: Geometry Modification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 Design Study Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 Exercise 25: Design Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

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Lesson 12: Thermal Stress Analysis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 Thermal Stress Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 Case Study: Bimetallic Strip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 Importing Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 Averaging Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 Examining Results in Local Coordinate Systems (Optional) . . . . . . 440 Saving Model in its Deformed Shape . . . . . . . . . . . . . . . . . . . . . . . . 442 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 Lesson 13: Adaptive Meshing Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 Adaptive Meshing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 Case Study: Support Bracket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 Geometry Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 h-Adaptivity Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450 h-Adaptivity Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 h-Adaptive Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454 Convergence Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454 Review h-adaptive Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 Strain Energy Error is NOT Stress Error . . . . . . . . . . . . . . . . . . 456 p-Adaptivity Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 p-Adaptive Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 h vs. p Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 Method Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 h vs. p Elements - Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464 Which Solution Method is Better? . . . . . . . . . . . . . . . . . . . . . . . 465 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 Lesson 14: Large Displacement Analysis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 Small vs. Large Displacement Analysis . . . . . . . . . . . . . . . . . . . . . . 468 Case Study: Clamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 Project Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 Part 1: Small Displacement Linear Analysis . . . . . . . . . . . . . . . . . . 469 Results Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 Contact Solution in Small and Large Displacement Analyses . . 471

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Part 2: Large Displacement Nonlinear Analysis. . . . . . . . . . . . . . . . 471 Permanent Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 SolidWorks Simulation Premium . . . . . . . . . . . . . . . . . . . . . . . . 474 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

Appendix A: Meshing, Solvers, and Tips & Tricks Meshing Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 Geometry Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 Defeaturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 Idealization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478 Clean-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478 Mesh Quality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Aspect Ratio Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Jacobian Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 Mesh Controls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 Automatic Trials for Solids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 Meshing Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 Failure Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 Tips for Meshing Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 Tips for Meshing Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 Tips for Using Shell Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 Hardware Considerations in Meshing. . . . . . . . . . . . . . . . . . . . . . . . 488 Solvers in SolidWorks Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 489 Choosing a Solver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 Appendix B: Customer Help and Assistance Customer Help and Assistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492

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PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Introduction

1

Introduction

The goal of this course is to teach you how to use the SolidWorks Simulation software to help you analyze static structural behavior of your SolidWorks part and assembly models.

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About This Course

SolidWorks 2012

The focus of this course is on the fundamental skills and concepts central to the successful use of SolidWorks Simulation 2011. You should view the training course manual as a supplement to, and not a replacement for, the system documentation and on-line help. Once you have developed a good foundation in basic skills, you can refer to the on-line help for information on less frequently used command options.

Prerequisites

Students attending this course are expected to have the following:

I I I I

Mechanical design experience. Experience with the Windows™ operating system. Complete the course SolidWorks Essentials. Completed the on-line SolidWorks Simulation tutorials that are available under Help. You can access the on-line tutorials by clicking Help, SolidWorks Simulation, Tutorials.

Course Design Philosophy

This course is designed around a process- or task-based approach to training. Rather than focusing on individual features and functions, a process-based training course emphasizes processes and procedures you should follow to complete a particular task. By utilizing case studies to illustrate these processes, you learn the necessary commands, options, and menus in the context of completing a design task.

Recommended Length

The minimum recommended length of this course is three days.

Using this Book

This training manual is intended to be used in a classroom environment under the guidance of an experienced SolidWorks Simulation instructor. It is not intended to be a self-paced tutorial. The examples and case studies are designed to be demonstrated “live” by the instructor. There may be slight differences in results in certain lessons due to service pack upgrades, etc.

Laboratory Exercises

2

Laboratory exercises give you the opportunity to apply and practice the material covered during the lecture/demonstration portion of the course.

SolidWorks 2012

A complete set of the various files used throughout this course can be downloaded from the SolidWorks website, www.solidworks.com. Click on the link for Support, then Training, then Training Files, then SolidWorks Simulation Training Files. Select the link for the desired file set. There may be more than one version of each file set available.

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About the Training Files

Introduction

Direct URL:

www.solidworks.com/trainingfilessimulation

The files are supplied in signed, self-extracting executable packages.

The files are organized by lesson number. The Case Study folder within each lesson contains the files your instructor uses while presenting the lessons. The Exercises folder contains any files that are required for doing the laboratory exercises.

Windows® XP

The screen shots in this manual were made using SolidWorks 2011 and SolidWorks Simulation 2011 running on Windows® 7. If you are running on Windows Vista, or XP, you may notice differences in the appearance of the menus and windows. These differences do not affect the performance of the software.

Conventions Used in this Book

This manual uses the following typographic conventions: Convention

Meaning

Bold Sans Serif

SolidWorks Simulation commands and options appear in this style. For example, “Right-click External Loads and select Force” means right-click the External Loads icon in the SolidWorks Simulation Study tree and select Force from the shortcut menu.

Typewriter

Feature names and file names appear in this style. For example, Restraint-1.

17 Do this step

Double lines precede and follow sections of the procedures. This provides separation between the steps of the procedure and large blocks of explanatory text. The steps themselves are numbered in sans serif bold.

3

Introduction

The SolidWorks and SolidWorks Simulation user interface make extensive use of color to highlight selected geometry and to provide you with visual feedback. This greatly increases the intuitiveness and ease of use of the SolidWorks Simulation software. To take maximum advantage of this, the training manuals are printed in full color.

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Use of Color

SolidWorks 2012

Also, in many cases, we have Radius 50mm used additional color in the illustrations to communicate concepts, identify features, and otherwise convey important information. For example, we Radius 5mm might show the fillet areas of a All Around Radius 6mm, 4 Places part in a different color, to highlight areas for mesh control, even though by default, the SolidWorks Simulation software would not display the results in that way.

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Introduction

What is SolidWorks Simulation?

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SolidWorks Simulation is a design analysis tool based on a numerical technique called Finite Element Analysis or FEA. SolidWorks Simulation belongs to the family of engineering analysis software products developed by SRAC, now part of SolidWorks Corporation. Established in 1982, SRAC pioneered the implementation of FEA into desktop computing. In 1995, SRAC entered the emerging mainstream FEA software market by partnering with SolidWorks Corporation and creating COSMOSWorks software, one of the first SolidWorks Gold Products. COSMOSWorks soon became the top-selling, add-in analysis software for SolidWorks Corporation. The commercial success of COSMOSWorks integrated with SolidWorks CAD software resulted in the acquisition of SRAC in 2001 by Dassault Systemes, the parent company of SolidWorks Corporation. In 2003, SRAC merged with SolidWorks Corporation. COSMOSWorks was renamed for 2009 to SolidWorks Simulation. SolidWorks is a parametric, solid, feature-based CAD system. As opposed to many other CAD systems that were originally developed in a UNIX environment and only later ported to Windows, SolidWorks has, from the very beginning, been developed specifically for the Windows operating system. SolidWorks Simulation has also been specifically developed for the Windows operating system. Full integration between SolidWorks and SolidWorks Simulation is possible because both of the programs are native Windows OS applications. SolidWorks Simulation comes in different “bundles”, or applications, designed to best suit the needs of different users. With the exception of SolidWorks SimulationXpress, which is an integral part of SolidWorks, all SolidWorks Simulation bundles are add-ins. A brief description of the capabilities of different bundles is as follows:

I

SolidWorks SimulationXpress

The static analysis of parts with simple types of loads and supports.

I

SolidWorks Simulation

The static analysis of parts and assemblies.

I

SolidWorks Simulation Professional

The static, thermal, buckling, frequency, drop test, optimization and fatigue analysis of parts and assemblies.

I

SolidWorks Simulation Premium

All capabilities of SolidWorks Simulation Professional plus nonlinear and dynamic analyses.

In this volume, we introduce SolidWorks Simulation through a series of hands-on lessons intermixed with FEA fundamentals. We recommend that you study the lessons in the order presented in the text. As you go through the lessons, note that explanations and steps described in detail in earlier lessons are not repeated later.

5

Introduction

SolidWorks 2012

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Each subsequent lesson assumes familiarity with software functions and the FEA background discussed in previous lessons. Each lesson builds on the skills and experience gained from the previous lessons. Before we proceed with the lessons, let us construct a foundation for our skills in SolidWorks Simulation by taking a closer look at what Finite Element Analysis is and how it works.

What Is Finite Element Analysis?

In mathematical terms, FEA, also known as the Finite Element Method, is a numerical technique of solving field problems described by a set of partial differential equations. Those types of problems are commonly found in many engineering disciplines, such as machine design, acoustics, electromagnetism, soil mechanics, fluid dynamics, and others. In mechanical engineering, FEA is widely used for solving structural, vibration, and thermal problems.

FEA is not the only tool available for numerical analysis. Other numerical methods used in engineering include the Finite Difference Method, Boundary Element Method, or Finite Volumes Method. However, due to its versatility and high numerical efficiency, FEA has come to dominate the software market for engineering analysis, while other methods have been relegated to niche applications. Using FEA, we can analyze any shape, use various ways to idealize geometry and produce results with the desired accuracy. FEA theory, numerical problem formulation, and solution methods become completely transparent to users when implemented into modern commercial software, including SolidWorks Simulation.

A powerful tool for engineering analysis, FEA is used to solve problems ranging from very simple to very complex. Design engineers use FEA during the product development process to analyze the design-in-progress. Time constraints and limited availability of product data call for many simplifications of the analysis models. At the other end of scale, specialized analysts implement FEA to solve very advanced problems, such as vehicle crash dynamics, metal forming, or analysis of biostructures.

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Introduction

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Regardless of the project complexity or the field of application, the fundamental steps in any FEA project are always the same, be it for example a structural, thermal, or acoustic analysis. The starting point for any analysis is the geometric model. In our case, this is a SolidWorks model of a part or an assembly. To this model, we assign material properties, and define loads and restraints. Next, as always the case when using a tool based on the method of numerical approximations, we discretize the model intended for analysis. The discretization process, better known as meshing, splits the geometry into relatively small and simply-shaped entities, called finite elements. The elements are called “finite” to emphasize the fact that they are not infinitesimally small, but only reasonably small in comparison to the overall model size. When working with finite elements, the FEA solver approximates the wanted solution (for example, deformations or stresses) for the entire model with the assembly of simple solutions for individual elements. From the perspective of FEA software, each application of FEA requires three steps:

I

Preprocessing

The type of analysis (e.g., static, thermal, frequency), material properties, loads and restraints are defined and the model is split into finite elements.

I

Solution

Computing the desired results.

I

Postprocessing

Analyzing the results.

We follow the preceding three steps every time we use SolidWorks Simulation.

From the perspective of FEA methodology, we list the following FEA steps: 1. 2. 3. 4.

Building the mathematical model. Building the finite element model. Solving the finite element model. Analyzing the results.

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Introduction

Analysis with SolidWorks Simulation starts with the geometry represented by a SolidWorks model of a part or assembly. This geometry must be meshable into a correct and reasonably small, finite element mesh. By small, we do not refer to the element size, but the number of elements in the mesh. This requirement of meshability has very important implications. We must ensure that the CAD geometry indeed meshes and that the produced mesh provides the correct solution of the data of interest, such as displacements, stresses, temperature distribution, and so on.

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Build Mathematical Model

SolidWorks 2012

Often, but not always, this necessity of meshing requires modifications to the CAD geometry. Such modifications can take the form of defeaturing, idealization, and/or clean-up, described as follows:

Defeaturing

Defeaturing refers to the process of suppressing or removing geometry features deemed insignificant for analysis, such as external fillets, rounds, logos, and so on.

Idealization

Idealization presents a more aggressive exercise that may depart from solid CAD geometry as, for example, when representing thin walls with surfaces.

Clean-up

Clean-up is sometimes required because the meshable geometry must satisfy much higher quality requirements than those commonly followed in Solid Modeling. For clean-up, we can use CAD qualitycontrol tools to check for problems, like sliver faces or multiple entities, that the CAD model could tolerate, but would make meshing difficult or impossible.

It is important to mention that we do not always simplify the CAD model with the sole objective of making it meshable. Often, we simplify a model that would mesh correctly “as is”, but the resulting mesh would be too large and, consequently, the analysis would run too slowly. Geometry modifications allow for a simpler mesh and shorter computing time. Successful meshing depends as much on the quality of the geometry submitted for meshing as on the sophistication of the meshing tools implemented in the FEA software. Having prepared a meshable, but not yet meshed, geometry, we define material properties, loads, supports and restraints, and provide information on the type of analysis that we wish to perform.

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Introduction

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This procedure completes the creation of a mathematical model. Note that the process of creating the mathematical model is not FEAspecific. FEA has not yet entered the picture. Idealization of geometry (if necessary)

Type of Analysis

Material Properties Supports Loads

MATHEMATICAL MODEL

CAD geometry

Simplified geometry

FEA Pre-processing

CAD

Build Finite Element Model

We now split the mathematical model into finite elements through a process of discretization, better known as meshing. Discretization visually manifests itself as the meshing of geometry. However, loads and supports are also discretized and, after the model has been meshed, the discretized loads and supports are applied to nodes of the finite element mesh. Discretization

Numerical solver

MATHEMATICAL MODEL

FEA model

FEA Pre-processing

FEA Solution

FEA results

FEA Post-processing

Solve Finite Element Model

After creating the finite element model, we use a solver provided in SolidWorks Simulation to produce the desired data of interest.

Analyze Results

The analysis of results is often the most difficult step of all. The analysis provides very detailed results data, which can be presented in almost any format. Proper interpretation of results requires that we appreciate the assumptions, simplifications, and errors introduced in the first three steps: building the mathematical model, building the finite element model, and solving the finite element model.

9

Introduction

The process of creating a mathematical model and discretizing it into a finite element model introduces unavoidable errors. Formulation of a mathematical model introduces modeling errors, also called idealization errors. Discretization of the mathematical model introduces discretization errors, and solution introduces numerical errors.

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Errors in FEA

SolidWorks 2012

Of these three types of errors, only discretization errors are specific to FEA. Therefore, only discretization errors can be controlled using FEA methods. Modeling errors, affecting the mathematical model, are introduced before FEA is utilized and can only be controlled by using correct modeling techniques. Solution errors, which are round-off errors accumulated by solver, are difficult to control, but fortunately are usually very low.

Finite Elements

As we have already said, the discretization process, better known as meshing, splits continuous models into finite elements. The type of elements created in this process depends on the type of geometry meshed, the type of analysis to be executed, and sometimes on our own preferences. SolidWorks Simulation features tetrahedral solid elements for meshing solid geometry, and triangular shell elements for meshing surface geometry. Why are we limited to tetrahedral, and triangular shapes? This is because the automeshers reliably mesh almost any solid or surface geometry using only those shapes of elements. Elements in other shapes, such as hexahedral (brick) elements, cannot be created reliably by the present-day automeshers. This limitation is not specific to automeshers used in SolidWorks Simulation. A reliable brick element automesher has not been invented yet. Before proceeding, we need to clarify an important terminology issue. What in CAD terminology we call solid geometry, in FEA is called volumes. Solid elements are used to mesh those volumes. The term solid has different meanings when it is used as solid geometry in CAD terminology and when it is used as solid element in FEA terminology.

Element Types Available in SolidWorks Simulation

Five element types are available in SolidWorks Simulation: first order solid tetrahedral elements, second order solid tetrahedral elements, first order triangular shell elements, second order triangular shell elements, and two-node beam elements. The next few paragraphs describe them in this order. SolidWorks Simulation terminology refers to first order elements as

Draft Quality elements and second order elements as High Quality

elements.

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SolidWorks 2012

First order (draft quality) tetrahedral elements model the first order (linear) displacements field in their volume, along faces and edges. The linear, or the first order, displacements field gives these elements their name: first order elements. If you recall from The Mechanics of Materials, strain is the first derivative of displacement. Therefore, strain (obtained by derivating displacement) and, consequently, stress are both constant in first order tetrahedral elements.

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First Order Solid Tetrahedral Elements

Introduction

Each first order tetrahedral element has total of four nodes, one in each corner. Each node has three degrees of freedom, meaning that nodal displacements can be fully described by three translation components. A more detailed description of degrees of freedom follows later in this chapter.

After deformation

Before The edges of first order elements are deformation straight and the faces are flat. These edges and faces must remain straight and flat after the elements experience deformation under an applied load.

This situation imposes a very severe limitation on the capability of a mesh constructed with first order elements to model displacements and stress fields of any real complexity. Moreover, straight edges and flat faces do not map properly to curvilinear geometry.

The failure of straight edges and flat faces to map to curvilinear geometry using first order tetrahedral elements is shown in the following diagram using an elbow geometry.

For demonstration purposes, excessively large (as compared to the model size) elements are used for this mesh. This mesh would not be sufficiently refined for any analysis.

11

Introduction

Second order (high quality) solid tetrahedral elements model the second order (parabolic) displacements field and, consequently, first order (linear) stress field (note that the derivative of a parabolic function is a linear function). The second order displacements field gives these elements their name: second order elements.

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Second Order Solid Tetrahedral Elements

SolidWorks 2012

Each second order tetrahedral element has ten nodes (four corner nodes and six mid-side nodes) and each node has three degrees of freedom.

The edges and faces of second order solid elements can assume curvilinear shapes if the elements need to map to curvilinear geometry and/or during the deformation process when the elements deform under a load.

Therefore, these elements map precisely to curvilinear geometry, as illustrated by the same elbow geometry.

After deformation

Before deformation

Again, for demonstration purposes, excessively large (as compared to the model size) elements are used for this mesh. This mesh is not sufficiently refined for analysis, even though it uses second order elements that require a significantly less-refined mesh compared to that for first order elements. For accurate stress results, it is generally recommended to use two layers of second order elements across the wall thickness.

Because of their much better mapping capabilities and because of their ability to model the second order displacements field, second order tetrahedral elements are used for the vast majority of analyses with SolidWorks Simulation, even though second order elements are more computationally demanding than first order elements.

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SolidWorks 2012

Analogous to first order solid elements, first order triangular shell elements model the linear displacements field and constant strain and stress along their faces and edges. The edges of first order shell element are straight and must remain straight while the elements deform.

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First Order Triangular Shell Elements

Introduction

Each first order shell element has three nodes (all in corners) and each node has six degrees of freedom, meaning that its displacements are fully described by three translation components and three rotation components.

After deformation

Before deformation

If we represent the elbow with a mid-plane surface and mesh this surface with first order shell elements, note the imprecise mapping to curvilinear geometry.

This result resembles the previously demonstrated result of first order elements mapping imprecisely to curvilinear geometry.

Analogous to first order solid elements shown before, these shell elements are too large for any real analysis. In the illustration, different colors are used to differentiate the element top (brown) and bottom (green). The orientation and colors are arbitrary and can be changed by “flipping” the shell elements. They do not refer, in any way, to model orientation or model geometry.

13

Introduction

Second order (high quality) triangular shell elements model the second order displacements field and the first order (linear) stress field.

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Second Order Triangular Shell Elements

SolidWorks 2012

Each second order shell element After has six nodes: three corner nodes deformation and three mid-side nodes. The edges and faces of second order shell elements can assume Before curvilinear shapes in the meshing deformation process when the elements need to map to curvilinear geometry and/or during the deformation process when the elements deform under a load. This shell element mesh created with second order shell elements maps precisely to curvilinear geometry as illustrated again with the elbow model.

While convenient to show element mapping capabilities, the element size is too large for analysis, even though second order shell elements require less refined meshes as compared to first order shell elements.

Beam Elements

Contrary to the first order solid and shell elements, two-node beam elements model the two out-of-plane deflections as cubic functions and the axial translations and torsional rotations as linear. The shape of a two-node beam element is initially straight, but it can assume the shape of a cubic function after the deformation takes place. Each two-node beam element features six degrees of freedom at each end node: three translations and three rotations.

The same mesh mapping considerations that apply to the first order solid and shell elements apply to a two-node beam element as well.

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After deformation

Before deformation

SolidWorks 2012

Certain classes of shapes can be modeled using either solid or shell elements, such as the elbow discussed earlier. The selection of element type: tetrahedral solid or triangular shell, used for modeling may depend on the objective of the analysis. More often, however, the nature of geometry dictates what type of element to use for meshing. For example, parts produced by casting lend themselves to be meshed with solid elements, while a sheet metal structure is best meshed with shell elements.

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Choosing Between Solid and Shell Elements

Introduction

A hollow plate, featured in the next chapter, can be meshed with either solid elements created by meshing solid geometry or with shell elements created by meshing mid-surface.

Draft vs. High Solid and Shell Elements

First order elements, both solids and shells, should be used only for preliminary studies with specific objectives, such as verifying directions of loads or restraints, or calculating reaction forces.

The studies ready for the final computations (where the correct setup has been verified by using the Draft elements, for example) and the studies where a stress distribution is of any interest (especially in the through-thickness direction) should be modeled using High quality elements.

Degrees of Freedom

The degrees of freedom (DOF) of a node in a finite element mesh define the ability of the node to perform translation or rotation. The number of degrees of freedom that a node possesses depends on the type of element that the node belongs to. Nodes of solid elements have three degrees of freedom while nodes of shell elements have six degrees of freedom.

In order to describe transformation of a solid element from the original to the deformed shape, we need to know only three translational components of nodal displacement for each node. In the case of shell elements, we need to know, not only the translational components of nodal displacements, but also the rotational displacement components.

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Introduction

SolidWorks 2012

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Consequently, built-in (or rigid) constraints applied to solid elements require only three degrees of freedom to be constrained. The same constraints applied to shell element require that all six degrees of freedom be constrained. Failure to constrain rotational degrees of freedom may result in unintentional hinge support in place of the intended rigid support.

Calculations in FEA

Each degree of freedom of each node in a finite element mesh constitutes an unknown. In structural analysis, degrees of freedom assigned to nodes can be thought of as nodal displacements. Displacements are primary unknowns and are always calculated first.

If solid elements are used, three displacement components, or three degrees of freedom (three unknowns) per node must be calculated. Using shell elements, six displacement components, or six degrees of freedom per node (six unknowns) must be calculated. All other aspects of the analysis, such as strains and stresses, are calculated based on the nodal displacements. In fact, some FEA programs offer solutions with stress calculation as an option, not a requirement. In a thermal analysis (which determines temperatures, temperature gradients, and heat flux), the primary unknowns are nodal temperatures. Since temperature is a scalar value, unlike displacement, which is a vector, then regardless of what type of elements are used, there is only one unknown (temperature) to be found for each node in the thermal analysis model. All other results available in a thermal analysis are calculated based on those nodal temperatures.

The fact that there is only one unknown to be found for each node rather than three, or six as is the case in structural analysis, makes thermal analysis less computationally intensive than structural analysis.

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SolidWorks 2012

The results of FEA are provided either in the form of displacements, strains and stresses for a structural analysis or in the form of temperatures, temperature gradients, and heat flux for thermal analysis. We now focus on the more intuitive structural analysis. How do we decide between a “passed” or a “failed” design?

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Interpretation of FEA Results

Introduction

To answer these questions, we need to establish some criteria to interpret FEA results, be they, for example, the maximum acceptable deformation, maximum stress, or the lowest acceptable natural frequency.

While displacement or frequency criteria are quite obvious and easy to establish, stress criteria are not.

Assume that we conduct a stress analysis in order to ensure that stresses are within an acceptable range. To assess stress results, we need to understand the mechanism of potential failure. If the part breaks, what stress component is responsible for that failure? Discussion of various failure criteria is beyond the scope of this manual. Any book in the field of the mechanics of materials provides information on this topic. Here we limit our discussion to outlining the differences between von Mises stresses and the principal stresses, which are both common stress measures used for evaluating structural safety.

Von Mises Stress

Von Mises stress, also known as Huber stress, is a stress measure that accounts for all six stress components of a general 3D state of stress.

Two components of shear stress and one component of normal stress act on each side of an elementary cube. Due to equilibrium requirements, the general 3D state of stress is characterized by only six stress components because of equalities: τxy = τyx, τ yz = τ zy, τ xz = τ zx

The von Mises stress equation can be expressed by stress components that are defined in a global coordinate system as: σ eq =

2 2 2 2 2 2 0.5 ( σ x – σ y ) + ( σ y – σ z ) + ( σ z – σ x ) + 3 ⎛ τ xy + τ yz + τ zx⎞ ⎝ ⎠

17

Introduction

The state of stress can also be described by three principal stress components: σ 1, σ2, σ 3 whose directions are normal to faces of an elementary stress cube.

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Principal Stresses: P1, P2, and P3

SolidWorks 2012

Von Mises stress is then expressed as: σ eq =

2 2 2 0.5 ( σ 1 – σ 2 ) + ( σ 2 – σ 3 ) + ( σ 3 – σ 1 )

Note that von Mises stress is a non-negative, scalar value. Von Mises stress is a commonly used stress measure because the structural safety of many engineering materials showing elastoplastic properties, such as steel, is well described by von Mises stress magnitude. For those materials, the yield factor of safety or the ultimate factor of safety can be calculated by dividing the yield stress (also called yield strength) or the ultimate stress (also called ultimate strength) of the material by von Mises stress.

In SolidWorks Simulation, principal stresses are denoted as P1, P2, and P3. P1 stress which is usually tensile, is used when evaluating stress results in parts made of brittle material, whose safety is better related to P1 than to von Mises stress. P3 is used to examine compressive stresses and contact pressure.

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SolidWorks 2012

Internally, SolidWorks Simulation uses the International System of Units (SI). As SolidWorks Simulation users, we are spared much confusion and trouble with systems of units. Data may be entered in three different systems of units: SI, Metric, and English. Similarly, results can be displayed in any of those three systems of units. The available systems of units are summarized in the following table:

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Units of Measurement

Introduction

International System of Units (SI)

Metric (MKS)

English (IPS)

Mass

kg

kg

lbm

Length

m

cm

in

Time

s

s

s

Force

N

kgf

lbf

Pressure/Stress

N/m^2

Kgf/cm^2

lbf/in^2

Mass density

kg/m3

kg/cm3

lb./in3

Temperature

Limitations of SolidWorks Simulation

o

K

o

C

o

F

With any FEA software, we need to take advantage of its strengths as well as work within its limitations. Analysis with SolidWorks Simulation is conducted under the following assumptions: I I I

material is linear structural deformations are small loads are static

These assumptions are typical of the FEA software used in the design environment, and the vast majority of FEA projects are run successfully within these limitations.

For analyses requiring nonlinear material, nonlinear geometry, or dynamic analysis, tools such as SolidWorks Simulation Premium can be used. Some dynamic analysis capabilities are also included in SolidWorks Simulation Professional, which features frequency analysis and drop test functions.

Note

SolidWorks Simulation also features a geometrically nonlinear solver to compute large displacement problems. However, because only a default set of the parameters for the nonlinear solver is available, the applicability of this SolidWorks Simulation feature is limited. For full scale nonlinear problems (both the geometry and materials), SolidWorks Simulation Premium suite must be used.

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Introduction

In all materials used with SolidWorks Simulation, stress is linearly proportional to strain.

STRESS

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Linear Material

SolidWorks 2012

Linear Material

Nonlinear Material

STRAIN

Using a linear material model, the maximum stress magnitude is not limited to yield or to ultimate stress as it is in real life.

For example, in a linear model, if stress reaches 100 MPa under a load of 1,000 N., then stress will reach 1,000 MPa under a load of 10,000 N. Material yielding is not modeled. Whether or not yield takes place can only be interpreted based on the stress magnitudes reported in results.

Most analyzed structures experience stresses below yield stress, and the factor of safety is most often related to the yield stress.

Therefore, the analysis limitations imposed by linear material seldom impede SolidWorks Simulation users.

Small Structural Deformations

Any structure experiences deformation under load. In SolidWorks Simulation, we assume that those deformations are small. What exactly is a small structural deformation? Often it is explained as a deformation that is small in relation to the overall size of the structure.

Small structural deformations

Large structural deformations

The preceding figure shows a cantilever beam in bending with small deformations and large deformations.

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Introduction

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If deformations are large, then the SolidWorks Simulation assumptions generally do not apply, even though SolidWorks Simulation has some large displacement analysis capabilities, which we will discuss towards the end of this course. Other analysis tools, such as SolidWorks Simulation Premium must be used to analyze this structure.

Note that the magnitude of deformation is not the deciding factor when classifying deformation as “small” or “large”. What really matters is whether or not the deformation changes the structural stiffness in a significant way. Small deformation analysis assumes that the structural stiffness remains the same throughout the deformation process. Large deformation analysis accounts for changes of stiffness caused by deformations. While the distinction between small and large deformations is quite obvious for the beam, it is not at all obvious for a flat membrane under pressure.

Pressure

For a flat membrane, initially the only mechanism resisting the pressure load is that of bending stresses.

During the deformation process, the membrane acquires membrane stiffness in addition to the original bending stiffness.

The stiffness of the membrane changes significantly during deformation. This change in stiffness requires a large deformation analysis, using tools like SolidWorks Simulation Premium.

Static Loads

All loads, as well as restraints, are assumed not to change with time. This limitation implies that loads are applied slowly enough to ignore inertial effects. Dynamic loading conditions cannot be analyzed with SolidWorks Simulation.

While all loads, in reality, change with time, modeling them as static loads is most often acceptable for the purpose of design analysis. Gravity loads, centrifugal forces, pressure, bolt preloads, and so on can be successfully represented as static loads.

Dynamic analysis is generally required only for fast-changing loads. A drop test or vibration analysis definitely require that we model dynamic loads.

21

Introduction

This short review of FEA fundamentals is not, of course, “all inclusive”. It is only intended to get us started with the hands-on lessons. As we progress through the case studies presented in the following lessons, we will occasionally digress from software-specific issues in order to discuss relevant FEA fundamentals.

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Summary

SolidWorks 2012

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PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Lesson 1 The Analysis Process

Objectives

Upon successful completion of this lesson, you will be able to: I

Navigate the SolidWorks Simulation interface.

I

Execute a linear static analysis using solid elements.

I

Understand the influence of mesh density on displacement and stress results.

I

Employ various methods to present FEA results.

I

Manage SolidWorks Simulation result files.

I

Access available help and assistance.

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Lesson 1

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The Analysis Process

The process of analyzing models consists of the same basic steps regardless of the type of analysis or model. We must understand these steps fully to have a meaningful analysis.

Stages in the Process

Some key stages in the analysis of a model are shown in the following list:

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The Analysis Process

I

Create a study

Each analysis performed on a model is a study. We can have multiple studies in each model.

I

Apply material

We apply a material which contains the physical information, such as yield strength, to the model.

I

Apply fixtures

Fixtures are added to represent the way the physical model is held.

I

Apply loads

Loads represent the forces on the model.

I

Mesh the model

The model is broken into finite elements.

I

Run the study

The solver calculates the displacement, strain and stress in the model.

I

Analyze the results

The results are interpreted.

Case Study: Stress in a Plate

In this first case study, we will determine the stress in a rectangular plate, with a hole in it, under a tensile load. We will use this simple model to familiarize ourselves with all the steps and the majority of the software functionality typically used in a static analysis of solid models. In spite of its simplicity, this is probably the most important lesson in this course. This lesson goes through all the required steps; however, after the lesson is complete, you should continue to explore other software functionality and other modeling assumptions, such as different material properties, loads, restraints, and so on.

Project Description

24

The rectangular plate with a hole is fixed at the shortend face. A 110,000 Newton load is uniformly distributed along the other end face.

SolidWorks 2012

Lesson 1 The Analysis Process

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In addition to learning SolidWorks Simulation functions, our objective is to investigate the impact of different mesh densities on the results. Using FEA terminology, the objective is to investigate the effect of different discretization choices on the data of interest, in our case, on deformation and stress. Therefore, we perform the analyses using meshes with different element sizes. Note that repetitive analysis with different meshes does not represent standard practice in FEA. We repeat the analysis using different meshes as a learning tool to gain more insight into how FEA works.

1

Open a part file.

Open rectangular hollow plate from the Lesson01\Case Studies folder. Review the dimensions of the model and note down the length, width, and thickness of the part in millimeters.

2

Start SolidWorks Simulation. Click Tools, Add-Ins. Select SolidWorks Simulation.

Click OK.

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Lesson 1

SolidWorks 2012

The Analysis Process

SolidWorks Simulation functions are accessed in the same way as core SolidWorks. To create an FEA model, solve the model, and analyze the results, we use a graphical interface in the form of icons and folders located in the SolidWorks Simulation Study tree window.

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SolidWorks Simulation Interface

Analysis Library

CommandManager tab

Toolbar

Simulation Study tree

Simulation Study Tree

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Simulation Study tabs

Once a simulation study is created, the Simulation Study tree will appear in the lower part of the FeatureManager design tree. Its visibility is controlled by a tab below the graphics area.

Simulation Advisor

SolidWorks 2012

Lesson 1 The Analysis Process

The Simulation menu provides a method to access all the commands for simulation.

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Pull-down Simulation Menu

Toolbars

The Simulation toolbar contains all the commands that have toolbar buttons. It can be customized to show only those commands you use frequently.

CommandManager

The CommandManager provides a universal toolbar for simulation. The Simulation tab provides the tools to setup a study and for analyzing the results.

Context menus

Functions can be selected by rightclicking geometry or items in the Simulation Study tree.

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SolidWorks Simulation Options

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Located on the Simulation menu, the Options dialog box enables you to customize the Simulation software to reflect the standards your company uses for analysis. There are two categories of options, system and default. I

System Options

System options apply to all studies. Included are the settings for the way the errors are displayed and the location of the default libraries.

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Default Options

Default options apply to new studies. As we do not use templates for simulation studies, this is where the options are set for units, default plots, etc.

Where to Find It

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Menu: Click Options from the Simulation menu

Open Options window.

Click Options on the Simulation menu.

4

Set default units for SolidWorks Simulation.

Under Default Options, select Units. Make sure that the Units system is set to SI (MKS) and Length/Displacement and Stress are in mm and N/mm^2(MPa), respectively.

5

Set default results. Under Default options, select the Results folder. In this lesson, the

analysis results will be created and stored in a sub-folder located in the SolidWorks document directory.

Under Results folder, select SolidWorks document folder. SolidWorks document folder is the folder where rectangular hollow plate.SLDPRT file resides on your computer. Select the Under sub folder check box.

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In the Under sub folder box, enter results. This will automatically create a sub folder results to store SolidWorks Simulation results. Under Default Solver, select Automatic.

Note

Solvers will be discussed later in the course.

Plot Settings

Upon completion of any static analysis, SolidWorks Simulation automatically creates the following result plots: I I I

Stress1 Displacement1 Strain1

The plot settings determine which plots will be automatically created and their units. To add an additional plot, rightclick Static Study Results and select the type of plot you wish to define. Each type of plot can be stored in a userdefined folder.

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The Analysis Process

Set default plots. Expand the Default plots subfolder located in the Plot folder. This

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6

section allows you to select default result plots to be generated after solving the analysis.

We will use the default settings in the Default plots folder for this lesson.

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Specify color chart options.

Under the Plot folder, select Color chart.

Set Number format to scientific (e) and No. of decimal places to 6. Explore all the chart options in this dialog. Click OK to close the Options window.

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Lesson 1 The Analysis Process

In the following steps, we will prepare the model for analysis. The preprocessing steps include:

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Preprocessing

I I I I I

New Study

Create a study Apply material Apply fixtures Apply external forces Mesh the model

Creation of an FEA model always starts with the definition of a study. The study definition is where we enter information about the kind of analysis we wish to perform. Each analysis we do is a separate study. When a study is defined, SolidWorks Simulation automatically creates a study folder (named in this case, default analysis) and places several icons in it.

Some of the icons are folders that contain other icons.

We use the Parts folder to define and assign material properties, the External Loads folder to define loads, the Fixtures folder to define fixtures, and the Mesh icon to create the finite element mesh. The Connections folder is not used in this lesson.

There is only one component, named rectangular hollow plate, in the Parts folder. If an assembly (and not a part) is analyzed, then the Parts folder contains as many components as there are parts in the assembly.

Renaming Studies

The name of the study can be changed at any point by click-pauseclicking on the study name (similarly to renaming files and folders in Windows).

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The Analysis Process

Assigning Material Properties

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We can assign material to the model in either the SolidWorks or the SolidWorks Simulation window. If a material was assigned in the SolidWorks window, the material definition will be transferred automatically to SolidWorks Simulation. In this lesson, we assign material to the part in the SolidWorks Simulation window, not because this is the preferred way, but to demonstrate this option. To assign a material: I I I

Select Material on the Simulation menu, then click Apply material to all. Select the component, then click Apply Material in the Simulation Main toolbar. Right-click the body/part/ assembly icon in the Simulation Study tree and select Apply/Edit Material.

The first method assigns the same material properties to all components in the model. The second method assigns material properties to one particular component and all the multi-bodies associated to the component. The third method assigns material properties to one particular body: in this lesson, the rectangular hollow plate. Because we are not working with an assembly but with a single part which contains only one body (i.e. this is not a multi body part) any of the above three ways of material assignment can be used.

Note

8

Create a study. Click Study on the Simulation menu.

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Name the study.

Studies can have any name; here we name the study default analysis. Type default analysis for the Name. Select Static for the Type of study.

Click OK.

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10 Assign material properties. Click Material in the Simulation menu. Click Apply Material to All.

Expand Solidworks Materials and assign AISI 304 from the Steel folder.

The required material constants are in red. The constants shown in blue may be required if specific load types are used (for example, the Temperature load would require the Thermal expansion coefficient). Note that you may add a new material library by right clicking any folder or existing material in the Material dialog window. The new material can be added by copying the existing material into a new location and editing its properties. Click Close.

The rectangular hollow plate icon in the Parts folder now displays a green check mark and the name of the selected material to indicate that a material has successfully been assigned.

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The Analysis Process

To do a static analysis, the model must be properly restrained so that it cannot move. SolidWorks Simulation provides various fixtures that can be used to restraint the model. Generally, fixtures can be applied to faces, edges and vertices using various methods.

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Fixtures

Fixture Types

The fixtures and restraints are grouped as Standard and Advanced. Their properties are summarized below: Standard Fixtures Fixture Type

Definition

Fixed Geometry

Also called a rigid support, all translational and all rotational degrees of freedom are constrained. Fixed Geometry does not require any information on the direction along which restraints are applied.

Roller/Slider

Use the Roller/Slider restraint to specify that a planar face can move freely in its plane but cannot move in the direction normal to its plane. The face can shrink or expand under loading.

Fixed Hinge

Use the hinge restraint to specify that a cylindrical face can move only about its axis. The radius and the length of the cylindrical face remain constant under loading.

Advanced Fixtures Fixture Type

Symmetry

Circular Symmetry

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Definition

This option is available for use on flat face; in-plane displacements are allowed and rotation in the direction normal to the plane is allowed. This option is used to restrain segments which, if periodically revolved around a specified axis of revolution, would form a rotationally symmetrical body.

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Advanced Fixtures Definition

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Fixture Type

Use Reference Geometry

On Flat Faces

On Cylindrical Faces

On Spherical Faces

Display/Hide Symbols

This option restrains a face, edge, or vertex only in desired direction(s), while leaving the other directions free to move. You can specify the desired direction(s) of restraint in relation to the selected reference plane, axis, edge, or face. The SolidWorks Flyout FeatureManager is useful for selecting reference geometry (plane and axis). This option provides restraints in selected directions, which are defined by the three principal directions of the flat face where restraints are being applied. This option is similar to On flat face except that the three principal directions of a cylindrical reference face define the directions in a cylindrical coordinate system; this option is very useful because you can apply a restraint that allows for rotation about the axis associated with the cylindrical face. Similar to On flat faces and On cylindrical faces; the three principal directions of a spherical face define the directions of the applied restraints in a spherical coordinate system.

Fixture and External Forces symbols can be displayed or hidden by doing one of the following actions: I I

Right-click Fixtures or External Loads and select Hide All or Show All. Right-click a Fixture or External Loads symbol for each restraint individually, and then select Hide or Show.

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11 Define Fixed Restraints.

In the Simulation Study tree, right-click Fixtures and select Fixed Geometry.

Rotate the model and select the face to apply restraints. The Flyout FeatureManager is available in the upper left corner of the graphics area to make selection easier for parts, bodies or features.

In the Type box, select Fixed Geometry, and then click OK to close the Fixture PropertyManager.

Having defined fixtures, we have fully restrained the model in space. Therefore, the model cannot displace without elastic deformation. In FEA terminology, we say that the model does not have any rigid body modes.

Renaming

Each boundary condition can be renamed to help us decipher the meaning later on.

Window’s standard click-pause-click technique can be used to rename fixtures, loads and connectors.

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Fixture symbols are displayed on the face where they have been applied.

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Fixture Symbols

In this case study, we select Fixed Geometry as the fixture type, meaning that all six degrees of freedom (three translations and three rotations) have been restrained.

The fixture symbols are arrows to indicate translational restraints and discs to indicate rotational restraints in respective directions. In this lesson, the fixtures are defined by the directions of the global coordinate system visible in the lower-left corner of the model window. If, instead of selecting Fixed Geometry as the type of fixture, we selected Roller/Slider, then the rotational degrees of freedom would not be constrained and the corresponding fixture symbols would feature only arrows, not discs.

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The Analysis Process

Once the model is restrained, we must apply external loads, or forces, to the model. SolidWorks Simulation provides various external forces that can be used to load the model. Generally, forces can be applied to faces, edges, and vertices using various methods. These external forces and their properties are summarized below:

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External Loads

Standard External Forces Force Type

Force

Definition

This option applies a force or moment to a face, edge, or vertex in the direction defined by selected reference geometry (plane, edge, face, or axis).

Note that a moment can only be applied if shell elements are used. Shell elements have six degrees of freedom per node (translations and rotations) and can assume a moment load. Solid elements have only three degrees of freedom per node (translations only) and, therefore, cannot assume a moment load directly.

Torque

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If you need to apply a moment to solid elements, it must be represented by appropriately distributed forces, or remote loads. This option applies torque about a reference axis using the Right-hand Rule. This option requires that the axis be defined in SolidWorks.

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Advanced External Forces Definition

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Force Type

Pressure

Gravity

Centrifugal Force Bearing Load

Remote Load/ Mass

Distributed Mass

Applies a pressure to a face. Can be directional and variable, such as hydrostatic pressure. Applies linear accelerations to parts or assemblies. Applies an angular velocity and acceleration to a part or assembly. Bearing loads are defined between contacting cylindrical faces. Remote loads apply loads that would normally be transferred by connecting structure.

Distributed masses are applied to selected faces to simulate the mass of components that are suppressed or not included in the model.

The presence of an external force is indicated by arrows symbolizing the load and by the corresponding icon.

12 Rename the fixture.

Use the Windows click-pause-click method to rename the fixture called Fixture-1 to Fixed side.

13 Define Force.

Rotate the model to reveal the face where the 110,000 N [24,729 lbf] tensile force is to be applied and select this face.

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Right-click External Loads and select Force to list the available options for defining loads. This action opens the Force/Torque PropertyManager.

In the Type area, select Normal, in the Units dialog make sure that SI is selected, and in the Force Value box, type 110,000.

Select Reverse direction. This is required to define a tensile force. Clearing the Reverse direction check box would result in a compressive force.

When defining a normal force we do not need to use any reference geometry. Load direction is sufficiently defined by the orientation of the loaded face when Normal is in effect.

Click OK

.

14 Rename the force.

Rename this force definition to Tensile force.

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The size and color of restraint and load symbols can be controlled both locally and globally.

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Size and Color of Symbols

The local settings of the symbols are controlled from the Symbol settings dialog in the Fixtures and External Loads PropertyManagers.

The global definitions for the symbols can be controlled by the SolidWorks Simulation Options in the Load/Fixture folder.

Display/Hide Symbols

The model now shows both loads and restraints symbols. To hide or show the symbols: I I

Right-click a particular restraint or load icon in the Fixtures or External Loads folder and choose Show or Hide. Right-click the Fixtures or External Loads folder to globally display or hide loads and restraints and choose Show All or Hide All.

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The Analysis Process

Now that we have assigned the material properties, fixtures, and external loads, we have fully defined the mathematical model, which we intend to solve with FEA.

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Preprocessing Summary

The mathematical model must be discretized into a finite element model. Before creating the finite element model, let us make a few observations about the following terms: I I I I

Geometry preparation Material properties External loads definition Fixtures definition

Geometry Preparation

Geometry preparation is a well-defined step with few uncertainties. Geometry that is simplified for analysis can be checked visually by comparing it with the original CAD model.

Material Properties

Material properties are most often selected from the material library and do not account for local defects, surface conditions, and so on. Generally, material definition has more uncertainties than geometry preparation.

External Loads Definition

External loads definition, even though done in a few quick menu selections, involves many background assumptions because in real life, load magnitude, distribution, and time dependence are often known only approximately and must be roughly estimated in FEA with many simplifying assumptions. Therefore, significant idealization errors can be made when defining loads. Nonetheless, loads can be expressed in numbers, which makes loads easier for FEA users to relate to.

Fixtures Definition

Defining restraints is where severe errors are most often made. A common error is over-constraining the model, which results in an overly stiff structure that underestimates deformations and stresses. The relative level of uncertainties in defining geometry, material, loads, and fixtures is qualitatively shown.

Idealizations and Assumptions

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Geometry Material Loads

Fixtures

Geometry is the easiest to define while fixtures are the most difficult, but the level of difficulty has no relation to the time required for each step, so the message in this bar graph may be counterintuitive. In fact, preparing CAD geometry for FEA may take hours, while defining material, and applying loads and fixtures involves only a few mouse clicks.

SolidWorks 2012

Lesson 1 The Analysis Process

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In all examples here, we assume that material properties, external forces, and supports are known with certainty, and that the way they are defined in the model represents an acceptable idealization of real conditions. However, we need to emphasize that it is the responsibility of the user of the FEA software to determine if all those idealized assumptions made during the creation of the mathematical model are indeed acceptable. The best automesher and the fastest solver do not help if the mathematical model submitted for analysis with FEA is based on erroneous assumptions.

Meshing

The last step before processing the FEA model is to mesh the geometry. In this step, the geometry will be divided into finite elements by an automesher. While the automesher will take care of the tedious part of the problem, we have input into the process to control the size and quality of the mesh.

Curvature Based Mesh

SolidWorks Simulation uses advanced technology to mesh the geometry into finite elements. The curvature based mesh algorithm generates a mesh with a variable element size that allows the accurate resolution of small features in the geometry.

Mesh Density

SolidWorks Simulation will suggest medium mesh density as the default that SolidWorks Simulation will use for meshing our model. Mesh density directly affects the accuracy of results. The smaller the elements, the lower the discretization errors, but the longer the meshing and solution times.

Element Sizes

The element size represents the characteristic element size in the mesh and is defined as the diameter of a sphere circumscribing the element (on the left in the following figure). This representation is easier to illustrate with the 2-D analogy of a circle circumscribing a triangle (on the right in the following figure).

h

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Because the curvature based mesh algorithm generates a mesh with a variable element size, the Maximum element size and Minimum element size define how big and smallare the elements. These parameters are established automatically, based on the geometric features of the SolidWorks model. SolidWorks Simulation uses the units of length specified in the SolidWorks model for the element size. Remember, however, that we can enter analysis data and analyze results in any one of three unit systems: SI, Metric and English.

Minimum Number of Elements in a Circle

The Min number of elements in a circle defines how the small features in the geometry will be resolved. For example, if the model had a hole, the number of elements in a circle will define how many elements will surround that circle. In the image to the right, we have defined a minimum of 10 elements to surround the hole.

Ratio

The ratio is used to define the transition of the mesh from the Minimum element size to the Maximum element size.

The Ratio parameter specifies the ratio between element sizes in consecutive transitional element layers. In our case, the default Ratio is used. The following shows the use of this option. a)

Minimum element size = 0.1 mm

Maximum element size = 1mm

Ratio = 2.0

b)

Minimum element size = 0.1 mm

Maximum element size = 1mm

Ratio = 1.1

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In the majority of analyses with SolidWorks Simulation, the default mesh settings produce a mesh that provides acceptable discretization errors while keeping solution times reasonably short.

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Tip

15 Generate the mesh. Right-click Mesh and select Create Mesh.

Expand Mesh Parameters and select Curvature based mesh.

The model will be meshed using High quality elements.

Expand all the sections of the PropertyManager to see all the available choices.

16 Set the mesh density.

The default mesh density will have the slider at mid-scale. Under Mesh Parameters, the Maximum element size and Minimum element size of the mesh is shown as 5.72453 mm [0.2254 in], the Min number of elements in a circle is 8, and the Element size growth ratio is 1.5. For the initial analysis, we will use the default settings.

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The mesh can be created with either a High or Draft mesh quality. The default is to use a High quality mesh. To use a draft quality mesh, you must select it in the PropertyManager under Advanced options.

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Mesh Quality

The difference between High and Draft quality is that: I I

Draft quality mesh uses first order elements. High quality mesh uses second order elements.

The differences between first and second order elements are discussed in Element Types Available in SolidWorks Simulation in the Introduction to FEA chapter.

17 Set mesh quality. In the Advanced section, clear Draft Quality Mesh.

We will review the other mesh options as we proceed with the class. Click OK to generate the mesh. The mesh appears after mesh generation is completed.

The Mesh icon in the SolidWorks Simulation Study tree window now displays a green check mark to indicate that meshing has been successfully completed.

Note

We named this study default analysis with the intention of using the default mesh size. Later on in this lesson the problem will be solved again with coarse and fine meshes.

Display/Hide Mesh

Mesh visibility can be controlled by right-clicking Mesh, and then doing one of the following: I I

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Select Hide Mesh. Select Show Mesh.

SolidWorks 2012

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18 Run the analysis.

Right-click the study icon, default analysis, and select Run.

You can monitor or pause the solution in the solver window while the analysis is running.

Postprocessing

After the analysis is complete, SolidWorks Simulation automatically creates the Results folder with the default results plots that we specified at the beginning of the lesson: Stress1 (-vonMises-), Displacement1 (-Res disp-), and Strain1 (-Equivalent-).

Result Plots

Each result plot can be displayed by doing one of the following: I

Double-click the desired plot icon (Stress1, for example).

I

Right-click the desired plot icon (Stress1, for example) and select Show under any folder.

While a plot is active (appears in the model window) you can rightclick the plot icon again to examine the plot control options.

19 Show and edit Stress1 (-vonMises-) plot. Double-click on Stress1 (-vonMises-) under the Results folder to

display the plot.

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Notice that the stress plot is in Mega-pascals (N/mm^2) units and the legend features scientific numbers with six digits, just as we requested in the Options at the beginning of the lesson.

We observe that the maximum value of Von Mises stress is 408 MPa, which significantly exceeds the yield stress of the material, 206 MPa, indicated by the red marker in following the chart.

Editing Plots

To edit a plot, right-click on the plot and select Edit definition.

The Display dialog lets you specify a stress component, units, and the type of plot.

The Advanced Options dialog lets you choose to plot either Node or Element values which is discussed below.

The Show as tensor plot option lets users plot the orientation as well as the magnitudes of the principle stresses (shown in the discussion below).

The Deformed Shape dialog lets the user specify the deformation scale for the plot. Automatic (default), True scale, and User Defined scale options are available. Students are encouraged to experiment with these options.

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The following figures show the nodal and elemental values of the Von Mises stress for our model.

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Nodal vs. Element Stresses

Node Values

Element Values

The stress plot that displays Nodal values appears “smooth”, while the stress plot that displays Element values appears “rough”. To understand the reasons for these different appearances, we need to explain the differences between nodal and element stresses. During the solution process, in each element, stress results are calculated at certain locations called Gauss points. First order tetrahedral elements (draft quality) have one Gauss point in their volume. Second order tetrahedral elements have four Gauss points. First order shell elements have one Gauss point. Second order shell elements have three Gauss points.

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Stresses in Gauss points can be extrapolated to element nodes. Most often, one node is shared by several elements, and each element reports different stresses at the shared node. Reported values from all adjacent elements are then averaged to obtain a single value. This method of stress averaging produces averaged (or nodal) stress results.

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Nodal Values

Element Values

Alternately, the stress values from all Gauss points within each element can be averaged to report a single elemental stress. Although these stresses are averaged between Gauss points, they are called nonaveraged stresses (or element stresses) because the averaging is done internally within the same element only. Element stresses and nodal stresses are always different, but too large a difference indicates that the mesh is not sufficiently refined in that location. See the exercise Exercise 1: Bracket on page 71 for the practical use of these quantities.

Show as Tensor Plot Option

This plot type helps visualize the directions as well as the magnitudes of the principal stresses P1, P2, and P3. Due to the considerable differences in magnitudes between these stress values, one must zoom in substantially to see all three arrows.

Modifying Result Plots

The Results plots can be modified in several ways to suit your needs. There are three primary functions to control the content, units, display and annotations of the plots. I

Edit Definition

Edit Definition controls the component (von Mises, 1st principal stress, X normal stress) and units to be displayed.

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Chart Options

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Chart Options control the annotations. Options include which annotations are shown as well as the color, type of units (scientific, floating, general) and the number of decimal places shown in the legend. The position of the legend and titles can also be adjusted.

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Settings

Settings are used to control the display of the model.

Where to Find It

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Shortcut Menu: Right-click a plot and select either Edit Definition, Chart Options or Settings

20 Modify the chart. Right-click Stress1 (-vonMises-) and select Chart Options.

Check Show min annotation and Show max annotation boxes to show the markers in the plot.

Note that you can also modify the limiting values in the legend, format of the numbers, and the color options.

If you select the legend, it will be framed. You can then drag the legend to any location on the plot. Click OK to save new settings.

Drag chart to new location

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21 Modify settings of stress plot. Right-click on Stress1 (-vonMises-) and select Settings.

Explore the Fringe, Boundary, and Deformed Plot Options in this dialog.

Other Plot Controls

There are several other plot types available to display specific results of the analysis.

Introducing: Section Plot

Sections plots allow a cutting plane to be positioned at any point in the model and the plotted results shown at the plane location.

Where to Find It

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Menu: Simulation, Result Tools, Section Clipping Shortcut Menu: Right-click an existing plot and select Section Clipping

Introducing: Iso Plots

Iso plots show that part of a model where the plotted parameter is a certain value or between certain values.

Where to Find It

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Menu: Simulation, Result Tools, Iso Clipping Shortcut Menu: Right-click an existing plot and select Iso Clipping

Introducing: Probe

A probe allows you to select a point or points on the model and display the plot parameter in both tabular and plotted form.

Where to Find It

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Menu: Simulation, Result Tools, Probe Shortcut Menu: Right-click a plot and select Probe

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Lesson 1 The Analysis Process

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22 Create section plot.

In many applications it is useful to cut the model and look at the distribution of the result quantity in the through-thickness direction. Right-click Stress1 (-vonMises-) and select Section Clipping.

From the SolidWorks fly-out menu, select Right plane as a Reference entity.

Students are encouraged to explore all the options and parameters in the Section dialog. Note that the user can also drag the triad to easily move the cut plane through the model.

and Clipping On/Off Use Reverse Clipping Direction control the cutting direction and to disable the section plot.

to

Click OK to close the Section dialog.

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23 Create Iso plot.

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Suppose that we wish to display portions of the model where the von Mises stress is between 170 MPa and 275 MPa. Right-click on Stress1 (-vonMises-) and select Iso Clipping. This opens the Iso Clipping PropertyManager.

In the Iso value box, under the Iso1 dialog, enter 275 N/mm^2 [MPa] [39,886 psi].

Check Iso 2 and in the Iso value box, enter 170 N/ mm^2 [MPa] [24,657 psi]. Click OK.

The black arrows on the stress legend indicate the values defined for the two iso surfaces. Experiment with the Iso Clipping window options using different numbers of iso surfaces and different cutting directions.

Use Reverse Clipping Direction and Clipping On/Off control the cutting direction and to reset the plot.

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24 Probe stress results. Right-click on Stress1 (-vonMises-) and select Probe.

Using the pointer, click the desired locations on the plot. It helps to zoom in on the area.

The stress results are listed in the Results dialog table and in the plot at the selected locations.

Select points in this direction

Under Report Option, you can save the results in a file, plot the pathgraph, or save the locations as sensors. (Sensors are discussed in detail later on in the class.)

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The Analysis Process

The figure above shows a Von Mises stress path plot for the selected locations.

25 Define P1: 1st Principal Stress plot.

Define a new stress plot. Right-click the Results folder and select Define Stress Plot.

Select P1: 1st Principl Stress as the stress component, keep all other default options, and click OK.

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The Analysis Process

We observe that the maximum value of the 1st principle stress, 416 MPa [60,304 psi], is very close to the maximum value of the Von Mises stress, 408 MPa [59,218 psi]. This is because the specified Tensile load is the only dominant load component resulting in predominantly tensile stress along the longitudinal direction of the plate.

26 Define displacement plot. Double-click the Displacement1 (-Res disp-) plot icon.

The post processing features that we practiced in the case of Stress1 (-vonMises-) are applicable to all other result quantities, such as Displacement. The displacement shows a maximum resultant displacement of 0.1435 mm [0.00565 in].

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The Analysis Process

We record the displacement result with 6 digits only to practice the plot options and to compare results from studies with different meshes. The uncertainties and simplifying assumptions used to create the model do not justify this accuracy.

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Note

27 Superimpose undeformed shape. Right-click on Displacement1(-Res disp-) and select Settings.

Select Superimpose model on the deformed shape. You can also adjust the transparency of the undeformed image. Click OK.

28 Animate displacement plot.

To animate the displacement plot, rightclick on Displacement1 (-Res disp-) and select Animate.

In the Animation PropertyManager you can start and stop the animation, set the number of frames, control the speed, and save the animation as an *.avi file. Try the options of the animation feature.

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29 Plot strain results. Double-click the Strain1 (-Equivalent-) plot icon to show the plot.

Note that strain results are dimensionless.

Strain results are shown as non-averaged (element values) by default as opposed to stress results, which are shown as averaged (node values) by default. Examine the strain plot showing Element Values.

To review the averaged strain plot, right-click on Strain1 (-Equivalent-) and select Edit Definition, and then select Node Values. To examine the available chart options, right-click Strain1 (-Equivalent-) and select Edit Definition.

All post processing features that we practiced for the stress plot are available for strain plots as well.

Other Plots

There are several other postprocessing quantities available to view at the end of the analysis.

Introducing: Factor of Safety Plot

Factor of Safety Plot show the safety of the design based on the

Where to Find It

I

Shortcut Menu: Right-click the Results folder and select Define

I

Factor of Safety Plot CommandManager: Simulation > Results Advisor > New Plot > Factor of Safety

Introducing: Fatigue Check Plot

design strength of the material (typically the yield strength). This plot is fully introduced in Lesson 7.

Fatigue Check Plot serves as a quick indicator if the fatigue may be of

any concern in the design of the component.

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The Analysis Process

Where to Find It

I

Shortcut Menu: Right-click the Results folder and select Define

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Fatigue Check Plot Important!

The fatigue check plot is only available if you have Simulation Professional.

30 Plot Fatigue Check Plot. Right-click on the Results folder and select Define Fatigue Check Plot.

Set the Loading type to On/Off Loading to indicate that the Tensile force may oscillate between 0 and 110,000 N.

Set the Surface Finish Factor to Machined. Keep the Loading Factor and Size Factor at their default values of Axial and 0.75.

Under Material keep the Scale this value and Minimum safety factor fields at their default values of 1. Click OK.

The areas in red indicate potential fatigue problems. Note that accurate calculations using the SolidWorks Simulation Professional fatigue modulus may be required.

Multiple Studies

We have completed the analysis of rectangular hollow plate with the default mesh and now wish to see how a change in mesh density affects the results. For this reason, we will repeat the analysis two more times using both coarser and finer density meshes. To repeat the analysis with coarsened mesh, we can create a new mesh while still in the default analysis study, but this action would overwrite the old results.

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Lesson 1 The Analysis Process

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To preserve the results of the study, we will create a new study, coarse analysis. Creating a new study can be done in several ways. Creating New Studies

New studies can be created in one of two ways: I

Create a new study from scratch.

I

Duplicate an existing study. Right-click the tab for the study you want to duplicate and click Duplicate. This is essentially the same as copying a study and pasting it into a blank study.

When we duplicate a study, SolidWorks Simulation displays the Define Study Name window. This will allow us to name the duplicated study and choose the model configuration to use.

Copy Parameters

When we create a new study, we can copy material, fixtures and external forces from existing studies rather than recreating them in the new study. To copy parameters, drag the parameter from the Simulation Study tree to the tab of the new study.

Note

When a study is duplicated, the study settings, Fixtures, External Forces, Mesh, and the study results will be copied as well.

31 Duplicate the study.

Right-click the default analysis tab and click Duplicate.

Type coarse analysis for the study name. The model only has a Default configuration, so we cannot change it.

32 Create new mesh in coarse analysis study. In the coarse analysis study, right-click Mesh and select Create Mesh. A warning window appears.

Remeshing will delete the results for study: coarse analysis.

Click OK to open the Mesh window.

Select Curvature based mesh under Mesh Parameters.

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Move the Mesh Factor slider all the way to the left. The Maximum element size and Minimum element size should read 11.4491 mm [0.4508 in]. Click OK.

The generated mesh is displayed to the right.

Notice that there is only one element across the thickness of the part. In the default analysis there were two elements across the thickness.

Note

The mesh is rather coarse. Later, we will discuss why this sort of mesh is not acceptable for reliable analysis results.

33 Display mesh details.

Having created the mesh, we can access the detailed mesh information by right-clicking Mesh and selecting Details. The same detailed information can of course be displayed for the “old” mesh in the default analysis study.

Many of the items in this list will be discussed in later lessons.

34 Run the analysis.

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35 View displacement and stress results.

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Record the maximum displacement (0.143 mm / 0.00563 in) and the maximum von Mises stress (403 Mpa / 58,393 psi).

Note

All plot settings remain the same as the default analysis study because the plot definitions are copied from that study.

36 Re-run the analysis with fine mesh. Repeat steps 31 - 34 to generate a new study with fine mesh named fine analysis.

When re-generating the mesh, move the slider all the way to the right. The Maximum element size and Minimum element size should read 2.86227 mm [0.1127 in].

The fine mesh generated using the above settings is shown to the right. Notice that we now have several elements in the through-thickness direction. You will later learn that this mesh is acceptable for reliable analysis results.

37 View displacement and stress results.

Record the maximum displacement (0.144 mm / 0.00567 in) and the maximum von Mises stress (415 Mpa / 60,252 psi).

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The Analysis Process

Now we must collect information from all of the studies (default, coarse and fine analysis) to compare the displacement and maximum von Mises stress results for the various mesh refinements. We can determine the maximum displacement and the maximum von Mises stress results in plots.

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Check Convergence and Accuracy

We must also determine the number of elements and the number of nodes in each mesh. These can be found in the Mesh Details window of each respective mesh.

Finally, we must determine the number of degrees of freedom (DOF) in each model. To calculate this number, we could count the number of unconstrained nodes by subtracting the number of nodes on the constrained face from the number nodes reported in mesh details. Then we could multiply this number by three because each node in a solid element mesh has 3 DOF. An easier method, however, is to right-click the Results folder in each study and select Solver Messages (see below).

38 View solver messages. Right-click on Results and choose Solver Messages. Note the number

of elements, nodes, and degrees of freedom.

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The summary of the results produced by the three studies is shown in the following table:

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Results Summary

Mesh density

Max. displacement [mm]

Max. von Mises stress [MPa]

Number of DOF

Number of elements

Number of nodes

coarse analysis

.1432014

402.608

7,128

1,173

2,427

default analysis

.1434608

408.292

44,037

8,677

14,844

fine analysis

.1435097

415.427

310,977

68,511

104,248

Note that all of the results of this table pertain to the same problem. The only difference is in the mesh density. You may find small differences between your own results and those presented in this table. This is due to service pack upgrades, etc. Having noted that the maximum displacement increases with mesh refinement, we can conclude that the model becomes less stiff (or softer) when the number of degrees of freedom increases. In our case, by selecting second order elements, we impose the assumption that the displacement field in each element is described by second order polynomial functions. With mesh refinement, the displacement field in each element is still described by second order polynomial functions; however, the larger number of elements makes it possible to approximate the real displacement and stress fields more accurately.

We can say that the artificial constraints resulting from element definition become less imposing with mesh refinement. Displacements are always the primary unknowns in FEA, and stresses are calculated based on displacement results. Therefore, stresses also increase with mesh refinement. If we continued with mesh refinement, we would see both displacement and stress results converge to a finite value. This limit is the solution of the mathematical model. Differences between the solution of the FEA model and the solution of the mathematical model are due to discretization error. Discretization error diminishes with mesh refinement.

The process of consecutive mesh refinements that we have completed is called the convergence process. Its objective is to determine the impact of our discretization choices (element size) on the data of interest, which, in this lesson, are the maximum resultant displacements and the maximum von Mises stress.

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The Analysis Process

An infinitely long rectangular hollow plate under a tensile load possesses an analytical solution [1]. We compare FEA results with analytical results.

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Comparison With Analytical Results

W, D and T denote plate width (100 mm), hole diameter (40 mm) and plate thickness (10 mm). P is the tensile load 110,000 N or 24,729 lb. For comparison with analytical results, it is more convenient to use the SI system because the SolidWorks model have been defined in mm.

σn is the normal stress in the cross section where the hole is located, Kn is the stress concentration factor, and σmax is the maximum principal stress. P 110000 σ n = ---------------------------- = ----------------------------------- = 183.33MPa ( W – D )xT ( 100 – 40 )x10 2

3

K n = 3 – 3.13 ⎛⎝ -----⎞⎠ + 3.66 ⎛⎝ -----⎞⎠ – 1.53 ⎛⎝ -----⎞⎠ = 2.23568 D W

D W

D W

σ max = K n xσ n = 183.33 × ( 2.23568 ) = 409.87MPa

Review the P1: 1st principal stress plot for study default analysis. The maximum value reached 415.78 MPa, which corresponds to approximately 60.3 ksi. Therefore, the difference is:

NumericalSolutions – THEORY 415.78 – 409.87 difference = -------------------------------------------------------------------------------------- = --------------------------------------- = 1.42 NumericalSolutions 415.78

The difference of 1.42% between the SolidWorks Simulation result and the analytical solution does not necessarily mean that the SolidWorks Simulation result is worse and has a 1.42% error.

We must be very careful in how we compare these results. Note that the analytical solution is valid only for a very thin plate where a plane stress condition is assumed. SolidWorks Simulation calculates a solution for a 3D model with substantial thickness (10 mm) and accounts for realistic stress distribution across the plate thickness. SolidWorks Simulation also takes into consideration the fact that the plate has a finite length (200 mm) rather that an infinite one, as the analytical solution does.

Furthermore, detailed inspection of the stress results show the stress gradient across the plate thickness, which is not accounted for in the analytical model. Thus, we can conclude that SolidWorks Simulation provides more detailed stress information than the analytical solution.

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Results may need to be recorded in report form for review, presentation or archive purposes.

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Reports

Reports can be published in Microsoft Word format. Different sections can be added to the report from a list of predefined commonly used topics. The default settings for the Reports can be found in the Simulation, Options menu. Predefined sections include:

I I I I I I I I

Description Model Information Units Loads and Fixtures Contact Information Sensor Details Beams Conclusion

I I I I I I I I

Assumptions Study Properties Material Properties Connector Definitions Mesh Information Resultant Forces Study Results Appendix

To edit the content of a section, select the section in the Included sections and fill in the appropriate section properties.

Where to Find It

I I I

Menu: Click Reports in the Simulation menu Simulation Toolbar: Click Report . CommandManager: Simulation > Report

.

39 Generate report in Microsoft Word format. Under SolidWorks Simulation menu item, select Report.

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40 Add sections. Under Report sections, select the required report parts. (For example, you could deselect the option Contact Information, as we do not have

any in this analysis.)

Enter your Header information and click Publish.

41 Examine the report.

Open the report in Microsoft Word and examine the results.

42 Save and Close the file.

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Lesson 1 The Analysis Process

We used a simple model of a hollow rectangular plate to introduce the SolidWorks Simulation interface and, at the same time, to go through all major steps in the FEA process.

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Summary

We created multiple studies to execute a linear static analysis with three different meshes. While preparing models for analysis and examining results obtained with different meshes, we introduced the concept of modeling error and discretization error. This first lesson was intended to provide an understanding of FEA methodology and the software skills necessary to complete the lessons that follow.

References

1. Young and Budynas, Roark’s Formulas for Stress and Strain, 7th Edition.

Questions

I

The pre-processing stage of the FEA includes the following steps: 1._________________________________________________ 2._________________________________________________ 3._________________________________________________ 4._________________________________________________ 5._________________________________________________

I

The density of finite element mesh (does / does not) have considerable impact on the analysis results.

I

In general, we would favor (finer / coarser) meshes to obtain reliable analysis results. Therefore, the time required to solve the analysis will (increase / decrease), but this is an unavoidable consequence. Ultimately, we will try to design optimum meshes providing reasonable accuracy levels and resulting in acceptable run times.

I

The primary unknown in finite element analysis is (displacements / strains / stresses). This quantity is therefore the most accurate.

I

The accuracy levels of (displacements / strains / stresses) and (displacements / strains / stresses) are approximately the same, but significantly worse than that of (displacements / strains / stresses). Therefore, to obtain good (displacement / strain / stress) results, the mesh must be reasonably fine.

I

(Refining / Coarsening) the mesh results in solutions approaching the analytical solution of a mathematical model.

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Lesson 1

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The Analysis Process

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SolidWorks 2012

Exercise 1 Bracket

Exercise 1: Bracket

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In this first exercise, you will analyze a simple part with a single restraint and one external force. This lab uses the following skills: I I I I

Problem Statement

Fixtures on page 34. External Loads on page 38. Meshing on page 43. Multiple Studies on page 60.

The aluminum part of an Bolt holes assembly will be analyzed for its maximum stresses and displacements. The part is bolted to the rest of the assembly through the two bolt holes, as indicated in the figure. The part is then subjected to a normal force of 500 N, applied to the counter bored face.

1

Open a part file.

Open part from the Lesson01\Exercises folder.

2

Specify SolidWorks Simulation options.

Select Options in the Simulation menu.

Select the Default Options tab, specify SI (MKS) as a default Units for this analysis. In the Units dialog, set the Length/Displacement and Pressure/Stress fields to mm and N/mm2 (MPa), respectively.

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Bracket

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The following default results plots are generated after each static study is completed: nodal von Mises stress and resultant displacement.

Right-click on the Static Study Results folder and select Add New Plot. Add an additional result plot for the nodal P1: 1st principal stress be generated as a default result plot.

Specify the subfolder results in the SolidWorks document directory as a location to store the result files.

3

Number format.

Select Color chart. Select Scientific and 2 decimal places.

4

Define a static study.

Create a new static study named stress analysis.

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Exercise 1 Bracket

Apply material properties. Right-click on the Part folder in the FeatureManager and select Apply/Edit Material.

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5

Specify Aluminum 1060 Alloy from the solidworks materials library.

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Bracket

Apply Fixtures. Apply Fixed Geometry to the two bolt holes, as shown in the figure

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6

below.

This restraint simulates the way this part is attached to the rest of the assembly.

Fixed Geometry fixtures are used in this exercise to model the bolted connections mounting the bracket to the other parts of the larger assembly. Also, the presence of the other parts to which this bracket is attached is ignored in this exercise.

You will learn in the later lessons that more accurate and elegant methods and features, such as bolt connectors and virtual wall, exist to simulate these conditions.

7

Apply external load. Apply normal force on the

face indicated in the figure. Specify a magnitude of 500 N.

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SolidWorks 2012

Exercise 1 Bracket

8

Mesh.

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Select Curvature based mesh under Mesh Parameters. Mesh the model using High quality elements with the default element sizes.

9

Run the study.

10 Plot stress results.

We observe that the maximum von Mises stress in the model is approximately 35.1 MPa, which is above the yield strength of the 1060 Aluminum Alloy (27.5 MPa).

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Exercise 1

SolidWorks 2012

Bracket

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The distribution of the P1: 1st principal stress indicates a maximum value of approximately 32.6 MPa. This value corresponds to the maximum tensile stress in the part (maximum compressive stress where the value is negative).

11 Probe stress on the fillet.

Later in the course you will learn that the fixtures may result in stress intensifications which are not real. For this reason, we will focus our attention to the filleted region between the horizontal and vertical bosses on the part. Right-click the Stress1 folder and click Probe.

Select On selected entities, then pick the seven faces of the fillet between the two bosses. Click Update.

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Exercise 1

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Bracket

Probing the results on selected faces we see that the maximum stress at this stress concentration region is 30.6 MPa [4,547 psi], which is slightly above the yield strength of 27.5 MPa [3,989 psi].

12 Plot displacement results.

We observe the maximum resultant displacement of approximately 0.068 mm [0.0027 in].

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Exercise 1

SolidWorks 2012

Bracket

Are our current results accurate enough? Visual inspection of our finite element mesh suggests that it may be rather coarse, especially in the regions where the fillets are present. Furthermore, inspection of the distribution of the elemental values of the von Mises stress indicates considerable stress jumps from element-to-element in the higher stress concentration areas.

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Coarse Mesh and Element Stress

We will repeat the analysis with finer mesh.

13 Create new static study. Duplicate the study stress analysis as a new study named stress analysis - refined.

The folders Fixtures, External Loads, Parts, Mesh, and Results will be copied into the new study as well.

14 Create fine mesh. Create High quality mesh. Slide the Mesh Density slider all the way to the right which will result in an Maximum element size of 2.198 mm and a Minimum element size of0.733 mm.

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SolidWorks 2012

Exercise 1 Bracket

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The resulting mesh shows significantly improved mapping of the model geometry. 15 Run the study.

16 Plot stress results.

We now observe that the maximum von Mises stress increased from 35.1 MPa to 39.1 MPa, which is above the material yield strength of the 27.5 MPa. This translates to a difference of nearly 11%. However, if we examine the plot, we will see that the maximum stress is at the sharp corner of the bolt holes. We will discuss this further in the next lesson.

17 Probe stress on the fillet.

Using the identical procedure described in step 11 probe the stress results on the filleted geometries.

We can observe the maximum von Mises stress on these entities increased from 30.6 MPa to 30.75 MPa, which is still above the yield strength but is a neglible difference from the previous study. We can therefore conclude that the mesh refinement confirmed the validity of our simulation and our results are converged. It should be noted that in other situations the difference in the stress results may be significant. In general, requirements on the good stress results translates into a necessity to generate finer meshes. In our present case further refinement does not produce further improvement in the stress results and we will thus conclude that they are converged.

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Bracket

18 Plot displacement results.

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The plot shows that the maximum displacement resultant increased from 0.0678 mm to 0.0683 mm; a difference of less than 1 %.

19 Save and Close the file.

Summary

80

In this exercise, we practiced the basic setup of the linear static study as well as the post processing features available in SolidWorks Simulation. We observed that the mesh quality has a significant impact on the results (especially the stress results). While the deviation in the resultant displacements obtained from the two studies was 1 %, the deviation for maximum von Mises stresses was nearly 11 % (often the difference in stresses is much greater). The greater difference in the maximum stresses is attributed to the following two phenomena: I

Displacements are the primary unknown in the finite element analysis and, as such, will always be significantly more accurate than strains and stresses. A relatively coarse mesh is sufficient for satisfactory displacement results, while significantly finer mesh is generally required for satisfactory stress results.

I

The extreme values of the stresses occur in the vicinity of the fixture where the stresses often assume unrealistically high values. This is a subject studied in the next lesson. The stresses at the filleted regions reported in both studies were closer in their magnitudes with a negligible difference. Finer meshes are required in filleted regions as stress results are of importance to us.

SolidWorks 2012

Exercise 2 Compressive Spring Stiffness

Exercise 2: Compressive Spring Stiffness

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In this exercise, we will use SolidWorks Simulation to determine the compressive stiffness of a coil spring. This exercise reinforces the following skills: I I I I I

Procedure

New Study on page 31. Fixtures on page 34. External Loads on page 38. Meshing on page 43. Result Plots on page 47.

The stiffness of the helical spring can be determined as follows:

1

Open a part file. Open spring from Lesson01\Exercises folder.

For convenient application of fixtures and external loads, disks have been added to both ends of the spring. The distance between the disks corresponds to the active length of the un-compressed spring.

Note

2

Set SolidWorks Simulation options.

Set the system of Units to SI (MKS) and the units of Length and Stress to mm and N/m2 (Pa).

3

Create study.

Create a Static study named spring stiffness.

4

Review material properties.

The material properties (Alloy Steel) are transferred from SolidWorks.

5

Apply Fixed restraint. Apply a Fixed Geometry fixture to the end face of one disk (item 1).

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Compressive Spring Stiffness

6

Apply radial restraint.

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Use an advanced fixture to apply a restraint in the radial direction to the cylindrical face of the other disk (item 2). This restraint only allows the spring to be compressed (or expanded) in its axial direction and to rotate about the longitudinal axis. 2

1

7

Apply compressive force.

Apply a 0.1 N compressive force to the end face of the disk with the cylindrical face constrained in the radial direction.

8

Mesh the model and run the analysis. Select Curvature based mesh under Mesh Parameters.

Use High quality elements with the default Maximum element size and Minimum element size of 2.787 mm and 0.557 mm, respectively.

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Exercise 2 Compressive Spring Stiffness

9

Plot z displacements.

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Displacement results indicate an axial displacement of 0.426 mm. The axial displacement is in the z direction.

Coil Spring Axial Stiffness

The axial stiffness of the spring can be calculated as 234.7 N/m. (k = f/x).

We use this result to define the spring connector in later lessons using the equation f= kx, where k=234.7 N/m.

Alternately, we could use an approximate formula for the stiffness of a helical spring (Mechanical Vibrations by S. S. Rao, 1995). 4 Gd K Axial = -------------3 8nD

where:

I I I I

G is the material shear modulus d is the diameter of the wire D is the mean coil diameter n is the number of active turns

Substituting our values (n = 8.75, d = 1 mm, D = 17 mm, and G = 7.9e10 Pa) into the above formula gives an axial stiffness of approximately 230 N/m. This result is very close to our actual result of 234.7 N/m.

10 Save and Close the file.

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Exercise 3

SolidWorks 2012

Container Handle

In this exercise, you will assess the safety of the waste container handle.

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Exercise 3: Container Handle

This exercise reinforces the following skills: I I I I I

New Study on page 31. Fixtures on page 34. External Loads on page 38. Meshing on page 43. Result Plots on page 47.

Base plates

Handle

Problem Description

The handle is used to attach the hook of the winch when loading the container on the rails of the transporting truck. The entire container is manufactured from AISI 304 steel. The handle is welded (double-sided fillet weld) to the two square base plates located symmetrically on both sides. The diameter of the handle is 30mm; the thickness of the steel plates is 5mm. Apply the most suitable fixtures to simulate the connection between the handle and the steel plates.

Loading Conditions

In the most extreme loading situation, when the container is pulled onto the truck rails, the handle is loaded by a 3000 N force inclined at 15 degrees. The force should be applied on the circular split face indicated in the figure above. The geometry of the handle structure with the base plates is shown in the figure to the right.

Goal

Decide whether the design of this handle is safe. Pay attention to the most appropriate representation of the fixture. The part for this exercise is located in the Lesson01\Exercises folder.

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Objectives

Upon successful completion of this lesson, you will be able to: I

Illustrate the differences between modeling and discretization errors.

I

Use Automatic transition option to mesh models.

I

Use mesh controls.

I

Describe when the lack of convergence of FEA results may occur.

I

Understand stress concentrations.

I

Analyze model in different SolidWorks configurations.

I

Run multiple studies in a batch mode.

I

Extract reaction forces.

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Mesh Controls, Stress Concentrations and Boundary Conditions

Meshes are rarely uniform in practical problems. It would be very inefficient to uniformly reduce the mesh size in a large model because of a local stress concentration. We would create large number of elements in areas of uniform or slowly changing stress resulting in an increase of computational time that in the end tells us little about the model.

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Mesh Control

Using different methods to control the mesh, we can use a small mesh in areas of rapid changing stress and a large mesh in areas with little change.

Case Study: The L Bracket

In this case study, we will determine the stress in an L bracket, under load. The L bracket presents the problem of stress at sharp corners and the effects of fillets and local mesh refinement.

The corner of the bracket is rounded by a small fillet. Since the radius of the fillet is small compared to the overall size of the model, it may be suppressed. We will solve the model with and without fillet, discuss the differences and the applicability of each approach.

We will also investigate the effect of different mesh sizes on the maximum displacement and stress results. Rather than refining the mesh uniformly in the entire model, which is called global mesh refinement, we refine the mesh locally, where high stresses are located. This is called local mesh refinement.

Project Description

Stages in the Process

An L-shaped steel bracket is fixed at the top and a 900 N load is applied to the lower end face. We will evaluate the displacements and stresses in the model.

Suppressed Fillet

Some key stages in the analysis of this part are shown in the following list: I

No fillet

The fillet will be suppressed to simplify the geometry and to observe the stress at the sharp corner.

I

Add fillet

The fillet will be unsuppressed to determine the effect of the fillet on the maximum stress in this part.

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Lesson 2 Mesh Controls, Stress Concentrations and Boundary

Conditions I

Mesh refinement

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As the fillet is small compared to the rest of the model, we will use different techniques to reduce the mesh size only in the area of the fillet.

Procedure

In the first part of this case study, we will examine the stress on this part without the fillet.

1

Open a part file.

Open L bracket.from Lesson02\Case Studies folder.

In the SolidWorks ConfigurationManager, examine the two configurations: fillet and no fillet. Make the no fillet configuration active.

2

Set the simulation options.

Click Options from the Simulation menu. Select the Default Options tab.

Select Units, then select SI (MKS) for the Unit system. Select mm for Length/ Displacement and N/m^2 (Pascals) for Pressure/Stress. Select Color Chart. For Number format, select Scientific (e) and 6 decimal places.

3

Define static study.

Create a new study named mesh1.

In the analysis Type list, select Static. Click OK.

4

Examine the Simulation Study tree.

The L bracket icon already has a check mark next to the name of the assigned material because the material definition (AISI 304 steel) has been transferred from SolidWorks. Also, note that a sharp re-entrant corner takes the place of the suppressed fillet.

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Apply a fixture. Now apply a Fixed Geometry fixture to the top face of the L bracket.

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5

Right-click Fixtures and select Fixed Geometry.

In the Standard list select Fixed Geometry. Click OK.

6

Apply an external load. Right-click External Loads and select Force.

Select Force.

We want to apply a shearing force and not a normal force, so we must define the direction of the force. Select Selected direction.

Select the indicated face to apply the force and the Top plane to specify the direction. Type 900 N [202.33 lbf] for the force.

Select Reverse direction to make sure the force is pointing as shown.

Click OK.

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Conditions

Mesh the model. Select Curvature based mesh under Mesh Parameters.

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7

Verify that the meshing option is set to High quality (Draft Quality Mesh is cleared), meaning that second order elements are created.

Mesh the model using the default Maximum element size and Minimum element size of 4.812 mm [0.1894 in].

Run All Studies

Multiple studies can be run at the same time. This allows you to setup multiple studies and then run them after hours.

Where to Find It

I

CommandManager: Simulation > Run > Run All

Studies

8

Create a duplicate study.

Study mesh1 is now ready to be analyzed. However, we will create two more studies and run all three studies at the same time using the Run All Studies command.

Duplicate study mesh1 into a new study mesh2 (see Creating New Studies on page 61 on how to duplicate a study). When creating the duplicate of the study make sure that the Configuration to use field says no fillet. Click OK.

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Mesh Controls, Stress Concentrations and Boundary Conditions

The second part of this case study will investigate the effect of using smaller elements in the model on the results. In Lesson 1, we refined the mesh uniformly throughout the entire model by controlling the global element size.

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Analysis with Local Mesh Refinement

Stress concentration

In this part of the case study, we will use a different technique. Note that a stress concentration is located near the sharp reentrant corner.

Knowing the location of high stress, we can refine the mesh locally in that area by applying local mesh controls.

Mesh Control

Mesh controls allow you to control the Maximum element size and Ratio locally on selected entities independent of the global Maximum element size and Ratio. As compared to global mesh refinement, this is a more numerically efficient technique. Small elements are placed where needed, while portions of the model with no stress concentration are meshed with larger elements.

Where to Find It

I

Menu: Simulation, Mesh, Apply Control.

I

Shortcut Menu: Right-click Mesh in the Simulation Study tree and select Apply Mesh Control.

Mesh Controls

Mesh controls can also be applied to vertices, faces, or entire

components of assemblies. Once mesh controls have been defined, the Mesh icon becomes a folder. Mesh controls can be edited using a shortcut menu displayed by right-clicking Control-1 and select Edit Definition in the Mesh folder, or directly by double-clicking on the Control-1 item.

The mesh, with applied control (also called mesh bias), features localized refinement along the edges. Meshing must be done after controls are defined.

Mesh control symbols are displayed along the affected edge.

Mesh Control Symbols

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Conditions

Mesh control symbols can be displayed or hidden by:

Mesh control symbols

Right-click Mesh and select Hide All Control Symbols Right-click Mesh and select Show All Control Symbols

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I I

The visibility of mesh control symbols can also be controlled individually for each mesh control.

9

Apply local mesh control for study mesh2.

Select the edge shown.

Right-click Mesh and select Apply Mesh Control. Use the suggested local Element size of 2.406 mm and the Ratio of 1.5.

Click OK to close Mesh controls PropertyManager.

10 Create mesh. Select Curvature based mesh under Mesh Parameters.

Create High quality mesh with the default settings.

11 Examine the mesh.

Note that smaller elements have been created along the edge where mesh control has been just applied.

With edge mesh control

No edge mesh control

12 Duplicate study mesh2. Name the new study mesh3.

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13 Apply local mesh control for study mesh3. In the mesh3 study, edit the definition of Control-1.

In the Element size box, enter 0.508 mm to locally refine the mesh along the sharp re-entrant edge. Keep the Ratio at its default value of 1.5.

With this mesh control, we will create very small elements along the sharp re-entrant edge. Click OK.

14 Mesh study mesh3. Mesh study mesh3 with High quality elements and the default mesh

parameter. Use the curvature based mesh.

We now have three studies: mesh1, mesh2 and mesh3. The only difference is mesh refinement along the sharp re-entrant edge.

Study: mesh1

Study: mesh2

Study: mesh3

15 Run all studies. Select the Simulation tab on the CommandManager. Select the down arrow under Run Study to flyout the other choices. Click Run All Studies. 16 Simulation progress log.

Once the analyses are completed, review the report in the MSG file located in the result folder.

17 Plot von Mises stresses.

Display the mesh with the plot by right-clicking the corresponding result plot and selecting Settings. Under Boundary options, select Mesh.

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Conditions

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Click OK.

Study: mesh1

Study:

mesh2

Study: mesh3

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18 Plot resultant displacements.

Study: mesh1

Study: mesh2

Study: mesh3

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Conditions

Reporting displacement results with six digits of accuracy is excessive as uncertainties in loads, restraints, and material properties definition do not normally justify this level of accuracy.

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Results

We used six digits of accuracy so that we can compare the minute differences in the displacement results calculated in the three studies we undertook in this lesson.

Results Comparison

Results for the maximum resultant displacement and maximum von Mises stress from mesh1, mesh2 and mesh3 studies are summarized in the following table:

Study

Max. displ. [mm]

Increase in max. displ. [mm][%]

Max. Von Mises stress [MPa]

Increase in Von Mises stress [MPa][%]

mesh1

0.28741

-

60.76

-

mesh2

0.28795

0.00054 (0.2%)

88.38

27.62 (45.5%)

mesh3

0.28856

0.00115 (0.4%)

177.42

116.66 (192.0%)

Each mesh refinement results in an increase in both the maximum displacement and the maximum stress. The increase in the displacement results is negligible and becomes less pronounced with successive runs. From this, we can say that the displacement results converge.

If we continue this exercise of progressive mesh refinement, either locally near the sharp re-entrant corner as we did by means of the local mesh controls, or globally by reducing the global element size as we did in Lesson 1, we would note that the displacement results converge to a finite value and that even the first mesh is adequate if we are examining only displacement results.

Stress Singularities

Stresses, however, behave quite differently. Each subsequent mesh refinement produces higher stress results. Instead of converging to a finite value like the displacement results, the stress results diverge.

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mesh3

mesh2

mesh1

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Mesh Controls, Stress Concentrations and Boundary Conditions

With enough time and patience, we can produce results that show any stress magnitude. All that is necessary is to make the element size small enough! The reason for divergent stress results is not that the finite element model is incorrect, but that the finite element model is based on the wrong mathematical model.

According to the theory of elasticity, stress in the sharp re-entrant corner is infinite; a mathematician would say that stress there is singular. The finite element model does not produce infinite stress results due to discretization errors, and these discretization errors mask the modeling error. However, stress results in the vicinity of the re-entrant corner are completely dependent on mesh size; therefore, they are totally meaningless at this location.

If our objective is to determine the maximum stress at this location, then the decision to suppress the fillet and analyze a model with a sharp re-entrant corner is a very serious mistake. The stress in a sharp reentrant corner is singular, or infinite. The fillet, no matter how small it is, must be included in the model if we seek to find accurate stresses in or near that fillet.

Suppressed Configuration

When the active configuration is different from the configuration used to create the study, the study is suppressed and all items in the study are shown in grey. To unsuppress the study, the configuration must be changed to that used to do the study.

Activate SW Configuration

To change the SolidWorks configuration to the one used for a study, we can activate the configuration from the Simulation Study tree.

Where to Find It

I

96

Shortcut Menu: Right-click the study in the Simulation Study tree and click Activate SW Configuration.

SolidWorks 2012

Lesson 2 Mesh Controls, Stress Concentrations and Boundary

Conditions

Case Study: Analysis of Bracket with a Fillet

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Now that we understand the problem caused by the sharp re-entrant corner, we must repeat this analysis using a model with the fillet. Obtaining the correct model requires unsuppressing the fillet.

1

Change SolidWorks configuration.

In the SolidWorks ConfigurationManager, make the configuration fillet active.

2

Examine the Simulation Study tree. With the fillet configuration active, the mesh1, mesh2 and mesh3

studies are greyed-out. You can access them again only after activating the SolidWorks configuration corresponding to these studies.

3

Create new study. Create a study mesh4 by duplicating the mesh1 study.

We copied the mesh1 study and not the mesh2 or mesh3 studies for convenience because mesh1 does not have mesh controls defined and mesh4 does not require mesh controls.

If we use mesh2 or mesh3, we have to edit or delete the mesh controls in the mesh4 study because the geometry of the model has changed.

4

Mesh the model.

Select Curvature based mesh under Mesh Parameters.

Mesh the model with High quality elements and the Maximum element size and Minimum element size of 4.813 mm [0.1895 in].

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Run the analysis.

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5 6

Plot Displacement results.

The maximum resultant displacement result (0.2845 mm) reported for the fillet study differs only insignificantly from the earlier displacement results. This small difference can be attributed to the change in the model geometry.

7

Plot von Mises stresses.

The stress results obtained by the model with the fillet indicate that the maximum von Mises stress is at the fillet location and its magnitude is 88.76 MPa.

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Conditions

8

Analyze the plots.

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Analyzing the stress distribution uniformity at the fillet location we see rather spotty behavior and no symmetry. This is another sign of insufficient mesh resolution for stresses. The displacement results are accurate in all studies solved in this lesson.

We will therefore apply a new local mesh control on fillet and rerun the study again.

9

Apply mesh control on fillet.

To get more accurate results, we will apply a local mesh control on the fillet face.

Apply mesh controls to the fillet face using 0.762 mm [0.030 in] for the local Element size, 1.2 for the Ratio.

10 Re-mesh model. Select Curvature based mesh under Mesh Parameters.

Mesh the model with High quality elements and the Maximum element size and Minimum element size of 4.813 mm [0.1895 in]. The resulting mesh can be seen at right.

This mesh is a little excessive in its size, but given the small size of the problem we can afford it.

11 Run the study.

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12 Plot von Mises stress.

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We observe that the maximum stress increased to 102 MPa. The details of the stress distribution are uniform and symmetrical. We could conclude that this stress value is accurate.

13 Extract reaction force. Right-click on the Results folder and select List Result Force.

Select the face where the bracket is supported and click Update. Make sure the units are set to SI. The Reaction force (N) dialog will list the resultant of the reaction on the selected face (or faces, if more supported faces exist and are selected) as well as on the entire model. We can see that the equilibrium is satisfied; the reaction force is equal to 900 N, which confirms the equilibrium and the correctness of the solution.

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Conditions

Note

Moment reactions are not reported since solid elements feature three translational degrees of freedom only. Nodes of the solid elements do not carry any moment.

Case Study: Analysis of a Welded Bracket

Now that we understand the stress concentration in the fillet, let’s repeat the analysis using a more realistic model where the edges of the faces are fixed rather than the entire face. This would more closely represent the face being welded to a plate.

1

Create a new study.

Create a static study named mesh5 by duplicating the study mesh4.

2

Edit the Fixture.

Edit the fixture and remove the top face. Add the four edges surrounding that face as shown.

This type of restraint would simulate the part being welded to a surface when only the edges are firmly attached to the structure, and not the entire face.

3

Run the analysis.

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4

Plot the stress results.

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Another stress concentration has appeared at the edges where fixed geometry was used. Again, a singularity of stress is formed due to the fixed geometry at the sharp end. Although perhaps a more realistic finite element model, the stress concentration is an artifact of the mathematical model. These types of effects must be understood to properly analyze model results.

5

Understanding the Effect of Boundary Conditions

102

Save and Close the file.

Boundary conditions are necessary in order to fix the model in space and solve the mathematical problem. In real life every part is connected to another and finally attached to the primary structure or the ground. We can, however, view the boundary conditions as a means to significantly simplify our simulation. As an illustration, consider the bracket assembly shown in the figure to the right, where the bracket is part of a larger structure.

SolidWorks 2012

Lesson 2 Mesh Controls, Stress Concentrations and Boundary

Conditions

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Then, before we even begin modeling in SolidWorks Simulation we have to decide whether to model the entire upper level assembly with the boundary conditions applied as shown in the figure above, or the full bracket only, or a part of the bracket (a model identical to what we had in Lesson 2). See the images below.

The decision is based on what is the objective of the analysis, i.e. what results do we truly need. The larger the model we chose, the more realistic it becomes. At the same time the size of the finite element model increases, resulting in significantly longer solution times. Boundary conditions therefore serve to express the fact how a specific part or sub-assembly is grounded or attached to another primary structure, and help us substantially reduce the size of the problem. Reduction of the problem comes at a cost, i.e. the stress results at the location of the boundary conditions may be singular and have to be ignored in such cases.

Also, we need to understand that the boundary conditions do effect our solution. In the three cases listed above the final results will be comparable, but not exactly the same. Therefore the selection, as well as the location, of the boundary condition must be done so that its effect on the results and the rest of the model is minimal.

Conclusion

The question may arise: which one study is the correct one?

The second to last study with the fillet and fixed face included in the model and the mesh control applied produce the most accurate results and is favored provided one can afford the increased size of the model due to the additional regions that must be meshed. Then what about the other studies where stress concentrations are seen?

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Mesh Controls, Stress Concentrations and Boundary Conditions

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These results are obtained by using the incorrect mathematical model. It does not make sense to debate which of the first three models produces the most accurate results and, therefore, which one was “the best” among the three. All models with sharp re-entrant edges or edges that are fixed are equally poor if we examine the stress on those edges. Thus, if we are interested in stress at or near a sharp edge (or a sharp corner for shell models), this edge must be modeled with a fillet, even if the fillet is very small. In addition, if the edge of the model is fixed, we must realize that the appearance of the stress concentration is artificial. In general, if stresses at these singularities are of no interest, these studies still produce good results for the overall model.

Summary

In this lesson, we illustrated what can go wrong when FEA is based on an incorrectly prepared model.

Using local mesh controls rather than the global mesh controls, we obtained solutions for different meshes and revealed stress singularities at a sharp re-entrant corner and at fixed geometries.

We used this lesson to further discuss modeling and discretization error, meshing techniques, and also to illustrate the integration between SolidWorks and SolidWorks Study tree.

Questions

104

I

Why do we often eliminate fillets and small rounds if such suppression can lead to locally inaccurate stress results? Does it imply that the stress results are inaccurate for the whole model?

I

Are displacements affected by the suppression of small features (fillets, rounds) as much as stresses? Why?

SolidWorks 2012

Exercise 4 C-bracket

Exercise 4: C-bracket

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In this exercise, you will analyze a bracket with two different configurations to determine the effects of the internal fillets. This exercise reinforces the following skills: I I I I

Problem Statement

Mesh Controls on page 90. Results Comparison on page 95. Stress Singularities on page 95. Suppressed Configuration on page 96.

A hanging bracket mounted on the ceiling will be supporting a sign mounted on the bottom flange of the bracket. The sign will be mounted onto the bracket with a flat ribbon like cable. A 900 N [202 lb.] force will be exerted on the bracket due to the weight of the sign and ribbon. We will evaluate the displacements and stresses for the bracket due to this loading. We are also interested in how modeling the bracket with and without fillets will effect our results. The effects of different boundary conditions will also be investigated.

Part 1: Analysis of Bracket with no Fillet

1

Open a part file.

Open bracket from Lesson02\Exercises folder.

2

Specify active configuration.

Make the configuration No Fillet active.

Notice that the rounded inside edges become sharp re-entrant corners. This configuration, suppresses all inner fillets.

3 4

Define a static study. Create a Static study named no fillet 1. Apply material properties.

Apply the material Alloy Steel from the solidworks material library.

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C-bracket

Apply a fixture. Apply a Fixed Geometry fixture to the top

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5

face as indicated.

We will assume that the compressive force of the screw is large enough to prevent any sliding or rotation about the screw.

6

Apply force. Apply a 900 N [202 lb] normal force to the top

face of the bottom flange. This force is due to the weight of the sign.

7

Mesh the model.

Select Curvature based mesh under Mesh Parameters.

Mesh the model with the default element size. Use High quality elements.

8 9

Run the analysis.

Plot stress results.

We find that the bracket has a maximum von Mises stress of 132 MPa [19.2 ksi] and does not yield. However, there is a high stress concentration at the sharp corners.

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Exercise 4 C-bracket

10 Plot displacement results.

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Maximum displacement is 1.25 mm.

11 Create a new study.

Duplicate the existing study and name it no fillet 2.

12 Apply mesh control.

Apply mesh control to each of the three edges on the inner faces of the bracket. Use the default mesh control size.

13 Mesh the model.

Mesh the model with the default element size. We have created a finer mesh at the inside edges of the bracket, while the mesh sizes are coarser at all other locations in the bracket.

14 Run the analysis.

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C-bracket

15 Plot stress results.

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The maximum von Mises stress is now 160 MPa [232 ksi], which is higher than the von Mises stress value obtained in the previous study with no mesh control. This shows the diverging stress results and verifies that the stress in the corners are indeed concentrations. Further refinement will continue this trend.

16 Create a new study. Duplicate the no fillet 1 study and name it no fillet 3. 17 Apply mesh control.

Add mesh control to the same three edges. Change the local Element size to 0.889 mm [0.035 in].

18 Mesh the model.

Mesh the model with the default element size. We have created a finer mesh at the inside edges of the bracket, while the mesh sizes are coarser at all other locations in the bracket.

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Exercise 4 C-bracket

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19 Run the analysis. 20 Plot stress results.

We find that the maximum von Mises stress is significantly higher than the value obtained in the previous study with a coarser mesh control. We see that, although we are refining the mesh, the stress results are not converging. This is due to the sharp re-entrant corners.

Part 2: Analysis of Bracket with Fillet

We will now look at a model with fillets and analyze its solution.

1

Change configuration.

Change the active configuration to Default. This configuration has the fillets unsuppressed.

2

3

Create a new study. Duplicate the no fillet 1 study and name it fillet. Mesh the model.

Mesh the model with the default local Element size.

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C-bracket

Run the analysis.

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4 5

Plot stress results.

The stress results obtained from the model with the fillet indicate that the maximum von Mises stress is approximately 127 MPa [18.4 ksi]. Because no sharp edges are present in the model, this value is close to the real stress magnitudes. Further mesh refinement would improve the results and eliminate the spotty stress distribution.

Part 3: Analysis of Bracket with Fillet and Fixed Hole

In this last study, we will change the way the part is restrained by editing the one fixture and holding the part by the cylindrical hole instead of the entire top face.

1 2

Create a new study. Duplicate the fillet study and name it fillet fixed hole. Use Fixed Geometry on hole.

Edit the fixture and remove the top face. Add the hole face.

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Exercise 4 C-bracket

3

Apply mesh control.

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Apply a mesh control with an Element size of 0.508 mm to the inner cylindrical surface of the hole.

4

Mesh control on the fillets.

Apply a mesh control with the default Element size of 1.9 mm to the three fillets.

5

Run the analysis.

The study will mesh and solve.

Add

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C-bracket

6

Plot the stress results.

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The stress results obtained from the model with the fillet and the fixed geometry on the hole produce a stress concentration around the edges of the hole. This is because a singularity of stress appears in this region due to the perfectly rigid support at those edges. This is similar to the singularity seen in the fixed edges of the L-Bracket in Lesson 2 and can be ignored. Change the scale of the legend to obtain a more realistic plot.

We can see that the stresses on the filleted faces increased from 127 MPa (see previous study) to nearly 145 MPa.

7

Modify the mesh controls.

Change the Element Size for both mesh controls to 0.1mm for the hole and 1.1mm for the fillets.

8

Run the Study.

The study will mesh and solve.

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Exercise 4 C-bracket

9

Examine the stress plot.

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As can be seen the stress near the support increased considerably and represents the maximum stress in the model. From Lesson 2 we know that this stress is unreal and will increase as we reduce the size of the elements.

Probing on selected entities reveals the maximum stress on the filleted faces as 150 MPa, a slight increase from the 145 MPa obtained from the previous run. This stress is real and approaching a finite value (we say it converges).

10 Save and Close the file.

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Exercise 5

SolidWorks 2012

Bone Wrench

Exercise 5: Bone Wrench

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In this exercise a bone wrench will be analyzed for its stresses and deformations when subjected to loads resulting from regular working conditions. The analysis will include a report generated automatically. This exercise reinforces the following skills: I I

Problem Statement

Plot Settings on page 29. Results Summary on page 65.

One side of the wrench is fixed, simulating a tight contact with a nut. The other side is subjected to a horizontal 150 N force exerted by an operator when tightening (loosening) the nut.

1

Open a part file.

Open bonewrench from the Lesson02\Exercises folder.

2

3

Set SolidWorks Simulation options. Set the Units to SI(MKS), and the units of Length and Stress to mm and N/mm^2, respectively. Define a static study.

Create a Static study named bone wrench analysis.

4

Apply material properties. Assign Alloy Steel as the material from the solidworks materials

library.

5

Apply fixtures.

The tight contact between the wrench and the nut will be simulated by the application of Fixed Geometry fixture on the faces (a total of eight faces), as shown in the figure.

Note

114

Restrained faces are featured in beige in the SolidWorks model.

SolidWorks 2012

Exercise 5 Bone Wrench

6

Apply force.

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Apply a force of 150 N [33.7 lbf] exerted by an operator, as shown in the figure below.

7

Mesh the model.

Select Curvature based mesh under Mesh Parameters.

Mesh the model using High quality elements. Use the default settings.

8

Run the analysis.

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Bone Wrench

9

Plot stress results.

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We observe that the resulting von Mises stress in the model is 244 MPa [35.4 Ksi], which is well below the material yield strength of the 620 MPa [89.9 Ksi].

10 Plot resultant displacements.

The absolute values of the displacements are very small, with a maximum value of 0.3 mm.

Note

The next task, extraction of the reaction torque requires a specification of the local cylindrical coordinates system. This is explained in Lesson 4.

11 Check the reaction moment. Right-click on Results folder and select List Result Force.

As shown in the following figure, in the Plane, Axis or Coordinate system field, select Axis1. SolidWorks Simulation will switch to the cylindrical coordinate system defined by Axis1. Select all the faces where the model is restrained (a total of 8 faces). Click Update.

The Reaction force (N) dialog reads Sum Y: -1391.7 N.

Note

116

This force could be negative or positive depending on which side of the wrench the force was applied.

SolidWorks 2012

Exercise 5 Bone Wrench

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This is the total value of the reaction force in the second cylindrical (circumferential) direction. To obtain a reaction moment, we have to multiply this value by a radius.

12 Compute the moment.

Because the opening is not circular, we will measure the outer and inner diameters and use the average as an approximation of the opening diameter. The average diameter is 17.321 + 15 ---------------------------- = 16.16mm . 2

Therefore, the total reaction moment is approximately equal to 16.16 ------------- x 1391.7 = 11244.94 Nmm 2

.

To calculate the loading moment, measure the distance between the centroid of the applied load and Axis1.

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Bone Wrench

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The measured distance is 75 mm. Therefore, the loading moment is equal to 75x150 = 11250Nmm , which confirms the equilibrium. Note

The slight difference in the two values is not caused by the inaccuracy of SolidWorks Simulation computations. It is merely a consequence of the approximate calculation of the average diameter of 16.16 mm.

13 Generate report.

14 Save and Close the file.

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SolidWorks 2012

Exercise 6 Foundation Bracket

Exercise 6: Foundation Bracket

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The foundation bracket is used to secure a table leg to the floor. In this exercise the foundation bracket will be analyzed for its stresses and deformations when subjected to loads resulting from regular working conditions. This exercise reinforces the following skills: I I I

Problem Statement

Mesh Controls on page 90. Stress Singularities on page 95. Results Comparison on page 95.

Model courtesy of Bosch Rexroth

One side of the foundation bracket is bolted to the floor by a single bolt. The vertical face is bolted to a table leg with two bolts.

Analyze the stress in the foundation bracket when the table leg is forced to displace by 0.5 mm in both the plus and minus X direction.

+X

Both of these displacements are rather large and would not occur under normal conditions.

Note

We will first analyze the stress when the table leg moves in the plus X direction.

1 2

Open a part file. Open bracket from the Lesson02\Exercises folder. Set options.

Select Units, then set the Unit system to use SI units, mm for length and displacement and N/m^2 (Pascals) for pressure and stress.

Select Color Chart, then set the number format to display Scientific units at 2 decimal places. Select Specify color for values above yield for vonMises plot. Leave the color as the default gray. Select Results, then select Automatic as the Default solver.

3

Create a study.

Create a new static study and name it stress analysis x+.

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4

Apply material.

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Apply the material Chrome Stainless Steel from the SolidWorks material library.

5

Add fixtures.

We are going to ignore friction along the direction of the slot and only constrain the surface that the bolt head and shank contact to zero displacement. Add an On Flat Faces fixture to the four faces shown. Set the Translations to zero for the direction Normal to Face. Rename the Fixture to Bottom bolt.

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Apply fixtures. Apply an On Flat Faces fixture to the four faces where the bolt heads contact the vertical plate. Rename this fixture to Top bolts-1.

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6

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Apply a displacement. Apply a 0.5 mm normal displacement to the two faces indicated using the On Flat Faces fixture. Select the face shown in blue as the

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7

direction.

Rename this fixture to Top bolts-2.

8

Mesh the model.

Select Curvature based mesh under Mesh Parameters. Mesh using the default element size.

9

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Run the study.

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Exercise 6 Foundation Bracket

10 Plot the results.

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The displacement plot shows a maximum displacement of 0.5 mm which was our input.

11 Examine the stress plot.

The stress plot shows high stress at the lower bolt and at the sharp edge. We can see that there is significant yielding as indicated by the gray color and the position of the yield arrow in the color band. We see that the part will yield around the areas of the bolts, and at the sharp corner between the back vertical face and the angled face.

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Foundation Bracket

12 Re-mesh.

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Re-mesh the model with a finer mesh. Move the mesh size slider all the way to the right and mesh. We now have two elements in the thickness direction.

Note

You will learn later in the course that at least two solid elements through the thickness are required in the bent regions to obtain acceptable stress results.

13 Run the study.

The choice of Automatic for the solver should cause the FFEPlus solver to be used.

14 Review the plots.

The stress plot shows essentially the same results as with the coarser mesh. We still have yielding around the bolts and the sharp corner.

15 Duplicate the study. Name the new study stress analysis x-.

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Exercise 6 Foundation Bracket

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16 Change the direction. Edit the fixture Top bolts-2 to switch the direction and have the

displacement applied to the two faces on the other side of the slot as we want to push, not pull, the material in the negative x direction.

17 Run.

Run the study with the fine mesh.

Note

No remeshing is necessary; the geometry was not modified.

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18 Examine the results.

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The stress on the inside faces looks similar to the stress found when the movement was in the +X direction, however we can now see additional yielding on the back face. From these results, we can see that we would need to possibly increase the thickness of the material to avoid yielding. However, we need to remember that we purposely subjected the bracket to a very large displacement, which is not likely to occur frequently.

19 Probe the result.

By probing several points in the yielded region on the back face, we can see that the stress is about 200 MPa.

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Exercise 6 Foundation Bracket

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20 Probe the face. In the Probe Results, select On selected entities, then select the

indicated face. Click Update.

By selecting the face, we now have Summary information that show the maximum stress is 351 MPa.

21 Conclusion.

Based on the analysis, we might conclude that the bracket is not strong enough in this configuration. We might consider a change to the design to avoid yielding, probably by increasing the material thickness to sustain the applied displacements. However, as the displacement applied is very large and occurs exceptionally, and the resulting maximum values of 224 MPa are close to the yield strength of the material, this bracket design is appropriate.

22 Save and Close the file.

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Foundation Bracket

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PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Lesson 3 Assembly Analysis with Contacts

Objectives

Upon successful completion of this lesson, you will be able to: I

Perform structural analyses of simple assemblies.

I

Apply and define contact conditions.

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Assembly Analysis with Contacts

When we analyze an assembly, we must understand how the components interact with each other so that our mathematical model correctly computes the stress and deformation.

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Contact Analysis

Different conditions must be considered where the parts can pull apart or penetrate each other and whether or not the surfaces can slide over each other.

Case Study: Pliers with Global Contact

In this lesson, we analyze a simple hand tool. It consists of four components: two identical arms, a hinge pin, and a piece of flat stock squeezed by pliers.

We are not interested in the contact stresses that develop between the arms and the piece of flat stock.

Therefore, we can simplify the model by suppressing the flat stock and replacing it with the appropriate fixture.

Project Description

Calculate the stresses that develop in the arms when a 225 N [50.6 lbf] “squeezing” force is applied to the end of each arm. The design strength is set at 138 MPa [20,016 psi], approximately 22% of the material yield strength.

Stages in the Process

Some steps in analyzing an assembly. I

Apply materials

Materials can be applied to all components together or individually.

I

Add fixtures

Fixtures are added in the same way they are done in parts to restrain the motion of the model.

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Apply component contact conditions

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Component contact conditions dictate how parts or sub-assemblies in contact or close proximity interact in the absence of local overrides.

I

Apply local contact conditions

Local contact conditions override the component contact.

I

Apply mesh control

The mesh can be refined in areas of stress concentrations or rapidly changing geometry.

I

Mesh the model

I

Run the analysis

I

Analyze the results

Determine if the results are accurate enough or further refinement of the analysis is needed.

Procedure

To begin this case study:

1

Open an assembly file. Open pliers from Lesson03\Case Studies folder.

2

Suppress flat.

Suppress the part flat in the SolidWorks FeatureManager design tree.

3

Create study.

Create a static study named pliers.

4

Examine the Simulation Study Tree.

There is now a Parts folder with three components because there are three parts in the assembly to be analyzed.

Applying Materials to Assemblies

You can apply the same material to all components of an assembly or to each component individually. To apply material to the components:

I I

To apply the same material to all components, right-click Parts and select Apply Material to All. To apply different material to each component, right-click a part and select Apply/Edit Material.

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Assembly Analysis with Contacts

Apply materials to components. Apply Plain Carbon Steel material

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5

properties to all components including the pin.

6

Apply fixed restraints.

Define Fixed Geometry fixture on both jaws.

The applied restraints simulate the suppressed piece of squeezed flat stock. This condition assumes that the flat is not sliding when held by the jaws.

7

Apply force to handles.

Apply a 225 N [50.6 lbf] force to both handles. The outer face of each arm has a split face so that the load is only applied to part of the face.

In the Force/Torque PropertyManager, select Normal.

Component Contact

Whenever we create a study of an assembly, a new folder named Connections is added to the Simulation Study tree. We use this folder to define how the assembly components interact with each other.

We have defined the fixtures and external loads, but we are not yet ready to mesh this assembly. We have to account for the contact between the two arms.

The Component Contact options defines the way components interact with each other. You can override the component conditions by defining different conditions locally for selected pairs of features. Local contact conditions are discussed later in this lesson.

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Lesson 3 Assembly Analysis with Contacts

The available options for the component contact are: Bonded, Allow penetration and No penetration. These options are explained in the following figure and table.

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Component Contact: Options

Part A

Part B

Bonded Contact

I I I

Part A

Part B

Allow penetration

Part A

Part B

No penetration

In the Simulation Study tree, right-click Connections and select Component Contact. Select Contact/Gap in the Simulation menu and then click Define Contact for Components. Select the Simulation tab in the CommandManager, then select Component Contact from the Connections Advisor pull-down list. Component Contact Types

Bonded

This is the default choice. Select this option when all touching faces are bonded and the assembly behaves as one part. The only difference between a part and an assembly with bonded parts is that in an assembly we can assign different material properties to individual components.

Allow penetration

Select this option when the assembly is a series of unattached components with no structural connection between them.

No penetration

Select this option when touching components can come apart, but cannot penetrate each other. The coefficient of friction can be specified in the component contact property manager.

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Assembly Analysis with Contacts

Component Contact: Default setting

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Default component contact setting is bonded contact between all touching faces for the top level assembly. Editing default component contact, Global Contact, shows that it is applied to the top level assembly.

Component Contact: Hierarchy and Conflicts

It is possible to delete and re-define the top level assembly contact condition. However, multiple top level component contact conditions would result in a conflict and are not permitted. Any additional component contact between parts and subassemblies must not be in conflict and will override the top assembly level component contact. If the conflict is detected a warning message will be displayed.

8

Check for existing interferences.

Click Tools, Interference Detection.

In the Options dialog, select Treat coincidence as interference and click Calculate. Three sets of faces in the assembly are touching.

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Lesson 3 Assembly Analysis with Contacts

In the parts of this assembly, the manufacturing clearance between the pin and the arms is ignored. That is why the coincident contact of cylindrical shape between the pin and the arms was detected.

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Note

9

Change top level component contact option.

In order to allow the relative movement of the arms while the model deforms under the load, change the default component contact (Global Contact) condition to No Penetration. Expand the Connections folder, edit the Global Contact item and change it to No Penetration. Click OK.

10 Mesh the model. Select Curvature based mesh under Mesh Parameters.

Mesh the assembly with Draft quality elements and the slider all the way to the right. This should produce the Maximum element size of 4.912mm, Minimum element size of 0.982mm, Number of elements in a circle as 8, and Ratio of 1.6.

Important!

Meshing must always be performed after the contact conditions are defined.

11 Run the analysis.

12 Switch to exploded view.

Switch to the exploded view.

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Assembly Analysis with Contacts

13 Plot von Mises stresses.

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Display the von Mises stress plot by double-clicking on the Stress1 plot icon.

We want to see if the von Mises stresses in any portion of the model exceed 138 MPa [20,016 psi], which is our design stress. To determine whether the von Mises stresses exceed the maximum we can change the plot options.

14 Change the plot.

While the plot is displayed, right-click Stress1 and select Chart options.

Under Display options, select Defined, and then enter the minimum stress as 0 and the maximum stress as 138,000,000. Click OK.

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15 Change Plot Settings. Right-click Stress1 and select Settings. Under Fringe options, select Discrete.

Click OK.

Viewing Assembly Results

Areas with stresses higher than 138 MPa would appear in red.

Note that an exploded view offers a very convenient way of examining the analysis results of an assembly, whereas, in normal viewing, components may obstruct the view. Another way of reviewing results of an assembly is to hide some assembly components.

16 Isolate the arm. Isolate arm.

17 Define stress plot of one arm.

In the Simulation Study tree, right-click the Results folder, and select Define Stress Plot. Click OK.

Note

You can also use the existing plot Stress1 after hiding an assembly component arm.

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Assembly Analysis with Contacts

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18 Max/Min annotations. In Chart Options, select Show max. annotation and Show min. annotation.

The maximum stress locations and their magnitudes are indicated for the displayed arm.

Conclusion

The maximum von Mises stress of approximately 93.0 MPa is produced by normal operation of the pliers when a 225 N force is applied to the handles. This load can be (perhaps with some difficulty) applied by hand and 93.0 MPa can easily be tolerated by the pliers’ material (which has a yield stress of almost 220 MPa). Before concluding that our design is safe, re-meshing the model and looking for stress convergence would be required.

Handle Contact

We wish to determine the maximum stress that the pliers undergo when squeezing a 5 mm stock plate. The maximum stress corresponds to the situation where the handles are blocked.

19 Show the hidden arm and pin. 20 Collapse the assembly.

21 Create UY: Y displacement plot.

To determine the force that brings the ends of the two handles together, we need to create a displacement plot showing the y component of the displacements. Double-click the Displacement1 plot icon to make the plot active. Right-click the Displacement1 plot icon and select Edit definition.

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Select UY as the Displacement Component, and select mm as the

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Units.

Under Deformed shape, select True scale. This option plots the deformation in 1:1 scale. Click OK.

Required Force

We see that under the 225 N force, the end of each handle travels 0.393 mm. Consequently, the distance between the two ends decreases by twice that amount, 0.786 mm. Since the original distance is 15.24 mm, the force magnitude must be increased by a factor of: 15.24 mm / 0.786 mm = 19.39

Therefore, the force required to bring both arms in contact is equal to 19.39 x 225 = 4362 N. This is based on fundamental assumptions of linear analysis where the structural response is assumed to be proportional to the applied load.

Pliers with Local Contact

We will now load the pliers with a force that significantly exceeds 4265 N to ensure that both arms come in contact. The appropriate definition of the contact will ensure that the handles can come together, but cannot penetrate each other.

1

Create new study.

Duplicate the study pliers and name the new study pliers with local

contact.

2

Edit force.

Edit the force magnitude to 4,500 N. This is an arbitrary magnitude based on our “rough” estimation of forces that will definitely bring the two arms together.

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Assembly Analysis with Contacts

The top level component contact condition remains the same (No Penetration) as in the previous study. However, now that the force is considerably larger in order to bring the two arms together, we need to specify a local contact condition that prevents their penetration (No penetration top level assembly component contact applies to initially touching faces only).

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Local Contact

This local contact condition has precedence over the component contact. In general, the hierarchy of the contact conditions can be explained by the pyramid shown in the following figure.

High precedence in contact hierarchy

LOCAL

OTHER COMPONENT CONTACTS

Low precedence in contact hierarchy

TOP LEVEL COMPONENT CONTACT

Top assembly level contact (only one definition is permitted) is overridden by other user defined component conditions. All component contacts are then overridden by local conditions. The local contact conditions can be defined by right-clicking on the Connections folder and selecting Contact Set.

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In addition to Bonded, No Penetration, and Allow penetration, the local contact features two more contact types: Virtual wall and Shrink fit.

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Local Contact Types

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Assembly Analysis with Contacts

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The table briefly describes the local contact condition types. Local Contact Types

No penetration

The features (both initially touching and separated by a gap) may move away from each other but preserve the physical requirement that they may not penetrate each other. Friction coefficient and initial geometrical offset can be specified in the contact options.

Bonded

The selected features will become bonded, similarly to the component level contact types. While component bonded contact only applies to touching faces, local condition is capable of bonding features separated by a gap.

Shrink fit

The program creates a shrink fit condition between the selected faces. The faces may or may not be cylindrical. This condition requires that the two parts exhibit a finite volume interference.

Allow penetration

The selected pair of features is free to move in any direction. Free features can penetrate into each other, a physical impossibility. You should use this option only when you are absolutely sure that the specified loading will not cause the features to penetrate.

Virtual wall

This provides a sliding support in a way similar to Roller/Sliding restraint, except that a friction coefficient and wall elasticity can be specified.

Each local contact type features various options described at various locations throughout the manual.

Note

3

Define contact set.

To define a contact zone between the ends of the two handles, we use the two small split faces on the inside of the handles to define a contact pair. Right-click Connections and select Contact Set.

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In the Contact Set PropertyManager, select No Penetration. Click one face to define it as the Set 1, and then click the other face to define it as Set 2. Click OK.

Note

The selection of the faces for Set 1 and Set 2 is arbitrary.

No Penetration Local Contact Options

The above image shows two properties of the two local condition, Friction and Gap (clearance).

No Penetration Local Contact: Advanced Options

I

Friction: Any value of the friction coefficient is permitted.

I

GAP (clearance): In many applications, two entities cannot come into full contact due to the manufacturing limitations and the modeling approaches that we use. This feature restricts such two entities from coming closer than the initial geometrical offset. For a more detailed explanation, please refer to Lesson 7.

The No Penetration contact also features advanced options accessible through the simulation study options. These options, generally not required, are discussed in Lesson 7.

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Assembly Analysis with Contacts

The default algorithm for the local contact is fast and suitable to most contact solutions. However, if contact stresses are of primary importance, or if the areas in contact are large and/or the default solution for contact stresses is spotty or discontinuous, Improve accuracy for contacting surfaces feature should be activated.

Introducing: Improve Accuracy for contacting surfaces

Improve accuracy for contacting surfaces feature employs advanced solution algorithm resulting in improved results. While such contact solution is more accurate it may take significantly more time.

Where to Find It

Shortcut Menu: Right-click , Properties and under the Options tab, click the Improve accuracy for contacting surfaces check box.

No Penetration Local Contact: Remarks

Edges and vertices in local No Penetration contact condition can onlybe selected in the first field (Set 1), while the second field (Set 2) accepts faces only.

Note

Because the friction forces are small and no initial geometrical offset exists in this case, neither the Friction nor the Gap (clearance) properties will be used. Since the contact stresses are of no interest in this simulation Improve accuracy for contacting surfaces option will not be utilized.

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No Penetration Local Contact: Accuracy

Because the contact conditions have changed, the warning signs indicate that remeshing and recalculation of the results are necessary.

4

Mesh the model.

Select Curvature based mesh under Mesh Parameters.

Mesh the model with High quality elements and the same element size as before.

5

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Run the analysis.

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Lesson 3 Assembly Analysis with Contacts

6

Large/Small displacement.

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While the study is running, the following message will appear: Excessive displacements were calculated in this model. If your system is properly restrained, consider using the Large Displacement option to improve the accuracy of the calculations. Otherwise, continue with the current settings and review the causes of these displacements.

Click No to complete the analysis as linear.

The large displacement dialog box warns us that the large displacements of some parts in the assembly were detected. The large displacement computations are the subject of Lesson 14. At this point, we will ignore this fact.

Note

7

Plot von Mises stresses.

After the analysis is complete, create a von Mises stress plot, with discrete fringes, the mesh showing, and the stresses scaled from 0 to 220 MPa [89,925 psi].

The region in red indicates the yielding material. We can observe that the maximum reported von Mises stress is approximately 1,806 MPa. This value is, of course, unrealistic. Yielding of the material indicates that a linear analysis is no longer valid and that a nonlinear analysis would be required.

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Assembly Analysis with Contacts

Contact Stresses

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After the handles are blocked, any further increase in force magnitude has little effect except for increasing the contact stresses where the handles touch.

Question:

Can we analyze the contact stresses in the current study?

Answer:

No, the element size in the contact area is much too large in comparison to the size of the contact area. This comparison is best seen in a side view.

The two handles touch only along the edge. For accurate modeling of contact stresses, we need several elements along the length and width of the contact zone.

8

Summary

Save and Close the file.

In this lesson we analyzed the simple assembly model of pliers with various contact conditions. To simplify the geometry, the flat was suppressed and its presence was simulated with the help of the fixed geometry fixtures on the jaws. When the analysis was run, we saw a maximum von Mises stress of 93 MPa. This stress is below our specified design strength of 138 MPa. To be sure of our stress results, a more refined mesh should be run to insure that the stress is converging.

Additionally, we saw that the maximum displacement produced was 0.402mm. We used this result to change our loading application to investigate what happens if the load was so large that the handles touch. The contact conditions can be grouped into two distinct categories: component and local. Both categories were introduces and practiced in this lesson.

The local contacts take precedence over all of the component conditions, while all user defined component contacts take precedence over the top assembly level component condition (essentially serving as the global contact condition for the entire assembly). While the component contacts apply to initially touching faces of parts or assemblies, the local conditions may feature gaps and initial separation. Various types (namely Bonded, Allow Penetration, No Penetration, Shrink Fit and Virtual Wall), properties and options of the contacts were discussed and practiced.

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A linearity principle (linear dependence of the input and output) was used to scale the magnitudes of the loads in order to close arms of the pliers.

Finally, the limitations of analysis with linear materials were examined and contact stresses were introduced.

Questions

I

As a review, the available component condition types are: ___________________________________________________ ___________________________________________________ The available local contact condition types are: ___________________________________________________ ___________________________________________________

I

I

The (component / local) No Penetration condition applies to the initially touching faces only, while the (component / local) contact may feature gaps and initial separation. To simplify the analysis in this lesson, the flat was suppressed and a Fixed Geometry fixture was applied on the jaws. Thus, we made an assumption that the stiffness of the flat is _____________________. This assumption can only be made if the stiffness of the plate is significant, relative to the stiffness of the rest of the assembly.

Can you propose a more accurate solution? (Hint: Browse through the available connectors types in the SolidWorks Simulation Connections folder.)

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Assembly Analysis with Contacts

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Exercise 7 Two Ring Assembly

Exercise 7: Two Ring Assembly

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Analyze a simple two ring assembly, in which the outer faces of the rings exert contact pressure on each other if tensile loading is applied. This exercise will show how models with surface contact conditions can be set up and analyzed. This exercise reinforces the following skills: I I I I

Project Description

Component Contact: Options on page 133. Viewing Assembly Results on page 137. No Penetration Local Contact Options on page 143. Contact Stresses on page 146.

A 3.5 MPa pressure load is applied to face of the plate with the Ubracket. The plate holding the large ring is held fixed. The outer faces of the rings exert contact pressure on each other. Partial Restraint

Fixed Restraint

Pressure Loading

Procedure

Open the existing assembly from the Exercises folder.

1

Open an assembly file.

Open TwoRingsAssem fromthe Lesson03\Exercises folder.

2

Set SolidWorks Simulation options.

Set the global system of units to SI (MKS), units of Length to mm and Stress to N/mm^2 (MPa).

3

Define a static study.

Create a Static study named Pressure Loading.

4

Apply material properties.

In the SolidWorks Simulation study tree, right-click Parts and select Apply Material to All. Select AISI 1020 from the solidworks material library.

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Two Ring Assembly

Apply fixed restraint. Apply a Fixed Geometry fixture to the back face of TwoRingsPart1.

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5

6

Constrain TwoRingsPart2 to move in the direction of the load. Right-click Fixtures and select Advanced Fixtures.

Select Use Reference Geometry.

Select Plane2 to specify the direction of the restraint. Select the three cylindrical surfaces to apply boundary condition.

Activate the Displacement components Along plane Dir 2 and Normal to plane, and set the values to 0 mm. Click OK.

7

Apply pressure.

Apply a 3.5 MPa pressure normal to the surface of the TwoRingsPart2.

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Exercise 7 Two Ring Assembly

Define contact set. Right-click Connections and select Contact Set.

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8

In the Contact Set PropertyManager, select No Penetration as the desired type of contact. Click one face to define it as a Set 1, and then click the other face to define it as Set 2.

It does not matter which face is selected as Set 1 and Set 2.

Note

Click OK.

9

Apply mesh control.

Apply mesh control to the indicated surface on TwoRingsPart2.

In the element size box, enter a value of 2 mm.

Take all other default mesh control settings.

10 Mesh the model. Select Curvature based mesh under Mesh Parameters.

Mesh the model with the default element size. Use High quality elements.

11 Run the analysis.

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Two Ring Assembly

12 Plot stress results.

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We see that the maximum stress in the model is 845 MPa. This is well above the yield strength of 351 MPa. If these truly were the in service loading conditions, the design needs to be re-evaluated and a new material or design should be selected.

13 Plot Displacement Results.

The maximum displacement in this model is 0.44mm.

14 Animate Displacement Results. 15 Save and Close the file.

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PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Lesson 4 Symmetrical and Free SelfEquilibrated Assemblies

Objectives

Upon successful completion of this lesson, you will be able to: I

Understand symmetry.

I

Displaying results using a cylindrical coordinate system.

I

Locate problems with the help of the What’s Wrong feature.

I

Use soft springs and inertial relief options to eliminate rigid body modes.

I

Presenting analysis results using eDrawings.

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Symmetrical and Free Self-Equilibrated Assemblies

When parts are assembled with a shrink fit, internal forces are developed in the absence of external forces.

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Shrink Fit Parts Case Study: Shrink Fit

We will analyze a wheel assembly where the rim is shrunk fit onto the hub to determine the stresses caused by the shrink fit.

A shrink fit causes stress within the parts without external forces being applied to the model. The parts initially have an interference fit. The directions of stress, strain and deformation are not plotted in Cartesian coordinates, but rather cylindrical coordinates so that we can determine radial, axial and circumferential (hoop) stress and deformation.

Project Description

A rim with an inside radius of 121 mm [2.382 in.] is pressed on a hub with an outside radius of 121.45 mm [2.391 in.]. Find the following stress results in both components: I I I

Symmetry

von Mises stress Hoop stress Contact stress

We can take advantage of the multiple symmetry of this assembly model and analyze 1/2, 1/4, or even 1/8 of the model.

To reduce the processing time, we will analyze a 1/8 section of the model.

Note that an axis, Axis1, has been defined in the assembly. We will use it as a reference to produce plots of hoop stresses and contact stresses.

Stages in the Process

Some key stages in the analysis of this part are shown in the following list: I

Symmetry

Determine if the model has symmetry that will allow only a portion of the model to be analyzed.

I

Defeature

Suppress features that will not have an effect on the analysis.

I

Stabilize the model

Eliminate rigid body motion.

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Define contact

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Because the parts have an interference fit, we must define the contact as a shrink fit.

I

Plot results

With shrink fit analysis, we display the results using cylindrical coordinates rather than cartesian coordinates.

1

Open an assembly file.

Open wheel assembly from the Lesson04\Case Studies folder.

2

Activate the configuration.

Activate the configuration called FEA. It unsuppresses the feature named cut 1/8 which is used for symmetry in the model. In addition, to defeature the model, the round features have been suppressed in both parts. I

rim rounds

I

hub round1 round2

Defeaturing

With this modification to the CAD assembly model, we have departed from the original CAD geometry and are now analyzing geometry specifically created for the purpose of analysis. Suppression of the rounds has left some sharp re-entrant edges.

These are permissible only because we do not intend to examine stresses along these edges or in their vicinity.

3

Set SolidWorks Simulation options.

Set the global system of units to SI (MKS), the units of Length to mm and Stress to N/m^2.

4

Create static study.

Create a static study named shrink fit.

5

Review material properties.

Notice that the Parts folder holds two icons, corresponding to the hub and rim components of the assembly, and that the material properties have been automatically transferred from SolidWorks.

Examine each part individually to confirm that the hub material is Plain Carbon Steel with a yield stress of 220 MPa [32,000 psi] and the rim material is Alloy Steel with a yield stress 620 MPa [90,000 psi].

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6

Define symmetry restraints.

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We use a 1/8 section of the wheel assembly, but want valid results for the complete model. Therefore, we need to simulate the remaining 7/8 of the assembly model. Applying symmetry boundary conditions to the radial faces created by the cut make the 1/8 section behave as if the wheel was still complete.

Apply Symmetry boundary conditions to all the faces that were created by the radial cut. Symmetry boundary conditions on both sides of the radial cut can be created in one step.

Select faces from both components on both planes of symmetry: four faces on the hub and two faces on the rim. Right-click Fixtures and select Advanced Fixtures.

Select Symmetry. Click OK.

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Rigid Body Mode

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With the symmetry restraints applied, the model can still move in the axial direction. Thus, one rigid body mode remains unconstrained. To eliminate this rigid body motion, it is enough to restrain just one vertex on each of the components (the total of two vertices) in the axial direction. Note that each part must be constrained individually because parts can slide in the axial direction, the shrink fit contact is frictionless. This is actually an artificial restraint simply for the purpose of removing rigid body motion, which is not allowed in structural FEA and causes the solver to terminate.

Alternatively, we can use the soft spring feature which is specified in the study properties. We will demonstrate this option in the second part of this lesson.

7

Eliminate rigid body mode in the model.

Restrain the model by one vertex on each of the two assembly components. Select one vertex on the rim and one on the hub (any vertex), right-click Fixtures and select Advanced Fixtures.

Select Use reference geometry.

Using the fly-out menu, select Axis1 as the direction.

Under Translations, specify that the displacement in the direction along the axis (Axial) is equal to 0.

Now the assembly is fully restrained; it has no unconstrained rigid body modes. Any other movement of the assembly must be associated with the deformation.

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Shrink Fit Contact Condition

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Because the rim diameter is smaller than the wheel diameter, there is an interference in the SolidWorks assembly. SolidWorks Simulation eliminates this interference by “stretching” the rim and “squeezing” the wheel if we define the contact conditions between the interfering faces as Shrink Fit. Shrink Fit is one of the several types of local Contact/ Gap conditions available in SolidWorks Simulation.

8

Explode the assembly.

The faces that are in contact are hard to select. It is easier to select them in the exploded view.

9

Define shrink fit condition. Define a Shrink Fit, right-click Connections and select Contact Set.

Select Shrink Fit, from the available types of contact conditions.

Selected Faces

Define one contact face as Set 1 and the other face as Set 2. The order of the faces is not important. Click OK.

Note

Under the Friction dialog, we could specify the coefficient of friction. In this analysis we will assume no friction.

10 Mesh the model. Select Curvature based mesh under Mesh Parameters.

Create a High quality mesh with the default settings.

Note that along the axial direction of the two faces in contact, eight elements have been created, which is adequate for this particular analysis.

If we expected high gradients in the contact stress distribution, then more elements along the contacting faces would be required to model contact stresses.

11 Run the analysis.

Note that the solution takes longer than if the model were treated as Bonded.

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12 Plot von Mises Stresses.

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Show the von Mises stress plot. Under Settings, change the Fringe type to Discrete.

Make sure that the deformed shape is in the True scale.

Right-click the Stress-1 icon in the Results folder and select Chart Options (alternatively, you can double-click directly on the legend). Under Display Options select Defined and set the maximum stress legend to 620,400,000 Pa, which is the yield stress of the rim material.

The von Mises stress results indicate that a portion of the rim experiences stresses above the material yield stress.

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Now we will prepare a stress plot showing hoop (circumferential) stresses. For this we must present stress results in a cylindrical coordinate system with the z axis aligned with the axis of the wheel assembly.

Cylindrical Coordinate Systems

Any axis defines a cylindrical coordinate system whose first direction is radial, second is circumferential, and third is axial.

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Plot Results in Local Coordinate System

Therefore, Axis1 defines radial, circumferential, and axial directions associated with the axis position. Using an axis as a reference redefines the meaning of the stress components SX, SY, and SZ, which are normally associated with the directions of the global coordinate system.

If an axis is used as a reference, definitions of SX, SY, and SZ undergo the following changes: I

SX becomes the stress component in the radial direction.

I

SY becomes the stress component in the circumferential direction.

I

SZ becomes the stress component in the axial direction.

13 Set units and select axis for stress plot reference. Right-click on the Results folder and select Define Stress Plot.

Select the SY stress component.

Set the Units to N/m^2.

Under Advanced Options, select Axis1 as the reference entity in Plane, Axis, Coordinate System.

Axis1 now defines a local cylindrical system used to plot the required

stress plot (the definition of this plot is continued in the next step).

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14 Plot hoop stresses.

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Because we are defining a stress plot showing hoop stresses, select the SY stress component. The SY stress component points in the circumferential direction, which is the hoop stress. Make sure that Average

results across boundaries for parts is

cleared.

Set the Deformed shape scale to the True scale.

15 Settings. Under Settings, select Discrete as the Fringe Option.

16 Chart Options. Under Chart Options, select Defined and set the maximum value of the stress legend to 620,400,000 Pa [90,000 psi].

Cylindrical System Icon

When a local cylindrical system is specified in the definition of the result plots, the familiar triad icon is replaced with a new symbol denoting a cylindrical system.

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17 Plot contact stresses.

Use exploded view and display a plot showing the contact stress on contacting surfaces: Right-click the Results folder and select Define Stress Plot.

Display an exploded view and select Axis1 as a reference. Set the Deformed shape scale to True scale. Plot the SX component of stress with respect to Axis1.

The SX stress component, which corresponds to the direction normal to the two faces in contact, is the radial direction and, hence, SX is the contact stress.

18 Plot contact pressure. Right-click the Results folder and select Define Stress Plot.

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Under Component, select CP: Contact Pressure.

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Click OK.

19 Probe stress results.

To probe the stress plot for detailed stress results, right-click the plot icon and select Probe. An undeformed plot is required if we want to probe for detailed stress results. Stresses on both surfaces are, of course, equal. The negative sign denotes stress towards the surface.

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Each plot created in a study can be saved individually in any of several formats available. To view the list of available formats, right-click any plot icon, select Save as to open the Save as window, and examine the options in the Save as type menu.

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Saving All Plots

Most likely you will find the eDrawings format the most useful when communicating the SolidWorks Simulation analysis results.

Rather than saving result plots individually, it is also possible to save them in one step either in JPEG or eDrawings format. Right-click the study or the Results folder to invoke the pop-up menu and select either Save all plots as JPEG files or Save all plots as eDrawings.

Using JPEG format, individual files will be created for each plot that has been defined in the study. Using eDrawings format, all plots will be stored in one file. In both cases, files will be located in the SolidWorks Simulation report folder. (The report folder can be selected in Simulation, Options, Default Options (New study), under Results.)

What’s Wrong Feature

Occasionally, when defining SolidWorks Simulation model or analyzing results you may notice warning symbols showing in Simulation Study tree. To find out what is wrong, right-click the item under a study (in Simulation Study tree) accompanied by the warning sign and select What’s wrong to open the What’s Wrong window. This window will list a description of the problem for that item only.

You can also see a summary of all the problems in a study. Right-click the Study and select What’s wrong to list all problems in the study.

Analysis with Soft Springs

Earlier in this lesson, we explained that to prevent rigid body movement along the axis of the assembly, at least one vertex on both the rim and the hub must be restrained in the axial direction. Without these restraints the assembly would have zero stiffness along the axial direction.

There are two alternative methods to prevent rigid body movements in the model without restraining the two vertices. These are to use soft springs or inertial relief.

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Theoretically, we do not expect the model to sway in the axial direction due to the action of some external loading (none that would cause such action exists in our model). All of the loads, which are applied in the form of the shrink fit contact condition, are inherently balanced. Finite element method, however, does not recognize this fact and a small inaccuracy, a numerical error, or mesh asymmetry may cause the model to displace uncontrollably in axial direction. All such cases can be stabilized by the Soft Spring option.

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Soft Springs

When this option is activated, the model is surrounded by springs with stiffness values that are negligible relative to the stiffness of the model (see the following figure). The finite element model is then stabilized and restrained against all rigid body motions.

This procedure works as long as the model is self-equilibrated, or the net magnitude of the external load is so small that the soft springs are able to compensate for it.

Inertial Relief

Another method to prevent rigid body movements is Inertial Relief. Rather than adding artificial stiffness to counteract the load imbalance, as is done using soft springs, this option adds an artificial balancing load eliminating any load resultant along unrestrained directions.

This option should not be used with the intention to stabilize an analysis where gravity, centrifugal or some thermal loads are defined.

In our case, both the Use soft springs to stabilize model and the Use inertial relief solver options can be used.

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20 Create new study.

Duplicate the existing study shrink fit into a new study called soft springs.

21 Suppress axial restraint. Under the soft springs study, right-click Fixture-2 and select Suppress to release the axial constraint. 22 Select soft spring option to stabilize model. Right-click the soft springs study and select Properties.

Under the Options tab, activate the Use soft springs to stabilize model option.

Select the Direct sparse solver. Click OK.

23 Run the study.

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24 Plot hoop stresses.

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Plot the distribution of hoop stresses. Set the Units to N/m2.

Under Settings, select Discrete as the Fringe Option.

Set the maximum value of the stress legend to 620,400,000 Pa.

Comparing the results above with the corresponding plot in the previous study, we see that they are indeed identical.

25 Save and Close the file.

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Symmetrical and Free Self-Equilibrated Assemblies

In this lesson, we calculated the von Mises stress, hoop stress (using cylindrical coordinates), and contact pressure. The stress magnitude was above the yield strength of the material for the rim, therefore we may want to select a different material so that yielding is avoided.

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Summary

Interference between assembly components is allowed only if a Shrink fit condition is present in the assembly. The results of a study with a Shrink fit condition are best viewed using a 1:1 scale of deformation. To see results on contacting faces, use exploded view.

The results for axi-symmetric parts are best viewed in cylindrical coordinate systems.

This observation particularly applies to stress components other than von Mises stress. Von Mises stress, as a scalar value, is insensitive to the choice of reference coordinate system.

To prevent the rigid body motions the model must be stabilized in the axial direction. The most straight forward method is to restrain one vertex (point) on each model in the axial direction. Alternatively, we used the Use soft springs to stabilize the model option which surrounds the model with a layer of soft springs to provide a minimum stiffness in unrestrained directions.

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Exercise 8 Chain Link

Exercise 8: Chain Link

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In this exercise, we will analyze a link in a chain that is under load. With chains, the relationship between load and elongation is important.

We will analyze the link several times. We will start with an entire link and see what problems develop. Based on the results, we will explore different solutions to get more accurate result without the need for long solution times. This exercise reinforces the following skills:

I I I

Project Description

Symmetry on page 154. Rigid Body Mode on page 157. Soft Springs on page 165.

Our goal is to develop the force to elongation relationship for this chain. We are not interested in the actual stress in the components as we are not designing them. All of the chain parts are made of AISI 304 steel.

Procedure

Follow the steps below:

1

Open an assembly file. Open Roller Chain from the Lesson04\Exercises folder.

The Default configuration consists of the sprocket, pivot and several links.

2

Change configuration.

Make the configuration Link-full active. This configuration shows a single link which is really an inner link and two halves of the outer link.

3

Create a study.

Create a static study and name it Link-full-soft springs.

4

Apply material.

Apply the material AISI 304 steel to all the parts in the assembly.

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5

Determine contacts.

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There are two types of contacts in this link, No Penetration and Bonded. All contacts between parts of the same link are Bonded. Parts that are in contact between an inside and outside link are No Penetration. Link Plate Roller Bushing

Link Plate Pin

Inside Link

Outside Link

Because of the number of contacts, we will start with a Global Bonded contact and then add the No Penetration contacts.

6

Explode the assembly.

Exploding the assembly will make it easier to see the contact sets.

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Add contacts. Right-click Connections in the Simulation Study tree and select Contact Set.

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7

In the Contact dialog select Automatically find contact sets. Under Options select Touching faces.

For Components, select the assembly, then click Find faces. Twenty four contact sets will be found.

In Results, select all 24 contact sets. Select No Penetration and click the Create contact sets button. Make sure all 24 contact sets are selected and added. Click OK.

8

Delete contacts.

We must now remove the No Penetration contact sets for contacts that are supposed to be bonded.

Select each contact set in turn and determine if it should be Bonded (contact between parts in the same link assembly) or No Penetration (between parts in different link assemblies or any contact with a Bushing). Delete the No Penetration contact for contacts that should be bonded.

When done, there will be 16 contact sets that are No Penetration. The eight contact sets that you delete will be Bonded by the Global Contact condition.

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Chain Link

In image 1, the contact is between the Pin and Link Plate of the same Inside Link assembly. The No Penetration contact must be deleted as these two parts are Bonded.

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Example

In image 2, the contact is between the Pin on an Inside Link and the Bushing from an Outside Link, so this contact does not get deleted as it should be No Penetration. 1

9

2

Collapse the assembly.

10 Apply a force.

Because we are interested in the force to elongation of the chain and we are doing a linear analysis, the actual force we apply is not important. We could apply the maximum force for the system, but it is not necessary.

Subject the link to the total axial force of 400 N (apply 200 N to all four faces indicated in the figure).

11 Boundary conditions.

This is a self equilibrated problem so theoretically no fixtures are required. We must however prevent the rigid body movement by adding soft springs, thus stabilizing the model. Right-click the study and click Properties.

Select Use soft spring to stabilize model and Direct sparse for the solver.

Note

172

Since multiple contatcs are defined in the study and the area of contact is found through several contact iterations, the Direct Sparse solver is preferred.

SolidWorks 2012

Exercise 8 Chain Link

12 Mesh.

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Select Curvature based mesh under Mesh Parameters.

Mesh the model using high quality elements and the default mesh size.

13 Mesh size.

Examine the mesh details. There are about 19,400 nodes which is over 58,200 degrees of freedom.

14 Run the study.

15 Plot the displacements.

Make sure that the plot uses Automatic for the Deformed Shape.

The assembly translates in the x-direction. The animation will reveal the effect of the soft springs on the unconstrained self-equilibrated model.

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16 Animate the displacement.

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The model translates.

This translation is caused by several factors: I I

The mesh is not completely symmetric. The model is not fixed in space.

These are rigid body translations and are very small. While they do not have any impact on the stress results, they significantly effect the displacements.

17 Plot the stress.

The stress plot should be symmetrical. If it is not, the reason is that the mesh is too coarse. Stress magnitudes may vary due to mesh size and stress concentrations.

Lets solve the problem again, but this time we will use symmetry to keep the model constrained axially.

Second Approach

1

174

Duplicate the study. Name the new study Link-full- soft springs and restraint.

SolidWorks 2012

Exercise 8 Chain Link

2

Edit the force.

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Edit the force so that it is only applied to one set of faces (400 N total force pulling the link in a single direction).

3

Apply a fixture. Apply a Roller/Slider fixture to the

two faces where the forces were removed.

This fixture now restraints any movement of the faces in the X direction. They can still move in the plane of symmetry (Y and Z directions).

4

Mesh.

Use the same mesh as in the previous problem which is a high quality mesh at the default element size.

5 6

Run the study.

Plot the displacement.

We have eliminated translation in the x-direction, however we now are left with rotation about the x-axis.

Because the model translated vertically, we need to verify the true extension of the chain link with the plot of the axial displacement.

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Chain Link

Magnify the displacements, Animate. Set the Deformed Shape for the above displacement plot to Automatic.

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7

Additional rigid body translations could occur in the vertical direction where the model is stabilized with the help of the soft springs. Animate the solution to see whether this phenomenon occurred in your solution.

Note

8

Axial displacement.

Additional rigid body rotation may have occurred at the unconstrained edge. The effect of the rigid body rotation can be easily seen in the plot of axial displacements (UX). Probe on two points on the unconstrained edge. Notice that there are two different displacement values. Without any rotation, we would have the same value for displacement. This result violates our symmetry assumption.

In conclusion, the correct chain link extension cannot be determined by this analysis as well.

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Exercise 8 Chain Link

To see how a correct axial extension of the chain link is determined, complete this exercise.

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Note 9

Plot the stress.

Create a plot of von Mises stress.

While displacements from the previous two approaches were affected by the rigid body displacements and remain undetermined, stress solution is not affected by this phenomenon (verify that the stress solution in both solutions is the same). Stress accuracy, however, depends on highly the mesh quality and can be much improved.

The mesh used in the previous two solutions was rather coarse to determine accurate stress distribution. To improve the stress results, we need to create a finer mesh.

Stresses Accuracy

1

Duplicate the study.

Name the new study Link-full- fine.

2

Refine the mesh.

Re-mesh the model with high quality elements and the slider set to Fine.

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3

Examine the mesh.

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The new mesh is now fine enough to get reasonably accurate stress results, but the number of nodes and degrees of freedom are high. With over 119,000 nodes, we will have to solve over 359,000 degrees of freedom. This will result in a much longer solution time.

4

Do not solve.

While we could run this study, the solution time is too long. Instead we will examine a different approach to get the small mesh size and accurate results.

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By taking advantage of the symmetry, we do not have to analyze the entire model, but instead only the smallest symmetrical element of the model. We must however remember that it is not just the geometry that must be symmetrical, but also the loads.

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Using Symmetry

If we look for symmetry, we can see that there are three planes of symmetry in this model.

If we cut the model through all three planes of symmetry, we get the following result which is one-eighth of the original model.

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Chain Link

Change configuration. Make the configuration Link-symmetry active.

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1

This configuration has three assembly cuts to reduce the model to oneeighth of its original size.

2

Create a new study.

Name the new study Link-symmetry.

3

Apply material.

Copy the material from the previous study.

4

Define contacts.

Using the same procedure as in step 7 and step 8 on page 171, create the contacts sets. You should have five No Penetration contact sets.

5

Add symmetry fixture. Right-click Fixtures in the

Simulation Study tree and select Advanced Fixtures. Select Symmetry.

Select all the symmetrical faces (there are 13 faces).

With symmetrical fixtures on three orthogonal faces, the model is now fixed in space so the soft spring stabilization is no longer required.

In the axial direction (X-direction), the symmetry fixture is applied on the face in the negative X-direction only. The face on the opposite side is used to apply the force in the next step.

Note

6

Apply force.

Apply a force of 100 N to the face indicated.

Question

180

Why do we apply 100 N? We have one-eigth of the model, why not 400/8=50 N?

SolidWorks 2012

Exercise 8 Chain Link

7

Mesh.

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Select Curvature based mesh under Mesh Parameters. Mesh the model using high quality elements and the default settings.

8

Examine the mesh.

We now have a mesh with elements smaller than in the fine mesh we tried to use earlier, but the total number of nodes is now only 16,783 or about 50,349 degrees of freedom. This is much less than the 359,000 degrees of freedom we had earlier.

9

Run the study.

10 Plot the displacement.

The maximum displacement is now 0.00246 mm.

Note that to obtain the chain axial extension, this displacement value would have to be multiplied by a factor of two (0.00246 x 2 = 4.9e-3 mm). While this result may, under some circumstances, be close to the real chain extension, it will be soon shown that it is still incorrect.

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11 Plot the stress.

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We can see a stress concentration where the Pin, Bushing and Link Plate join. To get a better look at this area we need to explode the assembly.

12 Explode the assembly.

If we show the mesh, we can see that the mesh is very coarse in the area of the highest stresses and that we have a stress singularity.

Any mesh refinement would improve the stress distribution but would not eliminate the stress singularity. In a real part, there would be a fillet and some yielding which would redistribute the stress into the neighboring regions of the elastic material. The displacement solution would also improve only marginally.

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Exercise 8 Chain Link

13 Post processing evaluation.

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Examine the displacement plot. We analyzed this assembly using symmetry and have obtained results.

Look at the displacement plot in the Top view. Make sure the setting is Automatic so that we see an exaggerated view of the displacement.

Important!

What is wrong with this analysis? There is something that is fundamentally wrong with this analysis, when you think you understand the reason that this analysis is wrong, discuss it with your instructor.

14 Save and Close the file.

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Chain Link 2

Exercise 9: Chain Link 2

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In the previous exercise, we ran an analysis that initially appeared to give us a correct answer, but in fact had a problem because the symmetry conditions were violated.

When we look closely at the displacement plot, faces 1 and 2 are perpendicular because of the symmetry fixture. Face 3 is were we applied the force and while it is required to be parallel to the face 1, it is not. 1

3

2

In this exercise, we will solve the same problem using a different technique that will give us the correct result. Rather than applying a force, which allows the face to tilt, we will apply displacement to the face and then determine the force from the solution.

1

Open an assembly file. Open the Roller chain assembly from the last exercise.

2

Duplicate the study.

Duplicate the study named Link-symmetry and name it Linksymmetry displacement.

3

Remove the force.

Suppress the 100 N force.

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Exercise 9 Chain Link 2

Add a displacement. Right-click Fixtures in the Simulation Study tree and click Advanced Fixtures.

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4

Select On Flat Faces.

Select the same face that used to have the force applied.

Enter a distance of 2.45e-3 mm for the displacement in the Normal to Face direction.

The face will now stay parallel with its original orientation; the symmetry of the model will therefore be satisfied.

The displacement of 2.45e-3 mm, an incorrect solution from the previous exercise, is chosen because it is relatively close to the correct solution. A principle of linear dependence will be used to scale the displacement to its correct value.

Note

5

Run the study.

Run the study using the same refined mesh as in the previous exercise.

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Chain Link 2

6

Display the displacement plot.

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If we examine the plot closely, we can see that all the correct faces are now orthogonal. 1

3

2

7

Extract the force. Right-click the Results folder and click List Result Force.

The force in the X direction is 119.24 N which is close to the loading force used in the last part of the previous exercise (100 N).

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Exercise 9 Chain Link 2

Having used the symmetry, the results now need to be converted for the full link chain model. To obtain the axial force corresponding to the full link, the above resultant force must be multiplied by a factor of four, i.e. 4 x 119.24 N = 476.96 N. To obtain the axial extension for the full link, the above prescribed displacement must be multiplied by a factor of two, i.e. 2 x 2.45e-3 mm = 4.9e-3 mm.

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Results for full link chain

We now have the two points (these results [4.9e-3 mm, 476.96 N] along with 0 mm, 0 N) with which we can establish the force to elongation plot.

To conclude this exercise, it remains to answer what is the correct extension of the full chain link when subjected to a load of 400 N. Using the principle of linear dependence the answer is:

What is the extension for 400 N force?

u(F=400 N)= 4.9e-3 x 400/476.96 = 4.109e-3 mm.

A point with coordinates of [4.109e-3 mm, 400 N] also lies on the same force to elongation plot. Force displacement graphs are common characteristics of the chains. The graphs always begin at a point [0 mm, 0 N] and feature a constant slope until a point where the material exhibits significant yielding and the force displacement relationship is no longer constant. The ultimate strength of the chain is then defined at a force causing the chain to break.

Note

8

Save and Close the file.

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Chain Link 2

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Objectives

Upon successful completion of this lesson, you will be able to: I

Use spring connectors.

I

Use pin connectors.

I

Use spot weld connectors.

I

Apply restraints in a local coordinate system.

I

Analyze results in a local coordinate system.

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Assembly Analysis with Connectors

Mate definitions in the SolidWorks assembly do not translate into contact definitions in SolidWorks Simulation. Therefore, from the point of view of SolidWorks Simulation, the components of the assemblies are un-attached until we define the proper contact conditions or connectors describing interactions between the assembly components.

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Connecting Components

We use mathematical connectors instead of actual models of the connectors to speed the analysis process as the mesh and contacts are reduced and solution can be found more quickly.

The main purpose of this lesson is to examine various other connectors available in SolidWorks Simulation.

Connectors

When analyzing assemblies with connectors, we frequently do not need to analyze the connectors itself, only the parts around the connectors. Replacing the connector model with SolidWorks Simulation connector speeds the analysis process as there is nothing to mesh and solve. SolidWorks Simulation provides the following types of connectors: I I I I

Connector Types

Rigid Spring Pin Elastic support

I I I I

Bolt Link Spot Welds Bearing

The following table lists the available connector options:

Connector Type

Definition

Rigid

Defines a rigid link between the selected faces. The connected faces do not deform.

Spring

Connects avertex or a face on a component (or solid body) to a face or a vertex on another component (or solid body) by distributed springs with the specified normal and shear stiffness. The stiffness values may be entered as distributed or total values. The two faces must be either planar and parallel to each other, or cylindrical and coaxial. You can specify a pre-load for the spring connector. The following types are available: Compression Extension Compression only Extension only

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Definition

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Connector Type Pin

Connects cylindrical faces of two components. The following two options are available in the pin definition: 1. With retainer ring (No Translation). Specifies a pin that prevents relative axial translation between the two cylindrical faces. 2. With key (No Rotation). Specifies a pin that prevents relative rotation between the two cylindrical faces. The stiffness values corresponding to the axial and rotational directions may be specified as well. The pin material and strength data can be specified to perform a pass/no pass pin check.

Elastic support

Defines an elastic foundation between the selected faces of a part or assembly and the ground. The faces do not have to be planar. A distributed stiffness at a point on the face represents the stiffness density associated with an infinitely small area around the point.

The tangential and normal stiffness components are assumed constant and directed in the directions tangential and normal to the face at every point. This connector can be found in the fixture menu.

Bolt

Defines a bolt connector between two components, multiple components or between a component and the ground. Bolts both with and without nuts are supported. Material specifications directly from the material libraries and various preload options are available. To see the definitions of the bolt connectors see Lesson 7 and Exercise 14: Bolt Connectors on page 271

Spot weld

Defines a connector simulating spot weld between two solid faces or two shell faces.

Edge weld

Defines a connector simulating edge weld bead between two shell features, or one shell and one solid feature.

Fillet and Groove welds, both single and double sided are available.

Link

Ties any two locations on the model by a rigid bar that is hinged at both ends. The distance between the two locations remains unchanged during deformation. Link does not restrict rotations at both ends.

Bearing

Simulates the interaction between a shaft and a support through a bearing.

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Assembly Analysis with Connectors

The vise grip pliers require the use of several connectors and various contact sets to be analyzed.

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Case Study: Vise Grip Pliers

Pins and springs will be used to simulate the physical parts and contact sets will be defined between the various parts.

Project Description

The vise grip pliers are clamping a piece of bar stock. The pliers are set so that they are not in the locked position. A 225 N force is applied to the handles. All components are made of Cast Carbon Steel.

Determine the maximum stress in the assembly and if any of the parts exceeds the yield strength.

Stages in the Process

The following are the major steps in this analysis: I

Create an analysis configuration.

Not all the parts need to be analyzed. Suppress the parts and detail that are not necessary.

I

Apply materials.

Either apply the materials in SolidWorks or through SolidWorks Simulation.

I

Apply fixtures.

The model must be restrained to represent the way it is held in the physical world.

I

Determine contact conditions.

Using interference detection, we can determine contact points between the parts. Contact sets are then created to represent these in the analysis problem.

I

Apply connectors.

The actual connectors are not part of the analysis so they will be represented by pin connectors.

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Apply external forces.

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Apply the loads that represent a hand squeezing the vise grip pliers. I

Mesh.

There are multiple parts and each must mesh with the correct contact conditions to satisfy the contact with adjacent parts.

I

Run the analysis.

Run the analysis and analyze the results to determine further action.

Procedure

Follow the steps below to analyze the vise grip pliers:

1

Open an assembly file.

Open wrench from the Lesson05\Case Studies folder.

2

Change configuration. Make the For analysis configuration active. In this configuration, the release lever and pincap parts have been suppressed. A simplified configuration of the screw is also used which removes the small

chamfers and holes as they do not affect the study.

3

Set the simulation options.

Click Options from the Simulation menu. Select the Default Options tab. Select Units, then select SI (MKS) for the Unit system. Select mm for Length/Displacement and N/m^2 (Pascals) for Pressure/Stress. Select Color Chart. For Number format, select Scientific (e) and 2 decimal places.

4

Create a study.

Create a static study named vise grip analysis.

5

Apply material.

Apply the material Cast Carbon Steel from the SolidWorks Materials database to all the parts.

6

Simulate bar stock.

We are not interested in the stress in the piece of bar stock, so it has been suppressed. To simulate it, add Fixed Geometry fixtures to the two flat faces of the jaw.

7

Check interference.

To determine where the different components are in contact, we can use the SolidWorks interference detection. Click Tools, Interference Detection in the menu.

Select the assembly file and Treat coincidence as interference. Three contacts are detected.

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8

Evaluate the contacts.

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Examine the model to determine the effects of each contact. I

I

I

Interference1 is a line contact between the screw and the end of the center link. We will add a contact set for bonded contact

between these two components because as long as the force is applied, these two components remain in contact. Interference2 is between the screw and the barrel of Arm1 where the threads engage. This contact will be handled with a help of the top level assembly component contact (Global Contact). Interference3 is between two different components of Arm1 that do not move relative to one another. This contact will also be handled with a help of the top level assembly component contact (Global Contact).

Interference1

Interference3

Interference2

Close Interference Detection.

9

194

Set the top level assembly contact. Confirm that the top level assembly contact (Global Contact) under the Component Contacts folder is set to Bonded.

SolidWorks 2012

Lesson 5 Assembly Analysis with Connectors

10 Explode.

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Explode the assembly to make it easier to select the faces and edges. 11 Add Contact. Add a Bonded contact set between the edge of the center link and the end face of the screw.

Bonded

Introducing: Pin Connectors

Pin connectors ensure that two cylindrical faces remain coaxial during the deformation process. The two faces are not allowed to deform and will remain cylindrical during deformation. The following options are available with pin connectors: I

With retainer ring (No translation): If checked, the two

cylindrical faces will not be allowed to translate axially relative to each other.

I

With key (No rotation): If checked, this option eliminates axial

rotation of the two cylindrical faces relative to each other.

I

Include mass: The mass of the pin can be included in frequency

analysis or if acceleration loads are applied in static stress analysis.

I

Axial and Rotational stiffness: If any of the two relative

displacements are unrestricted (axial translation or rotation), linear stiffness values in those two particular directions can be specified.

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Assembly Analysis with Connectors

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If the geometrical and material parameters of the pin are known, it can be conveniently tested at the end of the analysis. The following parameters are needed: I

Tensile stress area: cross chord area of the pin.

I

Pin strength: Design strength for the material of the pin (typically

the yield strength).

I

Safety Factor: Pin Design Safety Factor.

Alternatively, pin strength can be populated automatically by specifying the material in the material dialog window.

Note

Depending on the type of connector used, certain contact conditions have to be defined between connected components (such as No penetration contact between two bolted parts). We will need three pins to connect the components. Pin 2

Pin 1

Pin 3

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12 Add pins.

In the Simulation Study tree, right-click Connections and select Pin.

Select the inside face of the hole in the CenterLink part and the face of the shaft in the secondGrip part. Select With retaining ring and clear With key.

Check the box for Strength Data, input 1.2 mm^2 for Tensile Stress Area, 3.516e8 N/m^2 for the Pin Strength and 2 for the Safety Factor. Click Select material and select AISI 1020 steel. Clicks OK.

13 Add additional pins.

Repeat the above procedure to add the two additional pins with the same properties.

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Assembly Analysis with Connectors

Spring connectors are used to replace tension, compression or tension and compression springs.

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Introducing: Spring Connector

Spring Connector Types

Under Type, we can specify whether the spring is active in both compression and tension, compression only, or tension only. The options Flat parallel faces, Concentric cylindrical faces, and Two locations specify the characteristics of the spring end entities.

Spring Connector Options

Under Options we can specify the Normal and Tangential spring stiffness values. Both quantities can be expressed as Total (N/m or lb/in), or Distributed in the units of (N/m)/m2 or (lb/in)/ in2, for example. Both the Compression preload and Tension preload can be input.

Where to Find It

I I I

Use in Instructions

198

Menu: Simulation, Loads/Fixtures, Connectors Shortcut Menu: Right-click Connections, Springs CommandManager: Simulation > Connections Advisor > Spring

Select Springs from the Type list in the PropertyManager.

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Lesson 5 Assembly Analysis with Connectors

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14 Add a spring connector.

While we do not have a spring modeled into the assembly, we will add a connector spring to apply the appropriate force. Right-click Connections and select Spring.

Select Two locations. We have split faces on the appropriate features of each part to create vertices on which to connect the spring. Type 250 N/m for the Axial Stiffness. Select Tension preload force and type 5 N.

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15 Apply external loads.

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We will have to add two opposing forces, one to the Arm1 and the other to Arm2. As modeled, each of these components has an appropriate face on which to apply the loads.

Apply a 225 N force, normal to the Top plane to each of the surfaces shown.

Note

Make sure that the force applied to the top handle is 225N as a Total force.

16 Mesh.

Select Curvature based mesh under Mesh Parameters.

Mesh the model using High quality elements and the default settings.

17 Run.

Run the study.

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18 Plot the stress.

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We observe stresses well above the yield strength. To locate the high stress regions more in depth stress post processing analysis is required.

19 Chart Options.

We would like to see if any components yield. We can change the chart options to make the top of the scale equal to the yield stress of the Cast Carbon Steel material. Anything that yields will then be shown in red. Right-click the plot Stress1 and click Chart Option.

Select Defined and type the yield stress for Cast Carbon Steel (248,168,000 Pa) as the maximum limit of the legend.

20 Examine the plot.

There are several areas with stresses above yield. Some of these are sharp corners/singularities. We will focus on the area where yielding might occur at the line contact on the center link.

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21 Isolate the part.

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To get a better look at this one part, we will isolate it. Hide the stress plot. Right-click on the center link part and select Isolate. Create a new stress plot to visualize the stresses in the center link.

We can see that the problem is the area where we have defined line contact between the center link and the screw. This concentration (stress singularity), i.e. unreal distribution of stresses, was subject of Lesson 2. While it is not possible to eliminate it with the current geometry, we could minimize its impact on the rest of the stress distribution by refining the mesh.

22 Show all parts. Click Exit Isolate to show all the parts.

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The pins and bolts can be quickly designed, knowing the basic loads: shear and axial forces, bending moment, and torque. The figure below shows the directions of these loads.

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Pin/Bolt Force

Shear force

Bending moment

Torque

Axial force

Note

The x, y, and z components are reported in the global coordinate system. The sign of the axial force indicates tensile or compressive force.

List Pin/Bolt/Bearing Force

The pin, bolt and bearing forces are calculated and displayed in tabular form. The dialog lets you save data as a *.csv or *.txt file, which can be opened and edited in Excel or Notepad. Exported information can be used very effectively for the pin/bolt design. Provided the strength data was entered for each pin, the software will analyze each pin automatically.

Where to Find It

I I

Menu: Simulation, Result Tools, Pin/Bolt Force Shortcut Menu: Right-click the Results folder and click List Pin/ Bolt/Bearing Force

I

CommandManager: Simulation > Results Advisor > List Pin/

Bolt/Bearing Force

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Assembly Analysis with Connectors

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23 Extract the pin force.

Now that we have simplified the analysis by suppressing the pins, we have to extract the pin forces.

Right-click on the Results folder and select List Pin/Bolt/Bearing Force.

The Pin/Bolt Force dialog lists all important force loads on pin connectors.

We can examine the forces on each pin or the maximum values and which connector they are on. The red background indicates that the pin is failing with the safety factor of 2.

24 Save and Close the file.

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The focus of this lesson was to provide a summary of the available connector types and demonstrate the use of some of them.

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Summary

In the vise grip model we analyzed an assembly and used spring and pin connectors to simplify the model by eliminating the spring and pin. Of course, this approach is acceptable only if the spring and pins themselves are of no interest in the analysis.

We saw that due to the geometry of the center link, a stress concentration caused unrealistic stress results along the sharp edge. To better investigate this region, we would want to refine the mesh significantly. We could then attempt to compare the stress results to the yield strenght of the material.

We also successfully evaluated the pin connectors and showed that the pins were failing with respect to our input factor of safety. To remedy this, we would need to either select a new pin material or make the pins larger. Practice problems using additional types of connectors are found in the exercises following this lesson.

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Assembly Analysis with Connectors

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Exercise 10 Lift Assembly

Exercise 10: Lift Assembly

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Analyze a lift assembly, in which a weight is supported by four arms. This exercise will introduce another fixture called a hinge. This exercise reinforces the following skills: I I I

Problem Statement

Component Contact on page 132. Local Contact on page 140. Rotational and Axial Stiffness on page 256.

A scissor lift used to lift a 1,800 N. weight is operated by an external hydraulic cylinder connected to a slider traveling on a base.

1800 N

The load is assumed to be evenly distributed between the two rollers which, in turn, evenly split the load between the arms. This way each arm is loaded with a 450 N. force.

Find the displacements and stresses in the lift components at the collapsed position of the lift arms. We are not interested in contact stresses in the pin joints, nor the stresses in the base.

1

Open an assembly file.

Open lift from Lesson05\Exercises folder.

Familiarize yourself with the collapsed and extended configurations of this assembly. The goal of this analysis is to analyze the assembly in the collapsed configuration.

2

Activate the configuration collapsed. The weight, hydraulic cylinder, connecting pins, and many other details are not modeled, and the SolidWorks assembly lift depicts the scissor lift in a somewhat idealized way.

Base

Slider

3

Set SolidWorks Simulation options.

Set the global system of units to SI (MKS) and the units of Length and Stress to mm and Pa (N/m^2), respectively.

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Lift Assembly

Create study. Create a Static study named collapsed-without base.

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4 5

Assign material properties.

Specify Plain Carbon Steel for all of the components.

6

Check for assembly interferences.

There are only two parts in the assembly with touching faces.

Since we are not interested in the deformations and stresses in the base, we will suppress this part to simplify our mesh. At the same time, however, we must correctly represent the contact condition with the corresponding friction forces. This can be achieved by using a Virtual wall contact condition type, introduced in Lesson 7.

Note

7

8

Exclude the base part from the analysis.

Update all components.

Because the base part was suppressed after the study collapsed-without base was defined, we have to update the study components.

Right-click on the study collapsed-without base and select Update All Components.

Note

208

Alternatively, you can use Exclude from Analysis command which does not require suppression of the part in SolidWorks.

SolidWorks 2012

Exercise 10 Lift Assembly

Define Virtual wall.

Specify the bottom face on the slider as a Set 1 and the base plane as a Set 2.

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9

Specify the Friction Coefficient of 0.1. Under Wall Type, select Flexible.

Specify the values of 1.6537E+013 (N/m)/m2 [60.92e6 lb/in/in2] and 6.2216E+012 (N/m)/m2 [22.92e6 lb/in/in] as Axial stiffness and Tangential stiffness, respectively. Click OK to save the virtual wall settings.

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SolidWorks 2012

Lift Assembly

The connection between the lift arms and the base has to be simulated as hinges.

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Hinge Restraint

The Hinge type of restraint suppresses radial and axial translations, which are defined in the local cylindrical coordinate system associated with the cylindrical surface.

Exactly the same restraint can be defined using the On Cylindrical Face type of restraint where we restrain the radial and axial displacement components.

10 Define hinge restraint. Right-click the Fixtures folder and then select Fixed Hinge.

Select the two cylindrical faces initially connected to the base. Click OK.

Note

Using the Fixed Hinge restraint, we assume that the base is rather stiff and does not deform. If the elastic behavior of the base must be accounted for, it would have to be included in the analysis.

11 Define Pin connectors. Define two rigid Pin connectors between the four arms, and two rigid Pin connectors between the arm and slider.

For all the pins, allow the relative rotation and restrain the relative translation between the connected components.

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Exercise 10 Lift Assembly

12 Define restraint on slider cylindrical face.

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To model the support offered by the hydraulic cylinder restrain the cylindrical face on the slider in the global x- direction (in the direction of the piston).

Hint

Utilize Use reference geometry restraint type to define this boundary or condition.

Note

By applying restraints to the entire cylindrical face we ignore the realistic distribution of stresses between the cylinder pin and the lug. This modeling simplification is acceptable because we do not intend to investigate the contact stresses in the lug. The model is now fully constrained even though the assembly components are not touching each other.

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Exercise 10

SolidWorks 2012

Lift Assembly

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13 Apply 450 N force on link components. Apply a downward force of 450 N to each of the four cylindrical openings at the free ends of the four link components. The total weight

distributed equally between all four locations is thus 1,800 N.

Bearing Load

Applying the load to the entire cylindrical hole is an acceptable simplification because we do not intend to analyze contact stresses developing between the arms and roller pins.

Note that there is a more accurate way to apply load to a cylindrical hole that still does not require contact stress analysis. It is called a Bearing Load. A load defined as a bearing load is applied to a portion of the cylindrical face (this requires splitting the face), and its variation is described by a cosine function to simulate the contact pressure distribution.

14 Create mesh.

Mesh the model with High quality elements and the default settings.

15 Run the analysis.

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16 Plot von Mises stress and resultant displacement.

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We observe that the model is not yielding and the resultant displacements are rather small (the deformed shape is shown in the magnified scale).

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Lift Assembly

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17 List slider lug hole reaction force.

The reaction force in the x-direction, which is the direction of the hydraulic cylinder, is approximately 6,350 N.

18 List contact and friction forces.

List contact and friction forces on the bottom face of the slider.

The Normal force (ycomponent) is equal to 900 N, which amounts to half of the total load (the second half is carried by the two hinge restraints).

The Friction force (xcomponent) is equal to 45 N.

Is the friction force correct?

214

Can you verify whether the result for the friction force, 45 N, is correct? Why?

SolidWorks 2012

Exercise 10 Lift Assembly

19 Analyze deformation of slider.

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Define a new displacement plot of the slider in highly magnified scale. (You may hide all of the remaining components in SolidWorks to view the deformed shape more clearly). In the Deformed Shape dialog, un check the Show colors option.

We can see that the middle part of the slider detaches from the base; the contact is provided only by very small areas on both sides. Also note that, to accurately model the contact stresses, a highly refined mesh would be required.

20 Save and Close the file.

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Analysis with Base (optional)

The results from the previous study can be verified by running the same analysis with the base included in the finite element model.

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Exercise 11: Analysis with Base (optional)

Run the simulation again with the base included in the model and compare the solutions to verify that the virtual wall contact condition accurately models the real situation. This exercise reinforces the following skills: I I

216

Connectors on page 190. Pin Connectors on page 195.

SolidWorks 2012

Exercise 12 Shock Absorber

Exercise 12: Shock Absorber

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In this exercise, we will analyze a shock absorber. Results from Exercise 2: Compressive Spring Stiffness on page 81will be used in the application of a spring connection. This exercise reinforces the following skills: I

Problem Statement

Spring Connector on page 198.

The miniature shock absorber consists of a tube, a plunger, clamp, and a helical spring. We will investigate the stresses that develop in the plunger collar when the assembly is compressed with a 3 N force. We have already calculated the stiffness of the spring to be 255.7 N/m in Exercise 2: Compressive Spring Stiffness on page 81. This result will be used to set up a spring connector in this exercise. Stresses in the helical spring are not of interest, therefore we will remove the spring from the model and replace it with an equivalent spring connector.

Determine the maximum stress on the shock absorber components and the displacement under a 3 N load.

Procedure

Follow the steps below:

1

Open an assembly file.

Open shock from the Lesson05\Exercises folder.

Suppress the helical spring (part file Front Spring).

2

3

Set SolidWorks Simulation options. Set the global system of units to SI (MKS) and the units of Length and Stress to mm and N/m^2, respectively. Create study.

Create a static study named shock assembly.

4

Assign material. Assign Alloy Steel to all the components.

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Shock Absorber

Apply fixtures. Apply a Fixed Geometry fixture to the

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5

cylindrical face of the eye belonging to the Shock Tube (item 1).

2

This fixture fully restrains the Shock Tube component.

6

Restrain Shock Plunger. Apply an Advanced Fixture in the radial and

circumferential directions to the cylindrical face of the eye (item 2) belonging to the part Shock Plunger.

1

Use On cylindrical face as the type of fixture.

With these three constraints, the assembly model is left with one degree of rigid body motion. The Shock Plunger can slide in and out of the tube because the Shock Plunger and Shock Tube are disconnected. We connect these two parts with a spring connector.

Note

7

Define spring connector.

Right-click Connections and select Spring.

Under Type, select Compression Extension with Flat parallel faces. As shown, specify the selected face on the Shock Tube as the Planar Face of Component1 and the face on the Shock Plunger as the Parallel Face of Component2.

Note

218

Which face is selected as 1 and 2 is not important.

SolidWorks 2012

Exercise 12 Shock Absorber

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Under Options, select Total stiffness and enter 255.7 N/m in the Normal direction. The Shock Tube and Shock Plunger are now connected. Click OK.

8

Apply force to shock plunger.

Apply a 3 N load to the split face on the cylindrical face of the Shock Plunger ear in the direction of the rod. The load is applied normal to Plane1.

9

Apply mesh control.

Apply mesh control to the fillet face on the Shock Plunger where a higher stress concentration can be expected. Specify a local Element size of 0.5 mm and the default Ratio of 1.5.

10 Mesh the model. Select Standard mesh under Mesh Parameters.

Mesh the model with the default settings.

11 Run the analysis.

Run the analysis and note that the solver issues a warning about large displacements. Click No. The analysis will then complete.

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Exercise 12

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Shock Absorber

In this case, we ignore the warning because the large displacements caused by the spring connector are translations only. The rotations of the assembly components are restricted and the deformations are very small.

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Large Displacement Warning

You may run the solution with and without the Large Displacement Contact/Connector flag activated to verify that both runs produce the same results. Large displacement analysis is a subject of Lesson 14.

12 Plot von Mises stresses.

We note that the maximum stresses of 2.44MPa are well below the yield strength of the Alloy Steel (620 MPa).

For more accurate stress results, we could further refine the mesh around the fillet, but that is not the main purpose of this project.

13 Plot displacements.

Plot the distribution of the UZ: Z Displacement in the True Scale.

We observe the maximum displacement of 11.7 mm, which is in accordance with the linear spring equation (uz = F/k = 3/255.7 = 0.0117 m = 11.7 mm).

14 Save and Close the file.

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Exercise 13 Spot Welds-Solid Mesh

Exercise 13: Spot WeldsSolid Mesh

Spot Welds

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A tube is fabricated out of two sheets of galvanized steel that are joined by spot welds on each side. We will use FEA to investigate torsional stiffness of the assembly by finding the torque required to twist the tube.

The twist angle of 1o that we will use is arbitrary. We are not attempting to duplicate Spot Welds any real life test conditions. We intend to use the results of this numerical test to compare different spot welds configurations. The two-piece design is the first configuration we test. This exercise reinforces the following skills: I I I

Project Description

Spot weld on page 191. Cylindrical Coordinate Systems on page 160. Soft Springs on page 165

The tube is fabricated out of two sheets of galvanized steel 1 mm [0.04 in] thick. The two pieces are joined by 10 spot welds on each side. The spot welds are spaced 25.4 mm [1.0 in] apart and the diameter of each spot weld is 3.175 mm [0.125 in]. Determine the torque required to twist the tube by 1o.

1

Open an assembly file.

Open tube solid located in the Lesson05\Exercises folder.

Examine two configurations: complete tube and half tube. The assembly consists of two identical parts, tube 30. Examine part model tube 30 and note a split line added to locate the positions of spot welds.

2

Split Line

Assembly configuration.

Make the configuration complete tube active.

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Exercise 13

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Spot Welds-Solid Mesh

Set SolidWorks Simulation Options. Set the system of Units to SI (MKS), the units of Length to mm, and Stress to N/m^2.

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3

4

Create study.

Create a study named tube solid.

5

Review Material properties.

Verify that the material definition, Galvanized Steel, has been transferred from SolidWorks to SolidWorks Simulation.

6

Treat tubes as solids. Expand the Parts folder. Right-click the tube features and select Treat as Solid.

Spot welds are defined by the two faces which are connected by the weld. Additionally the weld location needs to be specified on either one of these two faces.

Introducing: Spot Welds

To specify the spot weld location you can use an assembly reference point (not a part reference point) or a vertex.

Where to Find It

I I

Shortcut Menu: Right-click Connections folder and select Spot Welds. CommandManager: Simulation > Connections Advisor > Spot Welds.

7

Define Spot Welds.

Right-click the Connections folder and select Spot Welds. Select Spot Weld First Face, as shown in the figure.

Then select the connected face on the other part (see the figure) as the spot weld second face. Then select Spot Weld Locations and select the ten vertices shown. In the Spot weld diameter, enter 3.175 mm [0.125 in].

This way, all spot weld locations on one side are defined in a single restraint.

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Click OK. Select 10 vertices

8

Repeat the process for the other side.

Similarly, apply spot welds at all the other 10 locations on the other side of the tube.

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Apply Torque

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We are going to apply torque to this assembly using two fixtures. On one end the geometry will be prevented from moving in the axial and circumferential directions. On the other end, we will apply a fixed movement of 1 degree.

9

Apply fixtures.

Select the Use reference geometry fixture under advanced and select the assembly axis as reference geometry. This way, the directions of restraints are aligned with the cylindrical coordinate system defined by this axis. The first component is radial translation, the second is circumferential rotation (expressed in radians), and the third is axial translation. Select the two faces on one side of the tube and restrain the Circumferential displacement component (enter 0 rad). Click OK.

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10 Prescribe rotation at the other end.

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Analogous to the previous condition, apply a 1deg (0.0174 rad) Circumferential displacement to the two faces on the opposite end.

11 Use soft springs to stabilize the model.

The prescribed displacements defined on both ends of the tube do not restrain the assembly in the axial direction. The model can move in the axial direction as a rigid body without experiencing any deformation. To stabilize the model, activate the Use soft spring to stabilize model option.

Contact Between Parts

Before meshing the model we have to make an important modeling decision, that is, how do the two parts interact. We are going to assume that the two halves of the tube interact with each other only through spot welds rather than through the flange faces.

Assuming that there is no interaction other than specified through the spot welds conveniently simplifies the model because we do not have to solve contact conditions. However, it is a reasonable assumption considering that thin spot welded sheets often “come apart” in-between spot welds. As a result of this decision, we model the contact condition between touching faces of the two halves as Allow Penetration.

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Spot Welds-Solid Mesh

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12 Define Contact.

Define a new component contact of type Allow Penetration.

13 Apply mesh control.

To avoid excessive element turn angle, apply a mesh control with the Element size of 3.0 mm [0.118 in] and the Ratio equal to 1.5, to all four rounds and flanges.

Element Turn Angle

Turn angle 45o means that one element face “wraps” over a 45o arc. Generally an element turn angle of 45o or less is preferred.

The figures below show the mesh with and without the mesh control definitions.

No Mesh Control Element Turn Angle 90 deg

Spot Welds Stress Concentrations

Mesh Control Applied Element Turn Angle 30 deg

Note that the mesh has only one element across the wall thickness. Generally two layers of second order elements are recommended. One layer is acceptable for the analysis of deformations but may produce high stress error in detailed stress results.

We accept one layer of elements because we intend to use this model for the analysis of deformations, not stresses. Besides, models with Spot welds connectors are not suitable for detailed stress analysis. Spot welds connector models point to point connections, which mathematically results in infinite stresses near the spot weld.

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Models with Spot welds are suitable for analysis of deformations and global stresses, which is our intention in this model. Also, the model geometry would be better meshed with shell elements than with solid elements. We use solid elements to practice Spot welds connectors with solid geometries. Later in the course we will solve the same model using shells.

14 Mesh the model. Select Curvature based mesh under Mesh Parameters.

Create a High quality mesh with the Mesh Density slider set to Fine.

15 Run the analysis.

16 Plot von Mises stresses.

Von Mises stress results indicate high stress near spot welds. As we said before, any stress results near spot welds are unreliable.

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Spot Welds-Solid Mesh

To calculate the resulting torque, we first list the y-component of the reaction force in the cylindrical coordinate system and multiply it by the radius (see Exercise 3 for an additional example).

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Resulting Torque Extraction

17 List reaction force in cylindrical system.

List the y-component of the reaction force in the cylindrical coordinate system defined by Axis1 (see the following figure). The circumferential component of the reaction force is 8314.8 N. Calculate resulting torque.

The average radius is 0.1265 m [4.98 in]. Therefore the resulting torque T is: T = 8314.8 N x 0.1265 m = 1051.82 N-m

18 Save and Close the file.

Note

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Exercise 18: Spot Welds - Shell mesh on page 319 shows how this problem can be solved using shell elements, a distinct modeling technique applicable to thin, sheet like structures.

PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Lesson 6 Compatible/Incompatible Meshes

Objectives

Upon successful completion of this lesson, you will be able to: I

Understand mesh compatibility in solid element meshes with various contact conditions.

I

Understand advanced incompatible mesh bonding (Mortar bonding) algorithm.

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Compatible/Incompatible Meshes

Compatible / Incompatible Meshing

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In the following example, we will learn the difference between compatible and incompatible meshing. A compatible mesh is one where the nodes of meshes of adjacent parts or bodies are merged to insure bonding. An incompatible mesh results if this condition cannot be met. We will use solid mesh part with unmerged bodies for this purpose.

Case Study: Rotor

In this case study, we will analyze a simplified four bladed rotor part. The blades and rotor disk are separate, unmerged, bodies. The rotor disk is a thick part and the blades are relatively thin which presents a problem in the way the mesh must be created in the area where the two type bodies join.

Project Description

The rotor will be subjected to a rotation of 1 rad/sec, causing stress in the blades. Both the rotor disk and blades are made from Alloy Steel.

Determine the maximum stress and deflection in the four-bladed rotor.

Procedure

To begin this analysis:

1

Open a part file.

Open rotor2a from the Lesson06\Case Studies folder.

2

Define a new study.

Create a new static study named rotor2a-compatible.

3

Apply mesh control.

Apply mesh control with the Element size of 2.3 mm and the default Ratio to all four blade bodies.

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Compatible Mesh

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When a compatible mesh is created, the parts or bodies in the assembly are meshed so that a smooth mesh transition between any two parts is achieved. The nodes along the interface are then imprinted one upon another. If bonded contact is requested, the nodes are then merged to ensure the bonding. If compatible meshing fails at some interface, the software will attempt to generate incompatible mesh for the two parts involved.

4

Set global compatible bonding.

Edit the top assembly level component contact (Global Contact). Make sure that Bonded is selected under the Contact Type dialog.

Under Options, select Compatible mesh.

5

Mesh part.

Select Curvature based mesh under Mesh Parameters.

Mesh this multi body part with High quality mesh and the default settings. The resulting mesh can be seen below.

Note that the mesh in the blade is rather dense and the nodes are nicely aligned along the blade/solid interface. In fact, the nodes along this interface are merged to ensure the prescribed bonding.

6

Hide one blade solid body.

Hide one of the blade bodies, as shown in the figure below. Display the mesh.

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7

Examine the mesh.

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A node-to node correspondence is also forced along the entire blade/solid interface. The nodes are subsequently merged to ensure the required bonding.

While merging the nodes is the most accurate way to ensure the bonding between two touching bodies in a part, or two parts in an assembly, it poses additional constraints on the mesher. All bodies and parts must be meshed together, causing the operation to become more complex and take longer.

8

Show the blade.

Show the blade that was hidden.

9

Material.

Assign Alloy Steel to all components.

10 Fixture.

Apply a Fixed Geometry restraint on the top face of the rotor.

11 External Load. Apply 1 rad/s Centrifugal load. Use Axis1 for

the reference.

12 Run the analysis.

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13 Displacement results.

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The displacement plot shows a symmetrical pattern of the deformation with a maximum resultant displacement of 4.2 e-7 m.

14 Von Mises stress results.

Stress distribution shows singularities in the vicinity of the blades.

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Compatible/Incompatible Meshes

When the nodes of adjacent meshes cannot be merged, we have an incompatible mesh. We can select an incompatible mesh which tells the mesher to mesh every body/part independently and ensure the bonding via the constraint equations (additional mathematical expressions).

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Incompatible Mesh

15 Define a new study. Duplicate study rotor2a-compatible as a new study rotor2aincompatible. 16 Set global incompatible bonding.

Edit the setting of the top level assembly component contact (Global Contact) and change the Options to Incompatible.

17 Mesh part. Select Curvature based mesh under Mesh Parameters.

Mesh the part with the default settings.

Automatic Switch to Incompatible Mesh

If a compatible mesh is requested and meshing fails due to the complexity of the contacts, remeshing model with the incompatible mesh often solves the problem.

Introducing: Automatic Switch to Incompatible Mesh

The option Remesh failed parts with incompatible mesh automatically re-meshes parts where compatible meshing was not successful.

Where to Find It

I

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Shortcut Menu: Right-click Mesh, Create Mesh and under Advanced select Remesh failed parts with incompatible mesh.

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18 Examine the mesh.

The solid bodies of the rotor and the blades are meshed independently and the nodes along the interface are not aligned. The bonding is ensured by means of the additional constraint equations.

19 Run the study.

20 Displacement results.

The results are the same when compared to those obtained in the study with the compatible mesh.

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Compatible/Incompatible Meshes

SolidWorks Simulation features several bonding algorithms when handling the bonds between bodies with an incompatible mesh. These options can be accessed in the study properties. In this section, we will discuss these options and their advantages and disadvantages.

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Incompatible Bonding Options

Simplified Bonding

When Simplified is selected, the traditional (node base) bonding algorithm is used. The source body is represented using its nodes, while the target is represented through the element faces (target must always be a face). However, depending on the density of the source mesh, not all target element faces may participate. This may lead to a generation of “patched” contact.

In the figure above we try to demonstrate a traditional, node based incompatible bond between an edge (source) and a face (target). Only the elements where a node uniquely lies on their faces will participate in the contact. This leads to a patched description of the contact which may lead to less accurate results.

More Accurate (Mortar) Bonding

When the More accurate (slower) option is used, source entities use full description of the geometry including edges (faces) between the nodes. This leads to a complete and accurate description of both the source and the target.

In the figure above the entire edge (continuos description) of the source as well as the faces of the touching target elements form the contact set; This description is more accurate but requires longer solution times. In general, when incompatible contact is used the size of the elements defining the source and the target should be compatible and the More accurate (slower) option should be used.

Automatic

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When the Automatic option is selected, the software will decide which is the most appropriate bonding type with respect to the model and solution times. It is suggested to leave this option as the default bonding type.

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21 Simplified bonding.

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In the study Properties activate the Simplified bonding option.

22 Run the study.

23 Displacement results.

The results are significantly different to those obtained in the study with the compatible mesh, automatic bonding.

24 Save and Close the file.

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Compatible/Incompatible Meshes

The interface on two of the blades is not properly bonded due to the simplified bonding algorithm. There are two reasons for this. First of all, the mesh sizes are very different between the two bodies. Additionally, the simplified bonding algorithm failed to accurately bond the two bodies. To obtain the correct solution, More accurate (Mortar) bonding must be used. By default Automatic bonding treats this contact correctly.

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Discussion

Summary

In this lesson we showed the difference between the compatible and incompatible meshing approach for solid element meshes.

Compatible mesh is somewhat more accurate along the interface because a node to node correspondence between the meshes is forced or the two corresponding nodes are directly merged. However it puts additional strain on the mesher and the meshing process may take longer to complete.

Incompatible meshing procedure generates mesh for each part independently which then reduces the time necessary for completion. The contact condition is then ensured by the additional constraint equations (Bonded contact). If possible, incompatible bonded contacts should feature elements of comparable sizes.

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Objectives

Upon successful completion of this lesson, you will be able to: I

Analyze more complex solid mesh assemblies with various contact conditions and connectors.

I

Use initial clearance in definitions of local No penetration contact conditions.

I

Auto-generate the local contact definitions.

I

Define bolt connectors.

I

Analyze and judge the quality of solid finite element mesh.

I

Use the Remote Load feature to simplify the analysis.

I

Use and define Design Check plot.

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Assembly Analysis Mesh Refinement

In Lesson 2 we learned how to apply mesh control when analyzing a part. In this lesson, we will apply mesh control when analyzing an assembly.

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Mesh Control in an Assembly

Once we have run the analysis, we will create a Design Check Plot to display the Factor of Safety of the model.

Case Study: Cardan Joint

In this case study we will analyze an assembly of a cardan joint. We will determine the various contacts in the assembly and apply different mesh controls to different contact conditions.

We will apply external forces to the assembly that bypass existing components using remote loads. This allows us to analyze the assembly faster as several components will not have to be meshed and solved. We will use a draft (first order) mesh to get an initial solution and then compare this with the results obtained with a high quality (second order) mesh. To determine the suitability of our design, we will create a Design Check plot to display the factor of safety of this assembly.

Problem Statement

The differential assembly is used to transmit a torque from the vertical direction to the inclined direction. The assembly is bolted to the base plate at the four locations on the back side of the bracket using M6 ANSI B18.6.7M countersink bolts. The base plate is then bolted to a secondary structure using two M8 counterbore bolts. The torque is generated by applying a 2.5 N horizontal force to the handle. (In the top view, this force is perpendicular to the handle arm.) The shaft is rigidly connected to the bottom yoke (Yoke_female) and passing through the bottom opening on the bracket. It is assumed that, due to improper manufacturing and elevated temperature from the friction in the shaft/ bracket contact, this interface becomes temporarily blocked and the shaft consequently transfers all the torque to the bracket. (Further increase in the torque would loosen this connection and the joint assembly would begin to rotate.)

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Furthermore, the geometry of the shaft ensures that the Yoke_female and the RevBracket do not come any closer than the initial clearance of 3.469 mm (see the figure above).

The goal of the analysis is to obtain the distribution of stresses and strains in the components of the Cardan joint and the internal forces in the bolts required for their subsequent design. The deformations and stresses in the shaft, Rev Bracket, and the full-crank-assy are of no interest at this time.

Part 1: Draft Quality Coarse Mesh Analysis

In the first part of the lesson we will define all of the appropriate contact conditions with the help of SolidWorks Simulation Find Contact Sets feature.

Procedure

Follow the steps below:

1

Open an assembly file. Open Cardan joint from the Lesson07\Case Studies folder.

2

Set SolidWorks Simulation options. Set the global system of units to SI (MKS), units of Length to mm and Stress to N/mm2 (MPa).

Store the results in the SolidWorks document folder in the results subfolder.

3

Activate configuration Without_crank. This step suppresses the crank-shaft, crank-arm, crank-knob and the Shaft.

4

Define static study. Define a new Static study. Name it stress analysis.

5

Assign material.

Right-click on the Parts folder and select Apply material to All.

Assign Alloy Steel material from the Solidworks Materials library to all parts in this assembly.

6

Modify material of the RevBracket and of the base-plate. Under the Parts folder, right-click on RevBracket-1 part and click Apply/Edit Material. Assign Aluminum 1060 Alloy to this part.

Repeat this step and assign Aluminum 1060 Alloy to the base-plate.

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Assembly Analysis Mesh Refinement

The Remote Load option allows the user to simplify certain assemblies prior to meshing, often helping reduce the size of the mesh.

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Remote Load Where to Find It

I

Menu: Simulation, Loads/Fixtures, Remote Load/Mass

I

Shortcut Menu: Right-click External Loads and select Remote Load/Mass

I

CommandManager: Simulation > External Loads > Remote

Load/Mass

Remote Load Example

Examine a pot supported by three outriggers. A load is applied to the tip of each outrigger.When analyzing an assembly, such as this pot with outrigger, we may not be interested in the deformations and stresses of the outriggers and we wish to concentrate solely on the analysis of the pot.

Taking advantage of the Remote Load option, we avoid modeling the outriggers and still are able to apply loads to the pot as if the outriggers were present.

Instead of analyzing the assembly, we analyze the pot as a part. Using the Remote Load menu, we apply a load to the split faces marking the area where the outriggers are attached to the pot.

The point of application of the Remote Load must be defined in the coordinate system selected in the Remote Load/Mass menu.

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There are three ways in which Remote Load can be defined: Load (Direct transfer) is applicable if the omitted component (the

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I

outrigger) can be assumed to be much more flexible than the analyzed part (the pot). The load that would have been applied to the outrigger is applied to the split faces of the pot and is expressed by means of equivalent loads and moments.

I

Load/Mass (Rigid connection) is applicable if the omitted

component is very rigid and can be assumed to displace as a rigid body. In this case the faces where the loads are applied are connected by invisible rigid bars to the point of load application.

This option also allows you to specify a remotely located, isolated mass. This feature is useful when the gravity (or another constant acceleration load) is included or when performing a frequency analysis.

I

Displacement (Rigid connection), the third option in the Remote Load definition, is also applicable when the omitted component is

very rigid and can be assumed to displace as a rigid body; however, the load needs to be applied as a prescribed displacement. In this case, the faces where the loads are applied are also connected by invisible rigid bars to the point of the load application.

7

Define remote load.

Because we are not interested in the stresses and the deformations of the crank arm, shaft, and knob, we will simplify the analysis by using a remote load feature. Right-click External Loads and select Remote Load/Mass.

8

Setup the remote load. Select Load (Direct transfer) under the Type, and select the faces on the Yoke_male knob where the torque will be transmitted.

Under the Reference Coordinate System dialog, specify User defined and select Coordinate System 1 from the SolidWorks fly-out menu. The remote location of the force will be specified in this local coordinate system.

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Assembly Analysis Mesh Refinement

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In the Location dialog, enter the following coordinates: X-Location: 57.15 mm, Y-Location: 24.6 mm, and Z-Location: 0 mm.

For the Force, specify -2.5 N in Z-Direction. The components of the force are also specified in the local coordinate system Coordinate System 1. Click OK.

By selecting Load (Direct transfer), we are accounting for the possibility of having looser connections between the crank subassembly and the Yoke_male part, and for the fact that the crank shaft, arm and knob are manufactured from material that is softer than Alloy Steel.

Note

9

Add Bolt Connectors.

Right-click the Connections folder and select Bolt. Under Type select Countersink with Nut.

Under Conical Face select one of the bolt head faces.

The Circular Edge of the Bolt Nut Hole field will populate the correct edge feature automatically.

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Since the bolt connection was defined using the Hole series feature in SolidWorks, the specification of the M6 bolt is automatically transferred in SolidWorks Simulation. Notice that Bolt Shank Diameter and Nut Diameter parameters read 6.6 mm and 9.9 mm, respectively. If different, these values can be modified to your real design values.

Bolt Tight fit and Diameter

The Tight fit option controls not only whether the bolt shank is in direct contact with the hole, but also whether the walls of the bolt hole may deform or not. I

If the stiffness of the bolt material is significantly smaller than the stiffness of the material of the bolted components, the presence of a rather soft bolt shank will not have a substantial effect on the deformation of the hole walls. In such a case, the Tight fit option should be cleared.

I

If the stiffness of the materials are comparable, or the stiffness of the bolt material is greater than the stiffness of the material of the bolted parts, the Tight fit option should be activated.

I

If the diameter of the bolt is smaller than the diameter of the bolt hole, the Tight fit option should always be cleared. In this case, the stiffness characteristics of the materials are not important.

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Bolt pre-load can be defined directly by entering an axial force or indirectly as torque. When the torque value (T) is entered, SolidWorks Simulation calculates the axial bolt force, which is the corresponding bolt pre-load, using the following formula:

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Bolt Pre-load

T F = -----------KxD

where D is the diameter of the bolt, and K is the friction factor (also commonly known as the torque coefficient).

The exact formula for the friction factor K is rather complicated and can be found in Mechanical Engineering Design by J.E. Shigley (1986). However, the value of K=0.2 is a very good approximation for most practical cases.

10 Add material and fit. Check the Tight Fit

check box and select the Shank Contact Faces

(see the figure).

11 Bolt material. Under Material, select Library. Click Select material and specify Alloy Steel from the Solidworks Materials

library.

Click Apply and Close the Material window.

12 Add preload. Under Preload select Torque.

In the Torque box, enter 30 N-m. Specify the Friction factor (K) of 0.2.

Click OK to complete the definition of this bolt connector.

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13 Hole Series.

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Because the bolted connections were defined using SolidWorks Hole series feature, SolidWorks Simulation will display the following message: Do you want to add bolt connectors to all holes in the Hole Series? Click Yes to propagate bolts to all holes. Click No to add a bolt to only the selected hole.

Click Yes in the above dialog box window to automatically generate the remaining three bolts connecting the RevBracket and the baseplate.

Connectors created based on the hole series are automatically grouped in a separate folder. Editing one connector from such group will automatically modify the definition of the others. It is possible to dissolve or restore the connector series at any point.

Note

The Tight Fit option is not copied to the rest of the holes. It must be added manually.

14 Bolt base-plate to the ground.

Add another connector.

In the Type list select Bolt.

Under Type select Foundation Bolt.

Under Circular Edge of the Bolt Nut Hole select the edge of the hole where the bolt head would rest.

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Assembly Analysis Mesh Refinement

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Under Target Plane select PLANE2 SolidWorks feature.

The Nut Diameter as well as the Bolt Shank Diameters will be prepopulated based on the specifications of the bolted connection in SolidWorks and can be modified if desired. In our case we will use the values of 13.5 mm and 9 mm, respectively. Select Tight Fit and select the only cylindrical face as Shank Contact

Faces.

Specify Alloy Steel for the Material and a Torque preload of 30 N-m with the Friction factor (K) of 0.2.

15 Hole series.

Again, you will be asked if you would like to copy the bolt to the other holes in the series. Click Yes to add the other bolt.

Note

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Again, you will have to apply the Tight Fit option manually.

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16 Locate all contacts in the assembly. From the Tools menu, select Interference Detection. Under the Options dialog, activate the Treat coincidence as interference field.

Click Calculate.

Browse through and analyze the identified contact interfaces.

Due to the significant number of the contacts the contact sets will be generated automatically.

17 Explode the view.

Explode the view for easier definition of the contact conditions.

18 Delete Global Contact.

To make sure that no two parts will be accidentally bonded, Global Contact will be deleted.

This is a good habit if analyzing complex assemblies. Any mistakenly omitted contact condition would likely result in a problem during the solution phase or visually erroneous displacement result. Delete the top assembly component contact (Global Contact).

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Assembly Analysis Mesh Refinement

We have deleted Global Contact to ensure that no two faces remain accidentally bonded. In most assemblies, one type of contact (in our case Allow Penetration) condition does not satisfy all interfaces, so we must adjust the contact condition at each contact set that does not meet the global condition.

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Local Contact Sets

Automatically Find Contact Sets

Automatically Find Contact Sets helps to automate the process of

Where to Find It

I

Menu: Simulation, Contact/Gaps, Contact Sets

I

Shortcut Menu: Right-click Connections and select Contact Sets

I

CommandManager: Simulation > Connections Advisor

defining contacts within an assembly.

>Contact Set

Use in Instructions

Under Contact select Automatically find contact sets

No Penetration Local Contact Options

No penetration contact was introduced in Lesson 3 where all basic

No Penetration Local Contact: Advanced Options

The advanced options of the No Penetration contact are accessible through the simulation study options. To activate them, Show advanced options for contact set definitions option must be activated in the simulation Default Options, under Mesh.

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options were described. In this section advanced options will be discussed.

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Lesson 7 Assembly Analysis Mesh Refinement

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The Advanced dialog in the No Penetration type of the Contact Set definition offers the following types of options: I

Node to node: Entities must be initially touching and no significant sliding or change in the contact region shape may occur. This option may not be used when the Large displacements option (see Lesson 14 ) is active.

I

Node to surface: No restriction on the initial configuration is imposed, i.e. the entities participating in contact do not need to be touching at the beginning of the analysis and sliding is permitted. Because the directions of the friction and normal forces are updated during the analysis, this option is valid for the Large displacements calculations. This type of contact is able to describe complex contact configurations and behavior, but it requires substantially more Set 1 computational effort.Typically, we would use this type of contact when Set 2 edge-to-face configuration is expected and if contact stresses are not of primary importance.

I

Surface to surface: This type of Set 1 No penetration condition is the most general and accurate one. Entities participating in the Set 2 contact are represented by the subsurfaces of the finite element mesh. As in the case of the Node to surface type, no restriction is imposed on the initial configuration and sliding is allowed. The directions of the contact and friction forces are updated during the analysis and this option is valid for the Large displacement computations. Typically, we would use this type of contact when a face-to-face configuration is expected or if accurate resolution of the contact stresses is required.

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Advanced options of the No Penetration contacts helps to set the accuracy/time required to compute the contact solution. To access the options below, Show advanced options for contact set definitions option must be activated in the simulation Default Options.

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No Penetration Contacts: Advanced Options

If these advanced options are not used, the default no penetration contact type will be Surface to Surface.

Where to Find It

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Menu: Simulation, Contact/Gaps, Contact Sets

I

Shortcut Menu: Right-click Connections and select Contact Sets

I

CommandManager: Simulation > Connections Advisor

>Contact Set

Use in Instructions

Under Advanced choose from Node to node, Node to surface or Surface to Surface.

19 Activate Advanced options of the No Penetration contact. Edit the simulation Default Options. Under Mesh folder activate the Show advanced options for contact set definitions option.

Right-click on the Connections folder and select Contact Sets.

20 Define local contact sets.

We will take advantage of the automatic contact generation feature in SolidWorks Simulation. Right-click on the Connections folder and select Contact Sets.

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Under Contact select Automatically find contact sets. Under the Options dialog, select Touching

faces.

In Components, select the top level assembly. Click Find contact sets.

All detected contact sets are listed in the Results dialog. You can browse through and view each by clicking on it.

Select all found contact sets under the Results dialog. Under Type and Options, select No penetration.

Under Properties activate Friction and specify the Friction Coefficient of 0.05.

Select All

Under Advanced select Surface to surface. Click OK twice. All the contact sets will be generated and listed under the Connections folder.

Note

Node to surface and Node to node, No penetration advanced contact options could also be used. Node to node option (global,

component or local) would, however, force the compatible mesh, while Node to surface option (local only) could result in less accurate contact stresses.

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As specified in the statement of the problem, the geometry of the Shaft ensures that the Yoke_female and the RevBracket do not come any closer than the initial manufacturing distance of 3.469 mm. We will simulate this constraint with the help of the No penetration contact condition with Gap (clearance) settings.

Gap (clearance)

This feature enforces the contact offset equal only to the initial geometrical distance between the participating entities. The options of this feature enables the user to select whether the initial geometrical offset should be applied to all of the selected entities within a specific contact set or only to those with the initial separation distance smaller than the user defined value.

Gap Example

Let us demonstrate this feature on the following example:

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No Penetration Local Contact Options

I

If the Always ignore clearance option is activated in the Gap (clearance) dialog, no node along the specified source edges will

be allowed to come closer than their respective initial geometrical separations of 3 mm and 7 mm. All the points along the source edges will, however, be permitted to separate further.

I

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If Ignore clearance if < 4 mm is specified, for example, the 3 mm contact will behave as described above, while the 7 mm contact will be allowed to fully close (if the appropriate load is specified).

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21 Define Yoke_female vs. RevBracket contact. Define a No penetration, Node to surface contact set with the edge of the contact face between the shaft and the Yoke_Female as the first component and the face on the RevBracket as the second component.

Select Gap (clearance) and select Always ignore clearance. Under Advanced select Node to surface.

Click OK.

Note

We specified a Node to surface contact since our first entity is an edge. The Surface to surface option would not be appropriate in this case.

Also, edge is used to simplify the solution. Full contact face between the shaft and the Yoke_Female could be used as well.

The above contact condition ensures that the two entities will not come any closer than the initial manufacturing distance of 3.469 mm, but allows them to separate.

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The last restraint must ensure that the cylindrical openings on the Yoke_female and RevBracket remain aligned and that these two openings remain connected for the transmission of the torque (they are physically connected by a shaft). Without this condition, the differential is free to rotate and our solution may fail or be inaccurate. Instead of using a model of the shaft, we will use a pin connector. In addition to providing the alignment between the holes, the pin connector must be able to account for both rotational and axial stiffness.

Rotational and Axial Stiffness

Assuming a cylindrical shape with a constant cross-section, the rotational stiffness can be calculated using the formula: JG KROT = ------L

4 πr -------where J = 2

is the polar moment of inertia for the circle with radius r,

G is a shear modulus of the material, and L is the length of the shaft connecting our two points (effective length of the shaft). Substituting our values into the above equation, we obtain KR = 18,403 N-m/rad.

The axial stiffness of a cylindrical shaft with a constant cross-section can be calculated using the formula: KAXIA = EA -------L

2

where E is the Young’s modulus and A = πr is the cross-sectional area of the circle with radius r. Substituting our values into the above equation we obtain KA = 4.3135e9 N/m.

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22 Define Yoke_female and RevBracket connector. Specify a Pin connector between the cylindrical openings of the Yoke_female and that of a RevBracket (see the figure below).

For Connection Type, make sure that both With retainer ring (No translation) and With key (No rotation) are cleared.

In the Advanced Option dialog, enter 4.3135e9 N/m for the Axial Stiffness and 18,403 N-m/rad for the Rotational Stiffness. Click OK.

Axial Stiffness Rotational Stiffness

The base-plate bolted to the ground using the foundation bolts is free to lift up at certain locations such as between the bolts and along the edges. To correctly simulate this behavior without the inclusion of the additional component to model the ground, a Virtual wall, local No Penetration feature can be conveniently used.

Virtual Wall, Axial and Tangential Stiffness

Two wall types are available: Rigid and Flexible Rigid type assumes infinite stiffness and can be used to simulate very stiff foundation plates. If Flexible type is requested, effective foundation stiffness values in Axial and Tangential directions must be specified. This approach allows users to simulate composite foundation walls without it being necessary to include them in the model. Both types support Friction Coefficient and the Gap (Clearance) contact features.

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To determine how to calculate the Axial and Tangential stiffness values for the virtual wall, it is convenient to use the Knowledge Base, which is an excellent compilation of numerous articles with images.

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Knowledge Base

Expand the Analysis Research tab and enter “virtual wall stiffness” in the Search Knowledge Base field. The article, which is the result of the search, gives full explanation and a simple formula which can be used for both single layered as well as composite foundation walls.

Where to Find It

Menu: Simulation, Research

Note

Internet connection and subscription are required to access the Knowledge Base database.

23 Virtual Wall.

Right-click on the Connections folder and select Contact Set.

For Type, select Virtual Wall.

Select the bottom face on the base-plate as the Set 1 and PLANE2 as Set 2. Under Wall Type select Rigid. This option is required for the Foundation bolt connector.

Enter 0 for the Friction Coefficient. (With Foundation bolts defined, friction has little effect on the results of the analysis.) Click OK.

Friction Coefficient

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All of the necessary contact conditions have now been defined.

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Our main concerns are the components of the differential; namely, Yoke_male, Yoke_female, Spider, and the Pins. We will use a finer mesh for these parts. To speed up the calculation in this lesson coarse mesh will be used instead.

24 Mesh the assembly. Select Curvature based mesh under Mesh Parameters.

Mesh the assembly with Draft quality elements. Move the Mesh density slider to the left for a coarse mesh with Maximum element size of 23.630mm, Minimum element size of 4.726mm, Number of elements in a circle as 8, and Ratio of 1.6. The resulting mesh is shown in the figure below.

25 Set properties of study. Specify Direct Sparse solver for this analysis.

Note

The Direct Sparse solver is specifically chosen because we have a larger number of contacts and connectors, but the size of the model is still rather small. We expect this solver to be more efficient than an FFEPlus iterative solver. In general, however, with the increasing size of the problem, the FFEPlus iterative solver becomes more efficient and would be our choice instead. For more information on solvers, see Appendix A.

26 Run the study.

The study may run for several minutes and then complete successfully.

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27 Display and animate stress results.

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Display and animate the distribution of the von Mises stresses in the model.

We observe that the stresses in RevBracket are rather high, above the yield strength of Aluminum 1060 Alloy (27 MPa). The stress peak is located at the bolt location where the stiff bolt connection condition is applied.

28 Isolate components. Isolate Yoke_male, Yoke_female, spider and the three PIN

components.

29 Analyze stress results on isolated components. Under the Chart Options make sure that Show Min/Max range on shown parts only option box is checked.

For better viewing explode the assembly.

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The stress values dropped to approximately 0.58 MPa, a value significantly smaller when compared to the yield strength of the material (620 MPa). It is apparent than the stress magnitudes in the components of our interest will be rather small.

However, note that our mesh is rather coarse and that Draft quality elements were used. For reliable stress results, we would have to refine the mesh and use High quality elements.

30 List Bolt forces.

Right-click on the Results folder and select List Pin/Bolt/Bearing

Force.

Select All bolts from the list. Examine the results.

Click Close.

Part 2: High Quality Mesh Analysis

In the second part of this lesson, we analyze the quality of the current mesh, generate a new High quality mesh, and post-process the results of the refined study. First, let us have a look at the quality of our current mesh.

31 Analyze details of current coarse Draft mesh. Right-click on the Mesh folder and select Details. Mesh Details lists the basic

information about our current mesh. Scroll all the way down and note the three rows that provide information about the Aspect Ratio. (For the detailed information on the Aspect Ratio, consult Appendix A.)

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Both the Maximum Aspect Ratio of 22.44 and the Percentage of elements with Aspect Ratio < 3

of 86.9 are acceptable.

The overall judgement about our mesh can be achieved by simple visual inspection. Two Draft quality elements per thickness of the Yokes’ walls, as well as in through-thickness direction in the pins, are not enough for reliable stress and strain results.

Required Number of Solid Elements in Thin Features

In general, we would require at least four Draft (two to three High) quality elements in the through-thickness directions when stresses or strains are of any concern and substantial bending or high curvature in the geometry is present. A fairly coarse mesh of the RevBracket and the base-plate is not a major concern. We would, however, still require a minimum of one (High quality) or two (Draft quality) elements through the thickness. The contact interfaces do not necessarily need to be refined any further, especially if in High quality elements, unless contact stresses are of any importance.

Note

A requirement on the minimum number of solid elements in the through the thickness direction can be relaxed if no significant curvature exists and no substantial bending or torsion (compression in nonlinear analysis) is expected.

Aspect Ratio Plot

The distribution of the Aspect Ratio in the mesh can also be displayed graphically. This plot allows for the detection of the location of the sliver elements with high Aspect Ratio values.

The value of the Aspect Ratio should be kept below 50 in the regions where stresses are of crucial importance. In all other instances the value should be limited by approximately 1000. It is typically straight forward to rectify the high Aspect Ratio problem by applying local mesh controls to the regions in the vicinity of such badly shaped elements.

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32 Aspect Ratio plot. Right-click on the Mesh icon and select Create Mesh Plot. Select Aspect ratio and click OK.

Edit the legend and select Show max annotation feature.

Note that the maximum value indicated in the plot is indeed 22.44.

Annotation for the maximum Aspect ratio value shows the location where the elements are rather sliver - bent in the sliver part of the yoke. If the stress and strain values were of importance to us we could use local mesh control to refine the mesh at this location.

33 Define new study.

Duplicate the study stress analysis as a new Static study named stress analysis refined.

34 Mesh the model. Select Curvature based mesh under Mesh Parameters.

Mesh the assembly with High quality elements. Move the Mesh density slider to the right for a fine mesh with Maximum element size of 5.908mm, Minimum element size of 1.182mm, Number of elements in a circle as 8, and Ratio of 1.6.

Note

A message appears warning you that the results will be deleted. Click OK to proceed.

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35 Examine the mesh.

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The mesh now has the recommended numbers of elements in throughthickness directions for all components. The resulting mesh can be seen in the figure.

36 Display the mesh details.

We note that the Maximum Aspect Ratio decreased to an acceptable value of 10.6 and that the Percentage of elements with Aspect Ratio < 3 increased to 96.6. Meshes with these parameters can be regarded as very good.

Notice that the number of Total nodes has increased 17 times to 50,152.

Jacobian

We have already discussed the Aspect Ratio as a measure of the mesh quality. Aspect Ratio plot was also demonstrated in step 32 on page 263.

Another mesh quality measure, which identifies highly curved and skewed elements is Jacobian. SolidWorks Simulation has an automatic check of this quantity during the solution phase and the user typically does not need to pay attention to it. However, the closer the value of the Jacobian to 1, the better. Its value also should never be close to 0 or negative; this may be a sign of a serious localized mesh problem. The Jacobian is only available for high quality elements.

37 Plot distribution of Jacobian. Right-click the Mesh folder and select Create Mesh Plot.

Specify Jacobian and click OK.

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The maximum Jacobian value for our mesh is 8.21 which is very acceptable.

Due to the time required, this study has been calculated and its results can be found in the completed - High Elements subfolder of the Lesson 7 directory.

38 Save and Close the file.

39 Open an assembly file. Open Cardan joint from the completed- High Elements subfolder.

40 Display stress results.

We can again observe high stress concentrations in the vicinity of the bolts.

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41 Isolate components. Isolate Yoke_male, Yoke_female, spider and the three PIN

components.

42 Display von Mises stress results. Under the Chart Options make sure that Show Min/Max range on shown parts only option box is checked.

We can observe a raise in the maximum von Mises stress magnitude from 0.58 MPa to approximately 1.44 MPa. This raise, while insignificant for the design of the components in this assembly (both values are well below the yield strength of the material 620 MPa), represents a significant relative increase of nearly 60%. Also, the location of the maximum stress has changed. This example demonstrates that good quality mesh is a necessity if stress are of importance to us.

We would, therefore, conclude that this assembly is designed with the sufficient factor of safety. Exit Isolate.

Factor of safety plot

A Factor of Safety Plot can be used to conveniently plot the distribution of the factor of safety in the assembly. The procedure to create a design check plot is a wizard that uses sequential steps to define the plot parameters.

Where to Find It

I

Shortcut Menu: Right-click Results folder and select Define

Factor of Safety Plot.

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43 Plot a factor of safety distribution. Right-click on the Results folder and select Define Factor of Safety Plot.

As nearly all standards (except the ASME Boiler and Pressure Vessel Code, for example) require the use of von Mises stress for the calculation of the factor of safety, choose Max von Mises stress in the first window.

Note

The inequality shown in the dialog window is not the definition of the factor of safety and the user should not be confused by this expression. It is a definition of the von Mises yield criterion used by the software to identify material points that experience yielding (with factor of safety < 1). Users should ignore this expression at this time. It will become clearer as the user becomes more proficient with the software and theory. Click Next.

44 Specify material constant.

The second step is to specify the material constant that will be used as a comparison against the von Mises stress selected in the previous step.

Select Set stress limit to Yield strength as most of the standards specify the material yield stress and the Material involved as 1060 Alloy.

Note

Remember that our computations are valid within the scope of the linear elasticity traditionally limited by the yield stress point on the material stress-strain curve.

Also note that the bottom of the dialog in the figure on the previous page lists the materials used in the assembly along with their corresponding yield strength information. The units can be set at the top of the same dialog window. Click Next.

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45 Specify factor of safety.

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The third step allows the user to specify the quantity to plot. Select Factor of safety distribution. Click OK to generate the plot.

46 Analyze the plot.

Change the maximum value of the legend to 100.

We can see that the lowest value of the factor of safety, 0.05, is very small due to the stress concentration. It is a good habit to set the lowest value to the design value of the factor of safety, 3.5 for example.

47 Edit the plot.

Change the lower limit of the legend to 3.5.

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We can see that the image did not change significantly. The red regions indicate the parts in the model which do not pass the design factor of safety criterion.

48 Iso Clipping.

Define an iso clipping of this plot that shows the regions where the factor of safety is below 3.5.

This plot indicates the regions that we should be concerned about failure. Turn off the iso clipping when you are finished.

49 Isolate components. Isolate Yoke_male, Yoke_female, spider and the three PIN components

and re-plot the factor of safety plot. We can observe that the minimum value of the factor of safety in the chart, 284, is very conservative.

50 Save and Close the file.

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In this lesson, we analyzed an advanced solid mesh assembly with various contact conditions and connectors. The creation of the local contact sets was shown and practiced.

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Summary

The pin connector with specified rotational stiffness was used to simulate a real shaft. The remote load feature was used to remotely apply the load without a need to model the linking parts.

We analyzed the quality of the finite element mesh and discussed the optimum size of elements with respect to the characteristic dimensions of the model.

Finally, a new postprocessing feature, Design Factor of Safety, was introduced. In this lesson, we used this feature to plot the distribution of the factor of safety and discussed various options available in the definition of this plot type. We saw that the yoke and spider parts were safe from failure, while the mounting bracket show a factor of safety less than 3.5. Before making conclusions, we should investigate a finer mesh on the bracket to see our stress results converging. We could then make a determination on whether or not we need to change materials or design to satisfy the 3.5 factor of safety.

Questions

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I

The minimum number of solid elements in the through the thickness direction is_____ if in Draft quality or_____ if in High quality.

SolidWorks 2012

Exercise 14 Bolt Connectors

In this exercise, we will use bolt connectors to replace the physical bolts and eye bolt. With the absence of the eye bolt, the external load is applied as a remote load.

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Exercise 14: Bolt Connectors

This exercise reinforces the following skills: I I

Problem Statement

Pin Connectors on page 195. List Pin/Bolt/Bearing Force on page 203.

A bar is attached to a base plate with two loose fitting bolts: bolt diameter is 12 mm, hole diameter is 12.2 mm. Eye bolt

Base Plate

Bolts

Bar

The base plate is supported along both sides. The eye bolt is loaded in vertical and horizontal directions with 1,100 N [247 lb] forces, as indicated in the figure below. It is assumed that the eye is rather stiff and provides a nearly rigid connection between the forces and the strip. Both the bar and the base plate are manufactured from steel AISI 1020. Fixed Support

Vertical Load 1,100 N.

Fixed Support

Horizontal Load 1,100 N

Determine the maximum stress and deformation for the components. Also determine the forces in the bolts.

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Bolt Connectors

Open an assembly file. Open bolt joints from Lesson07\Exercises

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1

folder.

The bolts, nuts and washers have been suppressed. This is because in this exercise we will use bolt connectors. To account for the missing eyebolt, we will apply the horizontal load as a remote load on the cantilever beam.

2

3

Set SolidWorks Simulation options. Set the global system of units to SI (MKS) and the units of Length and Stress to mm and N/m^2, respectively. Create Study.

Create a static study named two bolts - torque preload.

4

Apply material.

Apply AISI 1020 steel as the material for both parts.

5

Create Bolt Connectors. Create two Standard bolt

Edges defining bolt heads

connections with nut.

Use 24 mm for the diameter of the head and nut, and 12 mm for the diameter of the bolt. Make sure that the Tight Fit option is not checked- the bolts are loose fitting.

Use Alloy Steel for the Material.

Apply the Torque preload of 160 N-m [1416 lb-in] with the Friction factor of 0.2.

You can verify with hand calculations that the corresponding axial bolt preload force is 66,666N [16,860 lb]. Consequently, bolt tensile stress equals 590 MPa [96,160 psi] which is 95% of the yield strength of Alloy Steel.

Note

6

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Exercise 14 Bolt Connectors

7

Define Contact conditions.

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For correct modeling of bolted connections we need to define a contact condition between the two assembly components.

Because we expect a horizontal slide along the interface, a local No penetration, Node to surface or Surface to surface contact condition is required.

Define a No penetration, Node to surface contact set between the two components, as indicated in the figure.

8

Apply remote load.

As mentioned in the beginning of this problem, we assume that the eye bolt is rather rigid. Thus, use the Load/Mass Rigid connection option.

Select both the bottom and the top contact faces as Faces, Edges or Vertices for Remote Load/Mass. This reflects the reality in which most of the loads are transmitted through the friction forces between the bolt head/nut and the bar. Apply horizontal and vertical forces, both at a magnitude of 1,100 N, as indicated in the figure. Use local Coordinate System1 to specify the location of the force (0, 0, 51 mm) and the magnitude (1100 N, 0, 1100 N).

9

Apply fixture. Apply a Fixed Geometry fixture to the two side faces on the base plate.

10 Mesh assembly. Select Curvature based mesh under Mesh Parameters.

Create High quality mesh with the default settings.

11 Run the analysis.

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12 Review Results.

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Review the area where the highest stresses are located and notice that the size of the “hot spot” is smaller than that of the element size. Therefore, stresses in this area are reported with a large error. Mesh refinement would be required to obtain more accurate maximum stress results.

13 Plot details of deformation.

Analyze the details of the deformation in magnified scale.

It can be seen that the bar and the base plate separate from each other.

14 Review bolt forces.

The axial bolt forces in Bolt Connector-1 and Bolt Connector-2 are 66,667 N and 69,057 N.

As compared to the bolt preload of 66,666 N, the effect of the external load is very small. A negligible change in bolt axial load is desirable if we want to avoid bolt loosening.

15 Save and Close the file.

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Exercise 15 Awning

In this exercise, you will analyze a retractable awning.

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Exercise 15: Awning

This exercise reinforces the following skills: I I

Problem Description

Pin Connectors on page 195. Remote Load on page 242.

The retractable awning in the photograph is used to shield a vegetable stand from weather. The total area that the awning covers is 2m^2. Six springs are attached to the awning and keep it in the extended position. Each spring has a spring constant of 875N/m. In the extended position, the springs have a tension pre-load of 45 N. Assume that the awning is rigidly connected to the base with a 150 N-m pre-loaded bolt.

All parts in the assembly are made of AISI 1020 steel. Consider the pins that connect the pieces together to be rigid.

Goal

Calculate the maximum stresses and displacement in one side of the awning assembly when it is loaded with 152mm of snow (with density of 80 kg/m^3). With the snow on top, a 186 N horizontal load from the fabric roll and snow weight is generated.

Tip

The awning roll is attached in the global coordinate system at (-1259.84mm, 50.8mm, 3.175mm).

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Awning

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PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Lesson 8 Analysis of Thin Components

Objectives

Upon successful completion of this lesson, you will be able to: I

Create a mid-plane shell element mesh.

I

Create a shell mesh from selected surfaces.

I

Perform structural analyses and analyze results using shell elements on parts.

I

Evaluate mesh adequacy to model stress concentrations.

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Analysis of Thin Components

To this point, we have used solid tetrahedral elements to mesh our models. These work fine when the model does not have a thin cross section, but when one dimension is much smaller than the other two, such as in sheet metal parts, solid meshes can take a long time to solve.

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Thin Components

To mesh a model properly with solid elements, we would need to place at least two layers of tetrahedral elements across the thickness. Such a mesh calls for a very small element size to fit across the thin section of the model. These small elements are unnecessary in the other directions, so the mesher creates a lot more elements than are necessary for an accurate solution in those direction. Consequently, the large number of elements requires far more time to be created by the mesher and also requires a lot more time to evaluate the solution.

Case Study: Pulley

Shell mesh can be generated on faces of solid bodies or on surfaces. In such situations, all of the model boundary conditions and loads must be applied on the edges of the solid bodies or directly on the surfaces. If sheet metal features are used in the assembly, shell mesh is automatically generated on the midplane. Furthermore, all restraints and loads are correctly determined using the solid geometry directly. This lesson contains two case studies. The first shows how to model using shell elements when surface is used, the second then demonstrates the analysis with the sheet metal part. It is strongly recommended that both case studies and the following exercises are completed to fully understand shell modeling in SolidWorks Simulation software.

In this lesson, we analyze a stamped steel pulley used as an idler in an automotive belt drive. Because one dimension of the pulley geometry, its thickness, is much smaller that the other dimensions, meshing this geometry with solid elements will create a very fine mesh. We will first use solid elements to see the problem, then we will use shell elements and compare the results.

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Project Description

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A belt exerts a vertical resultant force of 500 N on the pulley. From this we can calculate that the belt force is equal to 353.55 N based on equilibrium. Determine the deformations and stresses that develop in the pulley.

Part 1: Mesh with Solid Elements

We will first analyze the pulley using solid elements, just as we have in previous lessons. We can take advantage of the symmetry of the geometry, loads, and restraints by analyzing one half of the pulley while simulating the missing half with symmetry boundary conditions.

In this case, the pulley is simple enough to analyze without using symmetry. Idealizations, such as using shell elements in place of solids and using one half of the model in place of the whole model, are utilized here only as a learning example.

Procedure

Follow the steps below to analyze the pulley with a solid mesh:

1

Open a part file. Open pulley located in the Lesson08\Case Studies folder.

Split lines define a face extending over a 90° section of the pulley. This area is where we apply a belt load as pressure exerted on the pulley.

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2

Make symmetry cut.

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Activate the configuration called FEA. 3

Create new study.

Create a new static study named pulley solids.

4

Set SolidWorks Simulation options.

Set the global system of units to SI (MKS) and the units of Length and Stress to mm and N/mm2 (MPa), respectively.

Store the results files in the results folder in the SolidWorks document folder.

5

Apply fixed restraint.

Select the face on the outside semi-cylindrical face and apply a Fixed Geometry restraint.

Symmetry Fixtures

Symmetry fixtures simulate the half of the pulley that is missing from the model. The fixture will prevent any displacement across the plane of symmetry but can allow displacements on the plane of symmetry.

Alternatively, rather that applying a Symmetry fixture to a face, we can apply the same condition manually to either one of the two edges of this face. The restraint will still be transferred to the edge of the surface that is meshed with shell elements. See the discussion in the second part of this lesson for more information on symmetry restraints.

6

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Apply symmetry restraint.

Faces with symmetry

Select the two faces in the plane of symmetry, and apply a Symmetry fixture.

boundary conditions

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Define pressure load. Right-click External Loads and select Pressure, and then select Normal to selected face.

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7

Select the face upon which the pressure load needs to be applied, and define a pressure load equal to 0.2 MPa (200,000 Pa). Click OK to save the definition.

Notice that we do not load the model by the forces in the belt. Rather, we apply a pressure value simulating the presence of the belt.

Note

Also, you may ask how we know that this 200,000 Pa pressure results in the desired 500 N reaction force in the vertical direction. A linear static analysis with an arbitrary magnitude of the pressure was run ahead of time. Based on the reaction force magnitude obtained in this study, we were able to scale the pressure to 200,000 Pa to obtain the 500 N vertical reaction. We already used a similar proportionality in Lesson 3.

8

Create mesh. Select Curvature based mesh under Mesh Parameters.

Mesh the model with High quality elements and the default settings.

9

Examine the mesh.

There is only one element across the thickness of the model. From the mesh details, we can see that there are 9,582 elements and 19,378 nodes.

10 Run the analysis.

Note

You can merge these two steps, mesh and run, if you select Run (solve) the analysis in the Options dialog of the Mesh command.

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11 Plot von Mises stresses.

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The maximum stresses on the outside and inside faces of the solid pulley are approximately 65.7 MPa and 81.3 MPa.

Note, however, that this mesh features one element through the thickness while two layers of high quality elements are recommended as a minimum.

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Part 2: Refined Solid Mesh

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Now we will refine the mesh so that we have two layers of elements across the thickness of the material and then compare the results with the previous analysis.

1

Create new study.

Duplicate the pulley solids study and name the new study pulley solids dense.

2

Mesh the model.

Select Curvature based mesh under Mesh Parameters.

Mesh the model with a Maximum element size and a Minimum element size of 1.1 mm. Additionally, use 8 as the Minimum number of elements in a circle and 1.5 as the Ratio.

This element size ensures that two layers of elements are placed across the wall thickness, which is 2 mm.

This mesh will take considerably longer to create, on the order of 15 times longer.

3

Examine the mesh.

This time we have 208,370 elements and 336,174 nodes (987,978 DOF).

4

Run the analysis.

Because of the large size of this mesh, we need to change to the iterative solver. Right-click the study and select Properties. Select the FFEPlus solver. Run the study.

Even using the iterative solver, this solution will take much longer to run.

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5

Plot von Mises stresses.

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Create a von Mises stress plot.

The maximum von Mises stresses on the outside and inside faces are 62.7 MPa and 87.0 MPa. The dense solid element mesh reports a more “regular” shape of the stress concentration.

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Solid vs. Shell

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Using the solid mesh required a very long mesh and solution time to get an answer that we could be confident with in this relatively simple model. If the wall thickness had been even thinner, the solution could take several hours, which would be unacceptable for a part of this simplicity. Now that we have done a solid mesh, we will construct a shell mesh using two distinct modeling techniques: I I

Shell mesh using mid-surfaces Shell mesh using outside/inside faces of solid bodies

Creating Shell Elements

Shell elements can be created on surfaces, faces of solid bodies or for sheet metals parts. In the following study, we will create mid-plane surface to act as our shell sheets.

Part 3: Shell Elements - Midplane Surface

The pulley does not feature any mid-plane surface. We must therefore first create surfaces that will be used as our shell sheets.

1

Create mid-plane surface.

Click Insert, Surfaces, Mid-surface from the menu.

2

Select surfaces.

Select the face on the outside as Face 1 and the matching face on the inside as Face 2.

Select Knit surfaces to make sure the command will create a single surface. Continue selecting faces until entire midplane is created. Click OK.

Tip

Click Find Face Pairs to find the faces automatically.

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The mid-surface location for the shell mesh is the most desirable. In some situations, however, extraction of the midplane is too difficult or not convenient. In such cases the shell mesh can be placed on either the outside or inside face of the solid geometry. Because shell elements are suitable for thin structures, the difference in results due to the different position of the shell is rather small. Students should complete Exercise 17: Shell Mesh Using Outer/Inner Faces on page 315 to verify the above in the case of the pulley model

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Note

3

Create study pulley shells -midplane. For now, let us skip the definition of loads and fixtures and go directly to the mesh creation.

Introducing: Exclude from Analysis

In parts and assemblies, there may be more components than we are interested in analyzing or we may want to limit the scope of the analysis to only certain components. Exclude from analysis essentially suppresses the component from the analysis.

Where to Find It

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4

Shortcut Menu: Right-click a part, body or surface in the Simulation Study tree and click Exclude from Analysis.

Exclude Solid body.

We have a solid body and a surface body, but we only want to analyze the surface body. To do this we must exclude the solid body that is not to be analyzed. In the Simulation Study tree, expand the pulley folder and right-click the solid body, then click Exclude from Analysis.

Note

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Notice that when we exclude the solid body, it is also hidden in the graphics window. Since we are using shell elements that are defined by surface geometry, we only want to select the surface geometry to apply our loads and restraints.

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Lesson 8 Analysis of Thin Components

Thin vs. Thick Shells

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Thin shell element technology assumes that the cross-section

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perpendicular to the midplane remains straight and also perpendicular to the midplane at the end of the deformation (Kirchhoff theory). As a consequence, this shell element ignores the shear deformation and stress in the through-thickness direction. Thin, membrane-like structures with the span to thickness ratio larger than 20 can be accurately modeled using this element.

I

Thick shell element technology assumes that the cross-section

perpendicular to the midplane remains straight after the deformation takes place, but it is no longer perpendicular to the deformed midplane (Mindlin theory). As a consequence, this element assumes constant distribution of the shear deformation in the through-thickness direction. Thicker shells where shear effects become noticeable can be accurately modeled using this element. THIN

THICK

BEFORE DEFORMATION

MIDPLANE

AFTER DEFORMATION

In both cases the distribution of the normal bending stresses can be seen as linear.

LINEAR DISTRIBUTION OF IN-PLANE STRESS IN BOTH THIN AND THICK SHELL

5

Define the shell.

Select the midplane surface body. Right-click either selected body and click Edit Definition.

Select Thin and set the thickness to 2 mm. Click OK.

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6

Mesh control.

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Apply a mesh control on the rounded face (see the figure) with the Element size of 1.5 mm. Keep the Ratio at its default value of 1.5.

7

Create mesh.

Select Curvature based mesh under Mesh Parameters. Create a High quality mesh with the default settings.

The resulting mesh can be seen in the following figures.

8

Examine the mesh. The Mesh colors section indicates that the shell bottom faces are

marked with an orange color. The shell top faces assume the part color, gray in this case. This fact is very important in the postprocessing phase. Furthermore, we see that the inside and outside are colored uniformly (i.e. gray and orange colors do not alternate on any side). Such aligned shell mesh is required for correct postprocessing.

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Shell elements have a top and bottom side. To indicate the side, the mesh is color coded with the top and bottom being shown in different colors.

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Shell Mesh Colors

To obtain proper results, all the mesh elements must be aligned properly with the tops on one side and bottoms on the other. Menu: Simulation, Options, System Options, General.

Where to Find It

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Changing Mesh Orientation

In some cases, however, we may wish to change the mesh orientation or the shell mesh may not to be aligned at the end of the meshing phase. In such cases, the mesh need to be aligned manually. We can practice flipping the top and bottom of the shell mesh with our current mesh.

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Flip the mesh on one face.

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9

Left-click on the face indicated in the figure.

Right-click on Mesh and select Flip shell elements.

The result of this operation can be seen below.

We can see that the colors are not uniform and the shell mesh is misaligned. While the finite element computations would be correct with such misaligned mesh, the postprocessing would show meaningless results along the lines of misalignment.

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Before proceeding further, we need to explain why shell element alignment is important. Shell elements can model bending; therefore, most often, different stress results are reported at the top and bottom of shell elements.

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Shell Element Alignment

Using the postprocessing options for shell elements, we can choose to display the stresses on the top or bottom. Additionally, stress distribution in the throughthickness direction can be divided into two components: bending and membrane. All four options are demonstrated in the figure to the right.

Let us depart for a moment from the pulley and examine a rectangular cantilever beam meshed with misaligned shell elements.

Say we want to display the P1 stress (maximum principal stress) at the top of the beam. Because the shell element orientation in the model is inconsistent, the stress plot is in error.

Now, instead of the P1 stress, we plot the von Mises stress.

The fact that the plot is erroneous again becomes obvious along the line of misalignment.

This error is because stresses are averaged before the von Mises stress is calculated. Averaging between the results on the top and the results on the bottom of the shell elements across the misalignment line results in nearly zero stress. Having explained the importance of shell element alignment, we now return to the pulley lesson.

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This option automatically aligns the surface of the generated shell mesh.

Where to Find It

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Automatic Shell Surface Realignment

Menu: Simulation, Options, Default Options

10 Align mesh.

Flip the mesh so that the bottom of the shell mesh faces the inside of the pulley model. Make sure that the mesh remains aligned, i.e. colors on both the inside and outside must remain uniform. The resulting mesh can be seen in the following figure.

Note

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Provided that the mesh is aligned, there is no need to flip the mesh. In our case, we flipped the entire mesh so that the bottom of the shell mesh coincides with the inside of the pulley. The postprocessing then becomes more intuitive.

SolidWorks 2012

Lesson 8 Analysis of Thin Components

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11 Add a pressure load. Apply a pressure of 0.2 MPa (200,000 Pa) to

the surface of the pulley where the belt would make contact.

12 Add fixtures. Add a Fixed Geometry fixture to the

surface where the pulley contacts the shaft.

Note

Fixed Geometry is used because shell elements have both translational and rotational degrees of freedom. Immovable would only constrain the translations.

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13 Apply symmetry restraint.

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In the case of the shell mesh using surfaces mesh type, the symmetry condition must be specified manually.

Apply Fixtures, Advanced Fixtures, Use reference geometry type. Select all the edges located on the symmetry plane.

Tip

Right-click on a particular edge and click Select tangency. Select Right plane as your reference entity.

Enter 0 mm in the Normal to Plane field under Translations.

Enter 0 rad in both Along Plane Dir 1 and Along Plane Dir2 fields under Rotations. Click OK to save this fixture.

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To illustrate a rule for applying symmetry boundary conditions, consider a point on the plane of symmetry. Any displacement that moves the point out of this plane must be restricted. Furthermore, any rotation that inclines the plane of the cut from the plane of symmetry must be restricted as well.

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Applying Symmetry Restraints

The following table summarizes symmetry boundary conditions in the three principal planes. Symmetry Boundary Conditions Plane of Symmetry

xy

yz

xz

x translation

free

constrained

free

y translation

free

free

constrained

z translation

constrained

free

free

x rotation

constrained

free

constrained

y rotation

constrained

constrained

free

z rotation

free

constrained

constrained

14 Define material.

Make sure the material AISI 1020 is applied to the mid-surfaces.

15 Run the analysis.

This analysis will run very quickly.

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16 Plot von Mises stresses.

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Display the distribution of the von Mises stress. Edit the definition of the plot to make sure that the results correspond to the top face of the shell mesh. Analogously, define a new plot for the distribution of the von Mises stresses on the bottom of the shell mesh.

Top

Bottom

We observe that the maximum von Mises stresses on the top and bottom of the shell mesh are 64.5 MPa and 80.6 MPa, respectively. The comparison of all of the results is shown at the end of the next section.

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17 List reaction forces. Right-click the Results folder and select List Result Force.

Select the supported face.

Set the Units to SI and hit the Update button.

The Reaction force (N) and Reaction moment (N-m) dialogs show the reaction resultants for the selected face in the global cartesian coordinate system.

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18 Examine the results.

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We observe, for example, that the global y and x components of the reaction force resultant are approximately 250 N and 116 N, respectively. The reaction moments resultants about the x axis is -0.73 N-m. Note that 250 N vertical resultant force for half of the pulley corresponds to the 500 N vertical reaction for the entire model.

The moment reactions reflect the fact that the pulley or the load is asymmetrical with respect to the xy and xz planes. As expected, the resultant reaction moment about the global z and y axes are nearly zero, i.e. the pulley as well as the load are symmetrical with respect to the yz plane.

Deformed Results

Deformed Plot displays toggles between the deformed and undeformed geometry of the SolidWorks model.

Where to Find It

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CommandManager: Simulation >Deformed Results to toggle between deformed and undeformed plots.

19 Animate deformation plot.

To verify that the symmetry boundary conditions are correct, animate the deformed geometry plot. Double-click the Displacement plot to make it active. Make sure Deformed Result CommandManager.

Show the undeformed shape over the deformed geometry. Right-click the Displacement1 plot and select Settings. Select

Superimpose model on the deformed shape. Adjust the Translucent slider to see both

shapes.

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is selected in the

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20 Animate the plot.

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Observe that the edge where the symmetry boundary conditions were applied remains in its original plane (remains flat) while the pulley is deforming.

The best way to report such results is to save the animation file in AVI format.

21 Save and Close the file.

Shell Mesh Using Outside Face

In Exercise 17: Shell Mesh Using Outer/Inner Faces on page 315 you will solve the shell problem using the outside faces of the pulley and compare the results with the three pulley studies in this lesson. It is recommended that you complete this exercise to fully understand shell modeling in SolidWorks Simulation.

Results Comparison

The following table compares the displacement and stress results from the four studies that we solved in this lesson. Displacement [mm]

von Mises Stress [MPa]

D.O.F.

pulley shells midplane

0.306

80.6 (bottom)

31,236

pulley shells outer faces

*

*

*

pulley solids

0.316

81.3

55,449

pulley solids dense

0.318

87.0

987,978

Study

Note

The values for the pulley shells - outer faces study will be computed in Exercise 17: Shell Mesh Using Outer/Inner Faces on page 315. Once you complete the exercise, fill in the remaining values in the table.

Computational Effort

The summary table also lists the number of degrees of freedom in each model. While the model is open, locate the file with the OUT extension in the SolidWorks Simulation database to view this information. The number of degrees of freedom can be used as a measure of computational effort required to obtain the solution. Lower computational effort is directly related to the time and cost required to run a study.

Note that the models produce practically identical displacement results.

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Compare the number of DOF for the pulley solids and pulley solids dense studies to see that the dense model is 18 times larger. The stress results of both solid models are within 5%, demonstrating that the model with two layers of elements is not really necessary in this case.

The reason for the 8% maximum difference in the stress results between shell and solid models is that shell elements can not account for the shift of the neutral bending layer towards the inside of the pulley curvature.

We must then conclude that solid elements provide more accurate results when analyzing models with highly curved walls in bending.

Case Study: Joist Hanger

Working with shell elements simplifies significantly for the sheet metal features. In this case study, we will analyze a sheet metal part used to support floor joists in buildings. Each floor joist is supported at each end by a joist hanger, so we can use symmetry to analyze one hanger with only half of the beam.

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Project Description

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The back face of the joist hanger is nailed to a wooden header. Each joist is supported by a joist hanger at each end and nailed in position. Calculate the maximum stress and displacement on the joist hanger and joist.

1

Open an assembly file.

Open Floor Joist for Analysis located in the Lesson08\Case Studies folder. This assembly has one joist hanger with only half of the beam.

2

Create a study.

Create a new static study named floor joist.

3

Set SolidWorks Simulation options.

Set the global system of units to SI (MKS) and the units of Length and Stress to mm and N/m2 (Pa), respectively.

Store the results files in the results folder in the SolidWorks document folder.

4

Add material.

Add the material Galvanized Steel to the joist hanger.

5

Add material.

Add new custom material for the wooden beam. Wood is not isotropic (the same material properties in all directions) but rather orthotropic (material properties are different in each perpendicular direction), so we will have to define a custom material and some custom properties.

Note

In reality, wood is a rather complex material for which orthotropic description is not exactly correct. Modeling wood as orthotropic material is therefore a common engineering simplification giving acceptable results.

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Select Linear Elastic Orthotropic for the Model Type. We can now define the material constants in three perpendicular directions oriented with respect to the selected reference geometry.

Select the Front plane as reference geometry. In this case, this selection makes the global coordinate x, y, z axes coincide with the x, y, z axes in the Material dialog window. Global x coincides with the width, y with the height and z with the length of the beam.

Enter the following values for Elastic Modulus, Poisons ratio, Shear modulus, and Mass density. Enter 50 N/mm^2 for the Yield strength.

Click OK.

Make sure that correct material data is entered in correct units of N/

Note

mm^2 (MPa).

6

Set global contact.

Edit the top level assembly component contact (Global Contact) and change it to No Penetration.

Note

302

The component contact handles this situation because the faces of the solid components are touching. In general, contacts in meshes with gaps must be specified with the help of the local contact conditions.

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Lesson 8 Analysis of Thin Components

7

Add fixtures.

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The hanger is nailed to the header beam. Add Fixed Geometry restraints to the eight cylindrical holes on the back face of the hangers. Because we have a sheet metal part, be sure to select the faces and not the edges of the holes. The fixture will automatically map to the shell edge.

8

Add symmetry boundary condition.

Add a Symmetry fixture on the end of the beam.

Effect of the nails

At this point a decision on the stiffness of the joint must be made. The side nails between the beam in the joist certainly add some stiffness to the joint. However, because the beam is placed in the joist before the nails are applied, nearly all of the load in the vertical direction is transferred into the joist through the bottom load bearing face. Nails then add some stiffness reducing the actual deflection of the wooden beam: this is, however, not the subject of this lesson. Our objective is to assess the performance of the joist; transferring all the load then provides more realistic and also conservative solution.

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Add external loads.

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9

Add a 500 N force to the top face of the beam. Because we are analyzing only half of the beam, the total load on the beam then represents 1,000 N.

10 Mesh.

Select Curvature based mesh under Mesh Parameters.

Mesh with the element size created with the slider all the way to the right. Use a Draft quality mesh. The beam will have solid elements and the hanger will mesh with shell elements because it is a sheet metal part.

Note

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Notice that the surface generation in SolidWorks is not necessary; sheet metal parts are shell meshed automatically.

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Lesson 8 Analysis of Thin Components

11 Run.

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Run the study. Specify Direct Sparse solver. Note

Since component contatcs are defined in the study and the area of contact is found through several contact iterations, the Direct Sparse solver is preferred.

12 Plot results.

We can observe that the maximum stress of 222 MPa is above the yield strength of the joist material (204 MPa). To understand the stress distribution correctly we will analyze the joist alone.

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13 Stress plot.

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We can observe that four support openings are exhibiting the stress peaks. As was shown in Lesson 2, these values are somewhat unreal and potential yielding with finer mesh can be ignored. More detailed analysis may be required.

The high stress on the flat load bearing face is of some concern; its value (92.61 MPa) is however, still below the yield. Also, applications of the nails (which were excluded from this analysis) would help somewhat to redistribute the load more evenly, thus reducing the stress a little.

Note

Either side of the shell can be selected since a sheet metal has been selected.

14 Save and Close the file.

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The pulley case study introduces us to shell elements and familiarizes us with concepts such as shell element thickness and orientation.

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Summary

The shell mesh using mid-surfaces modeling technique was introduced and used to build the finite element model.

In modeling thin objects, shell mesh can also be placed on the outside or inside faces of the solid bodies. The difference between the midsurfaces and either the outside or inside faces of the thin solid bodies is in general small. If the difference reaches significant levels, shell modeling then becomes inadequate and solid elements should be used (i.e. the parts are too chunky for shell elements). Students should complete Exercise 17: Shell Mesh Using Outer/Inner Faces on page 315 to verify that both approaches yield comparable results for structures with small thickness. Symmetry boundary conditions were used in both modeling techniques. Manual application of this restraint was introduced and practiced as well.

The concept of mesh adequacy was also addressed, and the results and modeling differences between shell and solid element models were discussed. It was concluded that solid elements may produce results that are slightly more accurate than those produced by shell elements, provided the solid mesh is sufficiently fine. This can, however, lead to a substantial increase in the problem size which may become intractable.

It was also shown that shell mesh may be generated on the faces of the solid bodies or surfaces. Sheet metal parts are mesh with shell elements automatically.

Tip

To model a sheet metal part as solid, i.e. to mesh it with solid elements instead, right-click the surface feature in the FeatureManager design tree and click Treat as Solid. In general this is, however, not desirable.

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I

When a model contains sheet metal features, the corresponding shell mesh will be formed automatically on the (outside face/ midplane/ inside face) of the sheet metal. The thickness of the shell features (must/may not) be specified manually.

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Questions

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When creating shell mesh manually, ideally it should be defined on the (outside face/ midplane /inside face). Placing them on the (outside face/ midplane /inside face), results in acceptable difference of (0.0001%/a couple of percent/ tens of percent). If the error is significantly larger, shell elements are not suitable for such structure and solid elements should be used instead.

I

Shell elements can be used to mesh thin sheet like components. The characteristic span length vs. thickness ratios indicating when to use solid, thin, or thick shells are. solid elements:

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L --t

<

L t

thick shells:

≤ --- ≤

thin shells:

≤ ---

L t

The figure below shows a flat plate with a thickness t=5mm, and planar dimensions of a=200mm and b=75. The bold and dashed lines indicate simply supported (hinged) and free edges, respectively. The best element type fit for this structure is solids/ thick shells/ thin shells. Simply supported edge

b=75mm

Free edge

a=200mm

I

I

308

To accurately model the stress and strain gradients when using solid mesh, a minimum of_____Draft quality or _____ High quality solid elements should be required in the through the thickness direction. If a sufficient number of elements is generated, (solid / thick shell / thin shell) elements will always provide the most accurate solution. We sacrifice a little accuracy by using shell elements to mesh thin features because______.

SolidWorks 2012

Exercise 16 Bracket

Exercise 16: Bracket

Analyze a sheet metal bracket. The analysis will use shell elements.

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This exercise reinforces the following skills: I I

Project Description

Creating Shell Elements on page 285. Shell Element Alignment on page 291.

A sheet metal bracket has been designed to support a side load of 450 N [101 lb] applied in the x-direction of the global coordinate system. We consider two design configurations:

I I

One without any welds One with welds connecting the miter flanges

Compute and compare the maximum displacements and maximum von Mises stresses for these two configurations.

1

Open a part file.

Open horseshoe located in the Lesson08\Exercises folder. Examine the two configurations: I

no welds



with welds

In the with welds configuration, a total of eight extrusions have been added to connect the mitre flanges.

no welds

Part 1: Analysis of Bracket With No Welds

with welds

The first analysis will be without the welds that would stiffen the part.

2

3

Activate the no welds configuration. Create study.

Create a static study named no welds analysis.

4

Define material properties.

Assign Galvanized Steel to the part.

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Bracket

Create mesh. Select Curvature based mesh under Mesh Parameters.

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5

Specify High quality elements and the default settings.

Shell mesh should be consistently aligned to ensure correct stress averaging along the boundaries’ separating faces.

Note

6

Fix the edges.

Select the end faces on both sides of the bracket and apply a Fixed Geometry restraint.

7

Apply 450 N force. Apply a 450 N forces to the top

face of the bracket, as indicated in the figure.

Moment Load

The Force definition window also allows you to apply a load in the form of moment. This option is possible because shell elements have six degrees of freedom (three translational and three rotational) and, thus, can be loaded with either a force or a moment.

8

310

Run the analysis.

SolidWorks 2012

Exercise 16 Bracket

Plot von Mises stresses on both faces.

The stress plot indicates that the outside face is yielding at the sharp reentrant edges of the sheet metal bracket. As you recall however from Lesson 2, the numerical values of these stress results are meaningless, as they are singular at these locations.

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9

Outside Face

Inside Face

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Exercise 16

SolidWorks 2012

Bracket

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The stress results are meaningful at a certain distance from the source of the singularity. See Lesson 2 on page 85 for the detailed discussion of this phenomenon.

10 Plot displacement results.

We observe the maximum resultant displacement of approximately 1 mm [0.04 in].

Part 2: Analysis With Welds

We will run the analysis again to see how much stiffer the part is when the flanges are welded together.

1

Activate the with welds configuration.

2

Create new study.

Create a study named with welds analysis using the same study options as in the previous analysis.

3

Copy external loads and fixtures. Even though the study no weld analysis is inactive, you can copy

external loads, fixtures and material.

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SolidWorks 2012

Exercise 16 Bracket

Mesh the model and align shell elements. Select Curvature based mesh under Mesh Parameters.

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4

Use High quality elements with the default settings.

5 6

Run the analysis.

Plot von Mises stresses.

The maximum von Mises stress results are not easily comparable because of stress singularity in the model without welds.

Outside Face

Inside Face

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Exercise 16

SolidWorks 2012

Bracket

7

Plot resultant displacements.

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Comparison of the resultant displacements between the model without welds and the model with welds shows a reduction of the maximum displacement from 1 mm [0.04 in.] to 0.04 mm [0.0017 in].

8

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Save and Close the file.

SolidWorks 2012

Exercise 17 Shell Mesh Using Outer/Inner Faces

Exercise 17: Shell Mesh Using Outer/ Inner Faces

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The mid-surface location for the shell mesh is the most desirable. In some situation however, extraction of the midplane is too difficult or not convenient. In such cases the shell mesh can be placed on either the outside or inside face of the solid geometry. Because shell elements are suitable for these structures, the difference in results due to different position of the shell is rather small. This exercise reinforces the following skills:

I

Creating Shell Elements on page 285.

We will set up a new study with the shell mesh created on the outside faces of the solid model and compare the results with those obtained in the previous lesson. We must apply the external loads, fixtures and materials again because we are using different position for the shell mesh. The setup steps are only outlined below as they are the same as in the previous example.

1

Open the part file.

Open Pulley used in the Lesson 8 case study.

2

Define new study.

Define a new Static study named pulley shells - outside face.

3

Hide and exclude mid-surface. Hide and Exclude from Analysis the surface feature used in the lesson

case study.

Make sure that the solid body is shown.

4

Define shells.

Right-click on the SolidBody in the pulley folder and select Define Shell By Selected Faces.

Select all faces on the outside of the pulley.

Specify Thin shell with the Thickness of 2 mm.

5

Apply material.

Apply the material AISI 1020 steel to the offset surfaces.

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Exercise 17

SolidWorks 2012

Shell Mesh Using Outer/Inner Faces

Apply fixed restraint. Apply a Fixed Geometry

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6

fixture to the outside semicylindrical face, as indicated in the figure.

All boundary conditions and loads must be applied on the face where the shell mesh feature was defined; in our case the outside face.

Important!

7

Apply symmetry restraint.

Manually create a symmetry fixture on the outside top edges of the pulley, as indicated in the figure.

Review the case study used in the lesson for the specification of the symmetry boundary condition on surface feature.

Hint

8

Apply pressure.

Apply a pressure of 0.2 MPa (200,000Pa).

Note that the pressure must be applied on the outside face where the shell feature was defined.

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Exercise 17 Shell Mesh Using Outer/Inner Faces

9

Apply mesh control.

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Apply a mesh control with a Element size of 1.5 mm to the rounded face, as indicated in the figure. Keep the Ratio at the default value of 1.5.

10 Mesh the model. Select Standard mesh and mesh the model with High quality elements and the global Element size of 4.5 mm and a Tolerance of 0.225 mm.

Make sure that the shell mesh is aligned. To be consistent with the first part of this lesson, orient the mesh so that the bottom of the shell mesh coincides with the inside of the solid pulley.

11 Run the analysis.

12 Plot von Mises stress.

Plot the von Mises stresses on both the bottom and the top of the shell mesh.

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Exercise 17

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Shell Mesh Using Outer/Inner Faces

13 Examine the plots.

We can see that the maximum von Mises stresses on the top and bottom are 83.7 MPa and 67.46 MPa, respectively. These values are very close to the results obtained in the lesson, where the mesh was located exactly at the midplane.

In many applications, the midplane extraction is not a trivial process. Given the fact that shell mesh is applicable to thin sheet-like structures, the above modeling error is rather small and commonly acceptable.

14 Save and Close the file.

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SolidWorks 2012

Exercise 18 Spot Welds - Shell mesh

Exercise 18: Spot Welds Shell mesh

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We will now return to Exercise 13: on page 221 where we practiced the use of the spot welds. We will now compare the results of that exercise with the results of a study using shell elements. This study will also show the use of spot welds for shell sheets that are not in direct contact.

1

Open an assembly file.

Open tube solid located in the Lesson08\Exercises folder.

For the result comparison purposes this assembly contains the results of Exercise 13: on page 221, where this problem was solved using the solid elements.

2

Create new study.

Duplicate the study tube solid and name it tube shells.

3

Treat tubes as sheet metal.

Right-click on both bodies in the Parts folder and select Treat as Sheet Metal.This will define them as shells and their thickness will automatically transfer from SolidWorks.

4 5

Assign materials. Make sure that Galvanized steel is assigned to both sheets. Re-Mesh the assembly.

Select Curvature based mesh under Mesh Parameters. Create High quality mesh with the default settings.

6

Apply soft springs and specify direct sparse solver.

7

Run the analysis.

8

List reaction force and calculate torque. Using the identical procedure as in Exercise 13: on page 221, list the

circumferential component of the resultant reaction force and compute the resultant torque.

Compare your answer with the results obtained in Exercise 13: on page 221.

9

Save and Close the file.

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Exercise 19

SolidWorks 2012

Edge Weld Connector

Exercise 19: Edge Weld Connector

Single sided fillet weld

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A segment of piping system, welded at several locations, is to be tested on the extreme loads: 3.5 mm vertical and 1o degree torsional displacements applied at the end of the segment.

We will use FEA and the edge weld connector to simulate this problem. The size of the edge weld beads will also be designed.

Single sided groove weld

Double sided 3.5mm vertical and fillet weld 1 degree rotational prescribed displacements

This exercise reinforces the following skills:

I I

Project Description

Edge weld on page 191. Cylindrical Coordinate Systems on page 160.

A segment of the piping system manufactured from 5mm thick AISI 1020 steel sheets is anchored to a solid steel wall. The other side of this segment, modeled as free, is loaded with a 3.5 mm vertical and 1o rotational displacements applied at the free edge. These loads are known as the most extreme conditions to which the system can be exposed at this location. The components are connected using fillet and groove welds, as indicated in the above figure. Determine the optimum size of the weld beads at all three locations.

1

Open an assembly file.

Open Pipes located in the Lesson08\Exercises folder.

2

3

Set SolidWorks Simulation Options. Set the system of Units to SI (MKS), the units of Length to mm, and Stress to N/m^2. Create study.

Create a study named extreme loading.

4

Review Material properties.

Verify that the material definition, AISI 1020 Steel, has been transferred from SolidWorks to SolidWorks Simulation.

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SolidWorks 2012

Exercise 19 Edge Weld Connector

Edge welds can be defined between two shell bodies, or one shell and one solid body. The terminated part must always be represented by shell body. The edge weld beads are defined by the two faces which are connected and the edge on the terminated part representing the location of the bead. Electrode type, weld strength and the estimated weld size must be specified manually or taken from the library.

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Introducing: Edge Weld

Where to Find It

I I

Shortcut Menu: Right-click Connections, Edge Weld. CommandManager: Simulation > Connections Advisor > Edge Weld.

5

Define shells.

Define Thin shells for the pipe and the supporting sheet. Specify Thickness of 5 mm.

6

Define Edge Weld.

First, we will defined the edge weld bead between the first section of the pipe and the solid component representing the stiff steel wall. Right-click the Connections folder and select Edge Weld. Under Weld Type select the Fillet, Single-Sided.

For Face for Set 1, select the face of the terminated component, as shown in the figure below.

For Face for Set 2, select the face of the second component (in this case face of the solid component). For Intersecting Edges, select the weld bead location on the first terminated component.

Specify the weld to be on side 1 under Weld Orientation. This will place the weld on the top surface of the shell

Note

If we specified the weld to be on side 2, it would be on the bottom surface of the shell. Be sure to check the mesh to make sure the top and bottom are defined correctly.

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Exercise 19

SolidWorks 2012

Edge Weld Connector

Under Weld Sizing, Select the American Standard.

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Select E60 for the Electrode and enter 4 mm for the Estimated weld size. Enter the Safety Factor as 1. The Weld strength field is populated automatically based on the selected electrode. Click OK.

For the custom electrode properties select Custom Steel or Custom Aluminum under Electrode.

Note

7

Repeat the process for the remaining two edge welds. Similarly, create one Fillet, Double-Sided and one Groove, SingleSided edge welds as indicated in the figure below.

Use the same properties as specified in the previous step. For the groove weld, specify the location on side 1.

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Exercise 19

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Edge Weld Connector

Fillet, Double-Sided edge weld

8

Groove, Single-Sided

Apply fixtures.

Apply Fixed Geometry fixtures to the four faces of the rigid steel wall and to the bottom edge of the supporting sheet, as indicated in the figure.

9

Prescribe displacements.

Using Use Reference Geometry fixture type prescribe 3.5 mm vertical displacement to the end edge, as indicated in the figure.

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Exercise 19

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Edge Weld Connector

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Using Use Reference Geometry fixture type prescribe 1o (0.0175 rad) rotational displacement to the edge of the pipe. Use the cylindrical face as a reference and make sure that the direction of the rotation is the same as shown in the figure.

10 Mesh.

Mesh the assembly with the High quality mesh of the default size.

11 Check shell orientation.

We specified the welds on side one (top of the shell). We need to make sure the shell is aligned properly. If necessary, flip the shells to be aligned as shown in the figure below.

12 Run. Run the simulation.

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Exercise 19 Edge Weld Connector

13 Resulting displacements.

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Create the plot of the resultant displacements.

Note

The following post processing options for the edge weld are only available for Simulation Professional.

14 Post process the edge welds. Right-click the Results folder and select List Weld Results.

Under Selection dialog select SI for the Unit and All edge welds for the Type.

The table above shows all of the resulting weld forces for all welds in the model along with the computed minimum weld sizes.

Notice that the edge weld between the pipe and the supporting sheet is plotted green, while the remaining two are red. This result indicates that the estimated weld size (4 mm) entered in step 6 on page 321 is sufficient for the middle weld, while the other two need attention.

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Exercise 19

SolidWorks 2012

Edge Weld Connector

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15 Edge weld connector 1. Under Type select Edge Weld Connector-1.

Note that the maximum of the Weld size (mm.) row indicates the required weld size of 9.76 mm, which is significantly larger than the estimated weld size of 4 mm. The weld is therefore plotted in red. The yellow sphere and the red arrow in the above figure indicate the origin and the orientation of the weld bead.

Click the Plot button to see the variation of the required weld size as a function of the weld bead.

Click OK to close the Edge Weld Results dialog.

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SolidWorks 2012

Exercise 19 Edge Weld Connector

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16 Weld Check Plot. Right-click the Results folder and select Define Weld Check Plot.

Click OK.

The dialog window provides easy overview of the welds while the transparent plot indicates all welds in the assembly. Again, welds beads in red color need attention because their estimated size was not sufficient.

Tip

The European Standard for evaluating welds is also available. It is recommended to investigate the results available when using this standard. Additional information about weld sizing is also located in the Help menu.

17 Save and Close the file.

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Exercise 20

SolidWorks 2012

Container Handle Weld

In Container Handle on page 84, we assessed the design of the waste container handle. In this exercise you will size the double-sided fillet welds connecting the container handle to the two square base plates.

Double-sided Fillet welds

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Exercise 20: Container Handle Weld

All necessary information Base plates required for this task can be obtained from the text of the assignment in Exercise 3: on page 84. The base plates, welded to the container webs, can be assumed as rigidly fixed. This exercise reinforces the following skills:

I I I I I

Procedure

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Create mid-plane surface. on page 285. Exclude from Analysis on page 286. Thin vs. Thick Shells on page 287. Define the shell. on page 287. Edge weld on page 191.

The assembly for this study is located in the Exercises folder. Choose the most suitable location of the shell feature.

PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Lesson 9 Mixed Meshing Shells & Solids

Objectives

Upon successful completion of this lesson, you will be able to: I

Construct good quality mesh with the appropriate mesh controls.

I

Set up various shell to shell and shell to solid contacts in mixed mesh assembly.

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Lesson 9

SolidWorks 2012

Mixed Meshing Shells & Solids

There are many cases where a model has both thick and thin sections. In these cases, the mesh needs to be a combination of both solid and shell elements.

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Mixed Meshing Solids and Shells

In this lesson we will use the mixed mesh capabilities of SolidWorks Simulation to construct a mesh where solid elements “coexist” with shell elements in the same study. However, we will see that it takes extra efforts to ensure mixed mesh connectivity.

You will recall from the first lesson that nodes of a solid element have three degrees of freedom, meaning that node displacement is fully described by three translational components. You will further recall that nodes of a shell element have six degrees of freedom. Displacement of a shell element node is described by three translational components and three rotational components. y

Y

ROT Y

ROT X

ROT Z

z

x

DEGREES OF FREEDOM OF A NODE OF A SOLID ELEMENT

Z

X

DEGREES OF FREEDOM OF A NODE OF A SHELL ELEMENT

We usually show these displacement components (or degrees of freedom) as aligned with global coordinate system. However, degrees of freedom may be presented in any coordinate system.

Because nodes of solid elements do not have rotational degrees of freedom as compared to nodes of shell elements, an attempt to connect shell and solid elements results in an unintentional hinge along the common edge.

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Lesson 9 Mixed Meshing Shells & Solids

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The rotational degrees of freedom of shell element nodes have nothing to “hold on to” at the interface with solid element nodes. Therefore, these rotations remain unconstrained, forming a hinge along the connecting edge.

Hinge

With a hinge joint present, we have a discontinuous displacement field (discontinuity of rotations) and possible rigid body nodes in the model.

Shell Elements

Solid Elements

The incompatibility between shell and solid elements that lead to unintentional hinges is not specific to SolidWorks Simulation. It occurs in any FEA software every time we try to connect elements of different type having nodes with different numbers of degrees of freedom.

Bonding Shells and Solids

As a consequence of the element type incompatibility, the shell and solid portions of the mesh remain completely detached. The software enforces auto-bonding between a face or an edge of shell and a solid through multi-point constraints internally when the mesh is not compatible. In some special cases, it is best practice to define proper local bonded contact sets along all connecting edges and faces.

Mixed Mesh: Supported Analysis Types

Mixed meshing is available for static, frequency, buckling, thermal, nonlinear and linear dynamic studies.

Case Study: Pressure Vessel

This case study will involve the analysis of a pressure vessel. It consists of some thin wall elements such as the vessels shell. It also has thick walled elements such as the flanges.

In this case study, we will prepare the shown pressure vessel for the analysis (mesh, loads, contacts and supports) and solve a simplified static analysis. No conclusions on the design safety and similar topics will be made. This is the subject of Lesson 11 in SolidWorks Simulation Professional training manual, where ASME Boiler and Pressure Vessel Code governing the design of pressure vessels is discussed and utilized.

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Lesson 9

SolidWorks 2012

Mixed Meshing Shells & Solids

A pressure vessel manufactured from low alloy carbon steel SA 515, grade 60 shown in the figure is to be analyzed. The vessel is orientated vertically and supported on four lugs (see the figure) with slotted holes allowing the vessel to expand freely in the radial direction (detailed lug subassemblies are not needed for this analysis and are not included in the model). The maximum operating pressure load for the vessel is 165 psi at a temperature of 700° F. Besides pressure no other loads are considered in this analysis.

Top head

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Project Description

Manhole nozzle

Vessel Section 1

Small nozzle

Steam inlet

Vessel Section 2

Lug

Bottom head

Analyze the Assembly

Before proceeding, we need to analyze each subassembly and decide upon the appropriate mesh type. I

Pressure vessel body, top and bottom heads: The

thickness of the vessel body manufactured from 0.5 in carbon steel is very small compared to the outside vessel diameter of 56 in. Therefore shell elements will be used for these components.

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Lesson 9 Mixed Meshing Shells & Solids

Nozzles: The Steam inlet nozzle shown in the above figure is

manufactured from the same grade carbon steel piping with a 1 in wall thickness and the outside diameter of 24 in. The Manhole nozzle is manufactured from typical piping with wall thickness of 0.1875 in and a 20 in diameter. The lug support reinforcements as well as pipings have a thickness of 0.25 inches which is very small relative to the diameter of the lug pipings. Shell elements will therefore be used for the modeling of all nozzles and their reinforcements. Nozzle flanges and the Manhole cover: Nozzle flanges are not very thin and may be exposed to significant bending moments (especially the manhole nozzle flanges). The Manhole cover is also relatively thick and is bolted to the flange. Solid elements will therefore be used to study the accurate stress results at these locations.

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I

I

Procedure

Due to the time required to set up the study some of the study components as well as contacts have already been defined in study partially completed. We will make use of them during the study setup procedure.

1

Open an assembly file.

Open Pressure Vessel located in the Lesson09\Case Studies folder.

The model already contains study partially completed with many steps partially completed. Continue working with this study.

2

3

Verify the default units. Verify that the English (IPS) are set as the default unit system. Make sure that in is used for Length/Displacement and psi for Pressure/ Stress. Explode.

Explode the assembly to make it easier to see the individual components.

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Lesson 9

SolidWorks 2012

Mixed Meshing Shells & Solids

Before beginning the analysis, we decided which features we wanted to be meshed as shell elements and which would be solid elements. SolidWorks Simulation can generate shell mesh on either surfaces or faces of the solid bodies. To place the shell mesh on the mid-surface, a preferred location for the shell mesh, additional surface features must be generated in each part file; this procedure can be time consuming. Alternatively, we can place the shell mesh on the outside/inside faces of the solid bodies. We can then offset the shell so that it is recognized on the mid-surface of the body. This approach will be favored in the present case because it eliminates the need to generate additional midsurfaces.

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Preparing the Model

In the following steps, we will define the thickness for the shell elements.

Introducing: Shell Offset

If it is inconvenient to create the mid-surface within the solid body for the definition of the shells, you can choose to create the shell on the surface of the solid body and then offset the shell so that the software recognizes it as a mid-surface.

In the Shell Definition property manager, you specify the location of the shell by selecting a surface as the reference geometry. You then specify if you have selected a mid-surface, top surface, or bottom surface. If a top surface is selected, the shell will be located at a distance of half the thickness below the selected surface. Likewise, if the shell is defined as a bottom surface, the shell will be located at a distance of half the thickness above the selected surface. Additionally, if your shell should exist at some other distance away from that surface, you can select Specify Ratio.

Important!

334

You must be careful when specifying top, bottom, or offset because the mesh will ultimately define the shell location based on what is the shell top or bottom.

SolidWorks 2012

Lesson 9 Mixed Meshing Shells & Solids

Vessel body shell.

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4

Right-click on the corresponding solid bodies in the Simulation study tree and select Define Shells By Selected Faces.

Then, select the outside faces and specify Thin shell formulation with a Thickness of 0.5 in.

Select the Bottom surface as the Offset. When we mesh the model, we must insure that this surface is in fact the bottom.

The rest of the shell features was already defined beforehand.

Note

Both head shells consist of a 2:1 elliptical and 2 in straight sections, as recommended in the ASME Boiler and Pressure Vessel Code. Make sure that both faces are selected in the definitions of the vessel head shells.

The remaining components in the manhole area, Manhole cover and the Manhole nozzle flange will be meshed using solid elements, as decided in the beginning of this lesson.

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Lesson 9

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Mixed Meshing Shells & Solids

The data for SA 515, grade 60 carbon steel material can be obtained directly from the ASME Boiler and Pressure Vessel Code, Section II, Part D- Properties and is summarized in the table below.

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Material

Ultimate Tensile strength (room temperature)

60,000 psi

Yield tensile strength (room temperature)

32,000 psi

Mean coefficient of thermal expansion (70° F - 700° F)

7.6e-6 /°F

Thermal conductivity (700° F)

5.56e-4 Btu/(s-in-F)

Young’s modulus (700° F)

25.3e6 psi

Poisson’s ratio

0.33

Specific heat

0.09 Btu/(lb-°F)

Alternatively the material data can also be found from other sources (see the discussion below).

Steel Identification Systems

Some steel types may be identified using different systems (or standards), each with different nomenclature. We use SA 515, grade 60 specification typical in the ASME Boiler and Pressure Vessel Code. Section II, Part D- Properties lists basic material constants as functions of temperature and provide alternate information on the alloy identification. For SA 515, grade 60- the code lists an alternative identification UNS # K02401.

UNS Index

The Unified Numbering System (UNS) was created by a joint effort of Society of Automotive Engineers (SAE) and ASTM. Its goal is to provide a unique identifying system for metals and alloys.

Other Indices

Many indices for steel identification exist. For example, American Society for Testing and Materials (ASTM), American Iron and Steel Institute (AISI), Deutsches Institut für Normung (DIN), Euronorm and many others. Ask your instructor about the standards common in your geographical region.

Introducing: Analysis Research

We can also use SolidWorks Simulation Research to find the corresponding material data. Analysis Research can search both the analysis data base and Matweb. Once Research is selected, a new Analysis Research tab will appear in the Task Pane.

Where to Find It

I

336

Menu: Simulation, Research . Select the Analysis Research tab .

SolidWorks 2012

Lesson 9 Mixed Meshing Shells & Solids

Search for material properties. In the Simulation menu, click Research. In the Analysis Research dialog, enter K02401 in the Search Matweb field and click OK.

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5

The search results return the information for ASTM A284 Steel, grade C which is an alternative identification for UNS # K02401 carbon steel.

The following are the material data obtained from the Matweb database:

Note

Ultimate tensile strength

60,200 psi

Yield tensile strength

29,700 psi

Bulk modulus K

20,300 ksi

Shear modulus G

11,600 ksi

Density

0.284 lb/in3

We will use the data from the ASME Boiler and Pressure Vessel Code for our simulation. (The yield strength listed above is slightly smaller than the value listed in the ASME Boiler and Pressure Vessel Code.) However, each engineer is responsible for collecting their own reliable material data.

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Mixed Meshing Shells & Solids

Bulk and Shear Moduli

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We are familiar with the elastic modulus E (Young’s modulus) and the Poisson’s ratio ν as constants required to characterize linear elastic material. Bulk (K) and shear (G) moduli are alternative material constants and are related to E and ν as follows: 9KG E = -----------------3K + G

3K – 2G ν = --------------------6K + 2G

These relations hold for the traditional 3-dimensional isotropic analysis only. If other special analysis dimensions are used, modified equations have to be used.

Note

Out of all four linear elastic material constants (E, ν , G and K) a combination of any two is unique. The remaining two constants can be evaluated using the above relations.

Substituting the data for the bulk and shear moduli for our material we obtain 29,232 ksi and 0.26 for the Young’s modulus and Poisson’s ratio, respectively. Again, for our simulation we will use the material data provided by the ASME Boiler and Pressure Vessel Code.

6

Create custom material.

Right-click the Parts folder and select Apply Material to All.

In the Material window create a new category Lesson 9 materials, and add a new material SA 515, grade 60. Enter the material properties provided my the ASME Boiler and Pressure Vessel Code shown in the figure below.

Click Apply and Close.

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Lesson 9 Mixed Meshing Shells & Solids

Entities with clearance between them must be always bonded using local Bonded contact set.

Shell Face to Shell Face Bonding

Face to face bonded contact between two shells is always incompatible and will be automatically enforced if the faces are planar and touching. The user needs to manually define bonding for touching non-planar faces that are meshed with shell elements. Compatible meshing with global bonding will be effective for two shells that directly share an area created using split lines.

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Bonding Entities with Clearance

7

Manhole nozzle reinforcement vs. Vessel section 1 contact. Create a local Bonded contact between the two outer top edges on the Manhole nozzle reinforcement and the Vessel section1 shell.

Note

Use the large face of the vessel as Set 2. Also, since a clearance exists between these shell features, incompatible meshing is default for this interface.

Shell Edge to Shell Face Bonding

Whenever the shell edge coincides with the split line on the shell face, no local bonding is required. The top level assembly component (Global Contact) compatible bonding condition ensures that the interfacial nodes are merged. Additionally, auto-bonding will be enforced if the shell edge and solid face/shell face are part of a local component contact definition. The criteria for bonding are determined by taking the shell thickness into consideration.If there is a clearance between the edge source and the face target, local bonding must be defined.

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Mixed Meshing Shells & Solids

Vessel section 1 to Manhole nozzle contact. Define a local Bonded contact between the outer edge on the vessel opening and the Manhole nozzle shell.

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8

9

Shell to Solid Bonded Contact

340

Manhole nozzle reinforcement to Manhole nozzle contact. Specify local Bonded contact between the edge of the Manhole nozzle reinforcement and the Manhole nozzle.

The majority of the interfaces featured in our model represent shell to solid contact type. If there is a clearence between the shell and solid, it is best practice that local bonded contact is created. Also, a shell entity (face or edge) must be Set 1, while faces on the solid components must be Set 2.

SolidWorks 2012

Lesson 9 Mixed Meshing Shells & Solids

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10 Manhole nozzle flange to Manhole nozzle contact. Specify local Bonded contact.

Use the nozzle shell face as Set 1 and the solid face of the flange as Set 2.

Note

The remainder of the bonded contacts in this study was already defined beforehand.

11 Manhole cover to Manhole nozzle flange connection.

Since we practiced the definition of the bolted connections in the previous lessons, all of the bolted connections have already been defined in this study.

12 Manhole cover to Manhole nozzle flange contact. Define No penetration, Surface to surface contact between the Manhole cover and the top face of the Manhole nozzle flange as

shown in the figure. Make sure that Gap (clearance), Always ignore clearance option is selected.

Note

The gap (clearance) contact option must be used because the gasket between the Manhole cover and the Manhole nozzle flange is not modeled, creating an empty space.

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13 Lug supports.

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Lugs are connected to the pressure vessel using slotted bolt connections (not modeled) allowing for the radial displacements of the pressure vessel wall. This way no unnecessary stresses due to the supports are generated in the vessel.

Use Right assembly plane as reference and restrain the two in plane translations on the two lug supports parallel to the Right plane (Lug and Lug ).

14 Constrain other lugs.

Constrain the other two lugs in the same way with the Front plane as the reference.

15 Create mesh.

To begin the meshing phase let us mesh the model with Draft quality elements. Use the Standard mesh with the Global size of 2.711 in. The creation of the mesh fails and a message is shown: Mesh creation failed for the following 1 parts: Manhole cover-1

You can start Failure Diagnostics by right clicking the mesh icon in the Feature Manager and selecting Failure Diagnostics from the menu.

This can happen often if no local mesh controls are used in complex assemblies. Click Mesh Failure Diagnostic in the window.

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When meshing fails, it can sometimes be difficult to determine the cause. The Failure Diagnostics tool is used to help locate the problem.

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Failure Diagnostics Where to Find It

I

Shortcut Menu: Right-click Mesh folder and click Failure

Diagnostics

Meshing Small Features

In most cases when a difficult meshing problem occurs a small feature (or proximity of small features) exists in the assembly (or part). To successfully mesh such regions, correct local mesh controls must be applied.

16 Analyze mesh failure. The Failure Diagnostics indicates that the

mesh has failed on one of the faces of the Manhole cover part.

Select the face to see where the mesh has failed.

We can see that the mesh has failed on the face with the bolt holes. Elements cannot be jammed in between the bolt holes and the lip on the manhole cover.

The failure diagnostics gives us some options on how to deal with this failure. We will try to apply a mesh control to this face.

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17 Apply Mesh Control. With the Face-1 selected in the Failure Diagnostics, select Mesh Control.

Enter an Element Size of 1.5 in and click OK in the Mesh Control PropertyManager. The model should immediately mesh.

Important!

When using the Failure Diagnostics, only the failed parts are remeshed. This can save a significant amount of time since the computer does not have to re-mesh all of the geometry.

18 Apply mesh controls to the remaining components.

Mesh controls would have to be applied on other remaining components of interest (nozzles, flanges, and nozzle to vessel junctions).

All the remaining components mesh controls have been defined beforehand.

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19 Examine the mesh.

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This step completes the definition of the mixed mesh and all the appropriate contact conditions. Notice that the resulting mesh is incompatible even though, under the global bonding menu, compatible mesh was requested. As no two faces or edges touch, mesh compatibility is not possible. Lesson 6 explains that the compatibility settings applies to initially touching faces only. Further more, solid to shell interfaces are always meshed incompatibly.

20 Check shell alignment.

Remember when we defined the shell, we said that it was located on the bottom of the face. If we notice the mesh, the shell bottom is represented as an orange color. If we had defined the shells on the top, we would have to flip the shell elements so that the tops were shown on the outside of the vessel.

21 Explode.

Explode the assembly to make it easier to select components and faces.

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22 Hide the mesh. 23 Internal pressure in vessel and the nozzles. Apply a 165 psi Pressure load on all

vessel and nozzle shells.

Note

Make sure the pressure arrows point outwards to simulate internal pressure.

24 Internal pressure on Manhole cover. Apply a 165 psi Pressure on

the raised face of the Manhole cover.

25 Study properties. Select the Direct Sparse solver.

Note

Since multiple contatcs are defined in the study and the area of contact is found through several contact iterations, the Direct Sparse solver is preferred.

26 Run the study.

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27 Resulting displacements.

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We can observe the maximum displacements of approximately 0.19 in [4.95 mm], a fairly small amount given the vessel diameter of 56 in.

28 Von Mises stresses.

The maximum stress of approximately 62.4 ksi [430.4 MPa] occurs in the support lug location.

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Zoom in and analyze the location of this maximum. The stresses are localized along the bonded interface. Due to the incompatible bonding interface, large size and draft quality of the mesh, the stresses reach unrealistically large values along these bonded edges. The ASME Boiler and Pressure Vessel Code treats these localized stress concentrations in a special way. This area is the subject of Lesson 11 of SolidWorks Simulation Professional training manual.

In this study we are interested in the resultant contact force that would be used for the design of the weld rather than stress values, which are highly localized in this region.

29 Save and Close the file.

Note

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As was mentioned at the beginning of this lesson, no conclusions on the vessel design will be made. An example of the vessel analysis with regards to the ASME Boiler and Pressure Vessel Code is shown in Lesson 11 of the SolidWorks Simulation Professional training manual.

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In this lesson we practiced a design of the mixed finite element mesh with a combination of the solid and shell elements.

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Summary

The pressure vessel assembly featured multiple shell to shell and shell to solid bonded interfaces. Due to the nature of the shell modeling clearances (gaps) were created between various components. This is overcome by generating incompatible meshes where nodes along bonded interfaces are not merged, but rather constrained by the additional equations. It was shown that local bonded contact is necessary to properly bond mixed interfaces and interfaces with clearances.

An example of the procedure for the mesh design and a failure diagnostics was shown. Very small features, or rather small proximity of the features in the model may cause meshing problems. Proper mesh controls applied on such features are necessary. No conclusions were made on the design of the pressure vessel. To make conclusions on the design, we would need to refer to the ASME Boiler and Pressure Vessel Code that deals with the stress concentrations. This area is the subject of Lesson 11 of SolidWorks Simulation Professional training manual.

Questions

I

After generating all bonded contacts and successfully meshing a complex assembly you attempt to solve the analysis. The solver displays the following error message:

Frequently some of the bonded contacts are defined incorrectly or not at all as it is easy to unintentionally forget to define some of the contacts. Lack of proper fixtures or bonded contacts makes models unstable, resulting in the solver displaying the above message. Propose a solution how to locate missing/incorrect restraints or bonded contacts.

I

A bonded contact between the shell and solid components (does / does not) require a local bonded contact condition.

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Exercise 21: Mixed Mesh Analysis

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In this exercise, we will analyze a pump impeller that requires a mixed mesh due to the differences in thickness between the blades and the hub. This exercise reinforces the following skills: I I I I

Project Description

Mixed Meshing Solids and Shells on page 330. Bonding Shells and Solids on page 331. Define the shell. on page 287. Shell to Solid Bonded Contact on page 340.

A water pump impeller operates at 2000 rpm. Analyze the impeller to determine the deformation of the blades and the stress magnitudes. The centrifugal force in this case doesn’t have a significant impact on the results of this analysis and will be neglected.

1

Open a part file.

Open Impeller01 from the Lesson09\Exercises folder.

2

Create study.

Create a Static study named centrifugal 01.

3

Apply Fixtures.

We assume that a solid circular shaft is rigidly connected to the impeller. Therefore, to simulate a presence of the shaft, apply FIxed Geometry boundary condition to the cylindrical face shown in the figure.

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Apply force load. Apply a 8.9 N Normal force

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4

on each of the blades. Make sure the force load points in the correct direction (see the figure).

The pressure resultant force was computed using SolidWorks Flow Simulation software for this problem.

Note

5

Shell surfaces.

Define 16 shell features representing the blades of the impeller. Specify Thin shell formulation with a Thickness of 1 mm.

6

Apply Material.

Assign Chrome Stainless Steel to all the components.

7

Apply Mesh control.

For more accurate resolution of the bonded contact between the shell features and the solid body of the impeller, specify a local mesh control on the blade edges. Use the Element size of 2.5 mm with the Ratio equal to 1.2.

8

Blades to the impeller body bonding. Specify local Bonded contact

between the blade edges and the body of the impeller. Use the 16 lower edges on the blades as Set 1 and the top face on the body of the impeller as Set 2.

Note

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The global bonded contact setting is not important. As explained in

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Exercise 21 Mixed Mesh Analysis

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Lesson 9, shell edge and solid parts bonding require local contact conditions. 9

Create Mesh.

You may now create a Draft quality Curvature based mesh with the default settings.

10 Study properties. Select the Direct Sparse solver. 11 Run analysis.

12 Radial displacement.

To view radial displacement results, construct a plot showing UX component displacement. Use the Axis1 of the model as a reference so UX becomes the radial component of displacement.

We can observe a radial displacement of -9.34e-4 mm at the tips of the blades.

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13 Von Mises stress.

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To plot von Mises stress we don’t need to use any reference geometry because von Mises stress is a scalar stress measure. To better picture stress results around the support, use a section view.

We can observe a very small von Mises stress value of 4.01 MPa depicted in the figure below. The stresses along the blade bonded to the impeller are localized; the actual stress magnitude along the bonded edges would be different due to the presence of the weld.

While stresses are rather small, displacements results are important due to the pump manufacturing clearances and effectiveness.

To obtain accurate results, finer mesh and high quality elements need to be used. Such detailed analysis on the entire model may take a significant amount of time, circular periodicity of the model can be used to simplify the problem.

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Any model which can be generated by revolving its part about an axis is said to be rotationaly periodic. All such components can be conveniently analyzed with the help of the cyclic symmetry boundary condition.

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Circular Symmetry

14 Activate configuration periodicity.

15 Study.

Define a new Static study named periodicity.

16 Exclude surface bodies

Exclude all surface bodies except SurfaceBody 4.

17 Simulate shaft. Apply Fixed Geometry restraint on the remainder of the cylindrical

face.

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18 Simulate circular periodicity. Apply Circular Symmetry

fixture on the pair of faces exposed by the cut. Use Axis1 as a reference Axis.

Note

You must select a pair of two faces where one can be created by the rotation of the first face about the reference axis (in this case Axis1, for example).

Specify the same Circular Symmetry conditions for the remaining two pairs of impeller faces exposed by the cut.

19 Shell feature.

Define one shell feature in contact with the solid part isolated by a cut. Specify Thin shell formulation with a Thickness of 1 mm. Exclude the unused blades from the analysis.

20 Apply load. Apply an 8.9 N Normal force to the shell feature. Make sure the

orientation of the force is the same as in the analysis of the entire model.

21 Material. Assign Chrome Stainless Steel to both solid and shell features.

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22 Mesh control.

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Apply a local mesh control along the lower blade edge in contact with the impeller face. Use 2 mm for the Element size and 1.2 for the Ratio.

23 Blade to impeller bonding. Similarly, create Bonded contact between the

lower edge on the blade and the top face of the impeller.

24 Create mesh. Select Curvature based mesh under Mesh Parameters.

Mesh the model with the High quality elements and the default settings.

25 Study properties. Select the Direct Sparse solver. 26 Run analysis.

Notice how quickly the study completes even when High quality elements are used.

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27 Radial displacement.

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We can observe that the radial displacement, at the indicated tip of the blade, changed to -9.20e-4 mm, which indicates a slight decrease compared to the radial displacements obtained from the full model. The difference is due to the high quality elements and finer mesh settings. You may try to generate a draft quality coarser mesh with the same parameters that were used in the analysis of the entire model to verify that results agree well.

28 Von Mises stress.

We also observe that the location as well as the maximum of the von Mises stress changed.

29 Save and close the file.

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In this model, we analyzed the stresses and displacements on the impeller. Typically, an impeller like this is loaded cyclically (i.e. dynamically). To continue this analysis, one would want to solve for the natural frequencies of the systems to verify that any locaing frequencies will not affect the dynamic response. This could be done using SolidWorks Simulation Professional. Additionally, a dynamic study could be utilized to solve the full dynamic solution. This could be done with SolidWorks Simulation Premium.

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Summary

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PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Lesson 10 Mixed Meshing Solids, Beams & Shells

Objectives

Upon successful completion of this lesson, you will be able to: I

Construct a mesh with beam, shell and solid elements.

I

Edit beam joints to add/remove beams from a joint (Exercise 23)

I

Set up various shell to beam and shell to solid contacts in mixed mesh assembly.

I

Display the results obtained with beam elements.

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To this point, we have used two types of elements to mesh our models. For most thick bodies we used solid elements. When the structure became thin in one direction, such as a sheet metal part, we used shell elements to avoid creating a very large number of elements. When the part becomes thin in two directions we use beam elements.

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Mixed Meshing

In some structures, we may have a combination of geometry that is best analyzed with beams for weldments, solid elements for thick components and shell elements for thin components.

Model courtesy of Tamoz, spol. s r. o.

Case Study: Particle Separator

In this case study, we will analyze the base of the particle separator. The base consists of a weldment with various gussets. The particle separator uses a combination of geometry that will require use of beam elements for the weldment base and shell elements for the various plates and the body of the separator. The weldment lends itself to analysis with beam elements, while the cross gussets are thin sections that are best analyzed with shell elements.

Project Description

The loads on the support frame consist of the weight of the particle separator structure itself that will be applied using gravity. An additional load of 150 N will be applied to the front of the structure in the downward direction to simulate the presence of an additional component that will be attached to the separator. Finally, on the intake of the particle separator, loads of 75 N and 45 N will be applied to simulate additional loading that the separator might experience during installation.

Element Choices

The frame can be analyzed using both solid and shell elements, but both would result in an excessive number of elements. Also, the construction of the mesh along with the corresponding contact conditions may take some time. In this lesson, we will use beam elements for the weldment structure which will allow us to greatly simplify the model with a minimum sacrifice on the side of the accuracy.

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Beam elements

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Beams are another class of structural elements where all of the crosssectional characteristics are accounted for during the derivation of the element stiffness matrix. As a beneficial consequence, these crosssectional characteristics do not need to be reflected in the finite element mesh, thus, greatly simplifying the model preparation and analysis.

In general, the beam element has two nodes with six degrees of freedom in each node. For more information, consult the Introduction chapter of this manual.

Stages in the Process

I

Create beam elements

When weldments are analyzed, beam elements will be created automatically.

I

Calculate joints

The existing joints between elements are created.

I

Merge joints that are too close

The joints are reviewed to determine if joints are too close to each other. Joints can then be merged to get a better mesh.

I

Specify joint types

The number of degrees of freedom at each joint is specified.

I

Apply fixtures and loads

The exterior constraints and forces are applied.

I

Mesh the model

A beam mesh is created.

I

Run the analysis

The study is run in the same way as any other mesh.

I

Plot and analyze the results

Examine the analysis results and determine further action.

1

Open an assembly file. Open particle separator 450 located in the Lesson10\ Case Studies folder.

Examine the assembly to familiarize yourself with the components.

2

Set SolidWorks Simulation options.

Set the global system of units to SI (MKS) and the units of Length and Stress to mm and N/m^2, respectively.

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3

Naming convention.

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For clarity, we will identify some of the parts by the names we will use in the following steps.

4

Separator body

Static study.

Continue working in the static stress study. Some features in this study have been completed beforehand to save time.

Mounting bracket

Cross Gusset

Feet

5

Examine the parts folder. There are four types of parts/bodies in the folder.

The three cross gussets, located where the diagonal braces cross, are modeled as solid bodies. They will be meshed as shell elements on the outer face of the solid bodies. The four feet on the end of each leg are modeled as solids and will use a solid mesh.

The remaining parts on the frame are all weldment parts and will be meshed as beam elements.

Shell

Solid

Beam

Shell

All components of the particle body are modeled as solids, but will be meshed with shells. Four mounting brackets are modeled as solid components.

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6

Cross gusset plates.

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Define shells for the three Cross Gusset plates. Use the outside faces of the solid bodies, and specify Thin shells with the Thickness of 5 mm.

7

Shells

Shell definitions and bonding for the separator body.

All shells and bonding conditions for the separator body have been defined beforehand.

8

Solid parts.

The eight parts named Feet are thick solids. We will not do anything with them in the tree and they will mesh as solids.

The four Mounting Brackets are solid bodies. The bonding with the separator body has already been defined.

9

Exclude unused surfaces. The three surfaces in the Cyclone Particle Separator subassembly are

used for the design of the particle separator body only. They will be therefore excluded from the meshing phase and the simulation. Exclude from Analysis the three

indicated surfaces.

Beam Mesh

To mesh any extruded or revolved solid feature with beam elements, right-click on the feature and select Treat as Beam. The icon in the parts folder will then indicate the beam mesh.

Similarly, to mesh any beam feature (for example weldments) as solid, right-click on the feature and selected Treat as Solid.

10 Weldment parts.

All the remaining parts are part of the weldment that we will mesh using beam elements. Select all the remaining parts, then right-click and select Treat selected bodies as beams.

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11 Examine the Parts folder. The Parts folder should look as below:

Solid bodies

Solid bodies of the separator body modeled as shells

Surfaces Excluded from analysis

Beams

Solid bodies of the cross gussets modeled as shells

Solid bodies

12 Apply material.

Apply the material AISI 1020 Steel to all the parts and bodies.

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All of the beam cross-sectional characteristics are already included as parameters during the derivation of the beam element stiffness matrix. The resulting mesh is, therefore, made out of lines connected by joints. The example of such lines representing the beams in our model is shown in the figure.

Joint 1

Joint 2

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Beam Joints: Locations

The joints define the straight or curved segments that will be meshed with beam elements. While the detection of the joints is automated in SolidWorks Simulation, the relative position of some joints may be too close and we may wish to merge them, i.e. merge two segments into one. In the figure, the joints 1 and 2 are relatively close and might be merged.

Sometimes the automatically generated joints must be modified manually.

Beam Joint Types

Each beam end point features six degrees of freedom that may be restrained or released to reflect various structural connection configurations. SolidWorks Simulation offers the following options to connect the end point of the beam element to the joint: I

Rigid - All six degrees of freedom are

tied to the joint. This connection type transfers all force as well as all of the moments from the beam element to the joint (and vice versa).

I

Hinge - Only three degrees of freedom are tied to the joint. The

connection is not able to transmit the moments from the beam to the joint (and vice versa).

I

Slide - The end can translate freely and does not transfer forces to

I

the joint. Manual - A custom designed connection type can be generated.

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All beam properties are computed automatically from the solid geometry. The beam section properties calculated by the program can be overwritten with userdefined values in the Section Properties dialog.

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Section Properties

I

Torsional Constant, K- Torsional

stiffness constant is calculated by the program. The values for commonly used beam cross-sections are available in literature (see Formulas for Stress and Strain, Roark and Young, Chapter 9, Table 20, for example).

I

Distance for Maximum Shear, CTOR- Distance from the center

of the section to the point of maximum torsional shear .

Where to Find It

I

Shear Factor in direction 1- Shear factor to account for non-

I

uniform shear stress in direction 1 of the beam coordinate system Shear Factor in direction 2- Shear factor to account for nonuniform shear stress in direction 2of the beam coordinate system

I I

Shortcut Menu: Right-click a beam element in the Simulation Study Tree and click Edit Definition. To see the shear center line of a beam, right-click Joint group and select Edit. Under Results, select Display shear center.

13 Edit joints.

Once we designated a body to be treated as a beam, a new item appeared in the Simulation Design Tree called Joint group. Right-click the Joint group and click Edit. For Selected Beams, select All.

Click Calculate.

The joints computed with the default settings can be seen in the figure.

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The beam joints are show as yellow or magenta spheres.

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Connected and Disconnected Joints

I

I

joints are connected to two or more beam members. joints are connected to a single member only and are therefore disconnected from the other beams. Such nodes may need to be manually connected to the adjacent beams elements or bonded to other parts.

Sphere Diameter Defining Beam Joint

By default, the software creates a joint between two beams touching end-toend (clearence is zero). It is, however, possible to modify the diameter of a hypothetical sphere defining the joint. All beam ends within such hypothetical sphere will form a new joint.

Treat as Joint for Clearance

I I

equal to zero: Creates a joint when beam ends are touching. less than:Beams ends within such clearance will be included in one joint definition. Keep modified joint on update must be

checked to retain the newly computed joints.

Where to Find It

I

Shortcut Menu: Right-click Joint Group in the Simulation Study tree and select Edit. Under Selected Beams select Treat as joint for clearance option.

14 Bond diagonals to gussets. Add a Bonded contact between

each set of two diagonal braces and the cross gusset.

Note

Make sure that you select the outside face of the cross gusset solid body used for the shell definition (step 6).

15 Explode the assembly view.

The exploded view will make it easier to create the contact sets between the sheet metal corner gussets and the frame elements.

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16 Bond Mounting Brackets to frame. Use bottom face of each Mounting Bracket to bond it to the top

beams of the frame, as shown in the figure below.

17 Collapse the assembly.

18 Add fixtures. Add Fixed Geometry Fixtures to bottoms

of four feet.

Applying Loads

The beams button allows us to apply the loads directly on the structural members. It is also possible to apply loads directly onto the joints or on faces, edges, or vertices of extruded bodies.

19 Apply External Loads. Apply a 150 N vertical load applied on the

indicated beam to simulate the additional weight of the component that may be added to the structure at a later time.

Note

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The distributed load is applied on the horizontal beam where no diagonal braces are present.

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75 N

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Apply 75 N and 45 N forces located at the back face of the inlet. These loads can be generated during the assembly phase.

45 N

Note

The forces must be applied on the faces used to define the shell features, as shown in the figure.

20 Gravity load.

Specify gravity load in the global positive Z direction.

21 Apply mesh control to beams Click on Beams under Selected Entities and

select the four horizontal beams. Select Element size and enter a value of 5 mm.

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22 Mesh.

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Mesh the assembly using High quality elements. Use the Standard mesh with the element Global Size of 25 mm.

23 Examine the mesh.

You can see the three different mesh element types.

You can see the three different mesh element types.

Render Beam Profile

It is possible to display the mesh and results for beams as cylinders (simplified representation) or the actual beam profiles. Displaying the mesh or results on the beam profiles may take longer for models with a large number of beams.

Where to Find It

I I

Menu: Simulation, Options, Default Options, select Mesh and activate Render beam profile. Shortcut Menu: Right-click Mesh and select Render beam profile.

24 Align the mesh.

Make sure that the shell top and bottom are aligned and consistent. This step is important for the correct postprocessing.

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Mixed Meshing Solids, Beams & Shells

Note

The default shell mesh alignment shown on the left image may vary. Align the mesh as shown in the right image.

Beam imprint

When the beam joint is bonded to a solid or shell face, the mesher creates an imprint of the actual beam cross-section on the touching face. This generates a more realistic representation of the joint leading to better results at the beam-solid/shell interface. Additional elements are created in the area of the imprint and the beam joint is connected to all the elements inside the imprinted area. In case the beam's crosssection is not entirely on the touching face, the imprint is created based on the partial touching cross-section.

25 Run. Run the study.

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26 Displacement Plot.

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Examine the displacement plot. The maximum displacement of 0.149 mm at the inlet location is rather small.

27 Stress plot.

The initial stress plot will show the Von Mises stresses in the solids and shell.

The maximum reaches approximately 11.93 MPa and is located in the Mounting Bracket where the vertical load is applied. Because this stress maximum is located at the junction of the bracket and shell, detail analysis of this connection may be required. Also, review of the stresses on both the top and the bottom faces of the shell elements is needed.

Note

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This plot only shows the stress distribution on the solids and shells. We will next see the stress distribution in the beams.

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28 Redefine the stress plot. Right-click the plot Stress1 and click Edit Definition.

Select Beams to show the stress in the beam elements. From the list, select Axial.

The maximum tensile stress of 0.91 MPa is in one of the diagonal braces whereas a compressive stress of -1.53 MPa is induced two of the legs.

Note

Again, this plot only shows the stress distribution in the beams.

Cross-section 1st and 2nd Directions

To post-process the bending component of the normal stress, 1st and 2nd directions must be specified.

1st direction is defined along the longest side of the cross-section, and 2nd direction is perpendicular to it.

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SolidWorks 2012

Mixed Meshing Solids, Beams & Shells

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29 Additional stress plots.

Define two new stress plots to show the bending in directions 1 and 2. Render beam profile should be selected.

Maximum bending stresses are 4.97 MPa and 5.37 MPa at the indicated locations.

30 Highest axial and bending.

Edit any of the plots and select Axial and bending. This will show the combined stress from axial and bending in both directions. The absolute maximum combined stress in any of the beam elements is 7.02 MPa.

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SolidWorks 2012

Lesson 10 Mixed Meshing Solids, Beams & Shells

More experienced users may produce a plot of the bending moment and shear force diagrams. They can be used to study how the internal bending moments and shear forces vary along the beam, or for the subsequent design of more complex composite beam members.

Where to Find It

I

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Bending Moment and Shear Force Diagrams

Shortcut Menu: Right-click Results folder and select Define

Beam Diagrams.

31 Show Bending moment diagram. In the Beam Diagrams dialog, under Display select Moment in Dir1. Specify the units of N-m.

Under Selected Beams click Select and select the beam shown in the figure.

32 List Beam Stress.

Right-click on the Results folder and select List Beam Forces.

Under List select Stresses, set the units to SI and click OK.

The List Stresses dialog window shows a complete list of maximum (minimum) normal and shear stresses for all beam elements.

33 Save and Close the file.

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Lesson 10

SolidWorks 2012

Mixed Meshing Solids, Beams & Shells

In this lesson, we analyzed a support frame model. Since all the structural members were thin and long, we used beam elements. Their use can greatly simplify the analysis and make the computations significantly faster.

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Summary

The model preparation consists of beam element and joint definition steps, both of which are automated in SolidWorks Simulation. Sometimes manual editing of the automatically generated joints may be required . If any two joints are generated too close, relative to the position of the remaining joints, they may be merged. Because beam elements feature six degrees of freedom at each end, various possibilities for the joint / beam element connection exist.

We usually show these displacement components (or degrees of freedom) as aligned with global coordinate system. However, degrees of freedom may be presented in any coordinate system.

Because nodes of solid elements do not have rotational degrees of freedom as compared to nodes of shell elements, an attempt to connect shell and solid elements results in an unintentional hinge along the common edge. To make final conclusions on the analysis, it could be important to review the stresses at the joint locations. Due to the limitations of the bonding between beam/shell and solid, the software does not produce an accurate result at the interface. A model with only solids could be run to better investigate the stresses at these locations.

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SolidWorks 2012

Exercise 22 Beam Elements

Exercise 22: Beam Elements

Defective weld

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The simplified model of a conveyor frame (shown in the figure) is manufactured from Plain Carbon Steel with all the joints welded.

Moment Foundation

During the inspection, it was found that the weld at the indicated joint became defective and was not capable of transmitting the moments.

In this exercise you will analyze the frame when subjected to the extreme operating loading conditions (combination of an isolated force and a moment). All six legs of the frame are bolted to the ground but only the two inclined legs can actually transmit the moments to the floor. This exercise reinforces the following skills: I I I I I

Procedure

Mixed Meshing on page 362. Beam elements on page 363. Beam Joint Types on page 367. Bending Moment and Shear Force Diagrams on page 377. Applying Loads on page 370.

Follow the steps below:

1

Open a part file.

Open Conveyor Frame located in the Lesson10\Exercises folder.

2

3

Set SolidWorks Simulation options. Set the global system of units to SI (MKS) and the units of Length and Stress to mm and N/m^2, respectively. Create new study.

Create a new static study named frame.

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Exercise 22

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Beam Elements

4

Beam elements.

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Expand the folder Conveyor Frame and you can see that all the solid bodies of the weldment have a beam icon .

Right-click the Cut List folder and select Delete. All the beams are now in the Conveyor Frame folder.

The sixteen beam elements were automatically generated because the part file was a weldment. There is also an additional folder called Joint group .

Slenderness ratio

Beam elements are typically used to represent long, slender components. For the beam formulation to produce acceptable results, the length of the beam should be 10 times larger than the largest dimension of its cross section.

The software automatically detects the ratio and warns the user about the beams having a slenderness ratio of less than 10.

5

Specify material.

Assign Plain Carbon Steel for all beam elements.

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Exercise 22 Beam Elements

Review the calculated joints. Right-click on the Joint group folder and select Edit. The automatically calculated

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6

joints will show on the screen.

If needed, the joints may be modified and re-calculated. In this exercise this step is not required.

7

Mesh the model.

Mesh the model with the default element size.

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Exercise 22

SolidWorks 2012

Beam Elements

8

Define faulty weld joint.

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The faulty weld in the indicated joint eliminates the possibility to transfer moments between the beam element and the joint. The moment ties can be released by specifying the pin connection type.

Under the Conveyor Frame folder, right-click on the beam element corresponding to the inclined member with the faulty weld and select Edit definition.

9

Create a hinge.

The two end points are graphically shown as red and blue circles.

Select Hinge for the upper connection between the joint and the beam. Click OK to confirm the settings.

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Exercise 22 Beam Elements

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10 Restrain the vertical legs. Apply an Immovable fixture to the bottom joints on all four vertical

legs.

11 Restrain the inclined legs. Apply a Fixed Geometry

restraint to the bottom joints on the two inclined legs.

12 Apply loads on top beams. Right click the External Loads folder and select Force.

Under Selection click Beams then select the two beams shown.

Apply 67,000 N [15,062 lb] force in the Normal to Plane direction (with reference to the Top plane). Select Reverse direction. Click OK.

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Exercise 22

SolidWorks 2012

Beam Elements

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13 Define loads on corner joint.

To apply a force or moment directly into the joint click the Selection (Joints) button in the Force menu (see the figure).

Apply a 45,000 N [10,116 lb] force and a 2,260 N-m [20,000 lb-in] moment to the corner joint. The force and the moment are oriented in the Normal to Plane and Along Plane Dir1

directions with reference to the Front plane, respectively.

14 Run the analysis.

Notice how quickly the study completes. If solid or shell elements were used instead, the computations would take considerably longer.

15 Plot resulting displacements. Define a RES: Resultant displacement plot.

Zoom closer to the section where both inclined members connect to the top of the frame. Notice that the member with the faulty weld rotated at the joint location, while the other member remains perpendicular irrespective of the structural deformations. This indicates that the faulty weld connection does not transmit moments, indeed.

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SolidWorks 2012

Exercise 22 Beam Elements

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16 Plot axial normal stress. Define an Axial stress plot.

The Axial stress plot indicates a component of normal stress evenly distributed across the cross-section of the beam element caused by normal (axial) force. We observe a maximum tensile value of approximately 13.4 MPa (1.94 ksi).

17 Plot normal stress due to bending. Define Bending in local direction1 and Bending in local direction2

stress plots.

Direction 1

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Exercise 22

SolidWorks 2012

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Beam Elements

Direction 2

These plots indicate the maximum and minimum values of the normal stress (extreme fibers location) caused by the bending moments. We can observe a significantly greater value (than in the Axial stress plot) of -569 MPa [-82.5 ksi] (negative sign indicates compression).

A total normal stress experienced by a cross-section is equal to the sum of the axial and bending components: the hightest axial and bending stress plot.

18 Plot the extremes of the total normal stress. Define an Axial and bending stress plot.

This plot adds the Axial and the Bending in local direction1 normal stresses. It is the plot of the most extreme normal stress experienced by the beam cross-sections. We can see that the maximum tensile stress of 446 MPa [64.7 ksi] significantly exceeds the yield strength of Plain Carbon Steel 220.6 MPa (32 ksi).

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SolidWorks 2012

Exercise 22 Beam Elements

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19 Plot bending moment diagrams. Right-click the Results folder and select Define Beam Diagrams.

Under Display select Moment in Dir 1 and the units of N-m. Under Selected Beams, click Select and pick the inclined beam with the faulty weld.

Click OK to plot the diagram.

We can see a linear variation of the bending moment in the elemental direction 1. Note that the moment at the faulty joint is zero.

The large negative value of -3850 N-m then corresponds to the moment along the elemental direction 1 transmitted to the floor.

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Exercise 22

SolidWorks 2012

Beam Elements

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20 List beam stresses. Right-click on the Results folder and select List Beam Forces.

Under List select Stresses, set the units to SI and click OK.

The List Forces dialog window shows a complete list of maximum (minimum) normal and shear stresses for all beam elements.

21 Save and Close the file.

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SolidWorks 2012

Exercise 23 Cabinet

Exercise 23: Cabinet

Analyze a cabinet with an applied load.

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This exercise reinforces the following skills: I I I I

Project Description

Beam elements on page 363. Beam Joints: Locations on page 367. Connected and Disconnected Joints on page 369. Applying Loads on page 370.

A cabinet manufactured from Aluminum 5052 H32 is loaded by an isolated 4,450 N [1000 lb] force and two 4,450 N [1,000 lb] loads distributed along the two corner beams of the cabinet, as shown in the figure. All other loads and masses (such as shelf loads, etc.) are not included in this analysis to keep the model simple. The bottom of the cabinet, along with the pedestal, are bolted to the floor. Compute the factor of safety of the model.

1 2

Open an assembly file. Open Cabinet Assy located in the Lesson10\Exercises folder. Create study.

Create a Static study named stress analysis.

3

Define shell thicknesses.

Using the inside faces, define shell features for the skins of the cabinet. Specify Thin shell formulation with the Thickness of 2.54mm [0.1in].

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Exercise 23

SolidWorks 2012

Cabinet

Define beam joints. Right-click on the Joint group folder and select Edit.

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4

At each of the eight corners, there should be either one or two joints, connecting all of the beams that converge on that corner. See the figure.

Note

Joints identified as yellow spheres are attached to a single member. Violet color identifies the joints which connect at least two beam members.

The joints can be merged by entering a user-defined value through Treat as joint for clearence.

Select less than and enter a value of 0.1 m. Click Calculate to update the joint definitions.

Click OK to complete the definition of the joints.

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SolidWorks 2012

Exercise 23 Cabinet

Optionally, the joints can also be merged by adding or removing a beam member. Right-click each joint to examine the components that form the joint.

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Tip

In the Select Joint Members window, click the components in the graphics window to add or remove them from the joint.

To save the new joint definition, close the Select Joint Members window. Make sure Keep modified joint on update is selected and click Calculate. Repeat the procedure for all the joints that need to be merged.

5

Assign materials.

Specify Aluminum 5052-H32 for all Solids, Shells and Beams.

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Exercise 23

SolidWorks 2012

Cabinet

Bond skins to the cabinet frame. Specify Bonded contact condition between the frame beams and the

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6

skin shell on the left hand side, as shown in the figure.

Click OK.

To select Beams for the Set 1, click the Beams

Note

under Type.

Repeat the definitions of the bonded contacts between the beams and the skin shells for the right, back, and top sides of the cabinet.

7

Bond frame bottom beams to the frame bottom plates.

The two solid frame bottom plates must be bonded to the two frame beams.

Frame Plates

These contacts have been defined in the Completed contacts study.

Copy all the contacts from the Completed contacts study into our current study, stress analysis.

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SolidWorks 2012

Exercise 23 Cabinet

Contact between Base and the frame. The frame side plates and the Base are bolted to the floor. For

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8

simplicity we will model this contact as bonded. Bond the circular edges of the bolt holes on the frame side to the top face of the base.

9

Fix the Base.

Apply a Fixed Geometry fixture to the cylindrical faces of the four holes in the Base.

10 Frame plates vs. base contact. Specify No penetration, Node to Surface contact between the bottom

faces of the frame plates and the base, as shown in the figure.

Note

We use the Node to Surface formulation here because the parts are initially touching and we expect little or no sliding between the two bodies.

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Exercise 23

SolidWorks 2012

Cabinet

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11 Concentrated joint load. Apply a 4450 N [1000 lb]

concentrated vertical force to the top corner beam joint, as shown in the figure. Make sure to select

Selected direction to

define the force on the joints.

Note

394

In mixed mesh analysis the Force can be applied to the faces, edges or vertices of the solid components or shells, beam joints and along the length of the beam components.

SolidWorks 2012

Exercise 23 Cabinet

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12 Distributed beam load. Apply 4450 N [1000 lb]

distributed vertical load on the two beams indicated in the figure.

13 Create mesh. Create a High quality Curvature based mesh

with the following

parameters: Maximum element size = 111.37mm, Minimum element size = 5mm, Min number of elements in a circle = 16, and Element size growth ratio = 1.6. .

Make sure that the shell tops and bottoms are consistent.

14 Mesh details.

Show the mesh details.

Combined mesh with beams, shells and solids resulted in approximately 39,200 nodes.

15 Run the study stress analysis.

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Exercise 23

SolidWorks 2012

Cabinet

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16 Plot von Mises stress.

It can be seen that the maximum von Mises stress in solid and shell feature, 142.68 MPa, is at a sharp corner. This is an area of singular stress and can be ignored. There is also some high stress in the vicinity of the holes that are bonded to the bottom plate(you can verify that both the Top and the Bottom indicate identical maximum value).

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SolidWorks 2012

Exercise 23 Cabinet

17 Plot beam stresses.

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Edit the definition of the stress plot and select Beams. Select Axial and Bending as the Beam Stress. Select the Render beam profile option.

The highest axial and bending stress plot in beam elements indicate a maximum stress of 43 MPa. We can therefore conclude that the factor of safety in strength is approximately 195 MPa/43 MPa = 4.5 (195 MPa is the yield strength of the Aluminum 5052 H32). This result indicates that the cabinet frame is designed with sufficient factor of safety.

18 Plot resultant displacements.

The maximum displacement of the cabinet is approximately 1.31 mm.

19 Save and Close the file.

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Exercise 24

SolidWorks 2012

Frame Rigidity

In this exercise, you will calculate the torsional rigidity (i.e. applied torque divided by radial displacement) of a car frame.

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Exercise 24: Frame Rigidity

This exercise reinforces the following skills: I I I

Problem Description

Cylindrical Coordinate Systems on page 160. Beam elements on page 363. Beam Joints: Locations on page 367.

There are many ways to measure the torsional rigidity of a frame. In one experiment, the front and rear wheels are mounted on beams. The suspension components are assumed to be fixed so that all of the load applied is transferred to the frame itself. The rear of the vehicle is held stationary (fixed) while a load is applied to the beam with the front wheels to simulate the torque as shown in the figure below.

Force

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courtesy of: Stephen Maxfield, University of Wisconsin

Force

SolidWorks 2012

Exercise 24 Frame Rigidity

Remember, all of the components aside from the frame are assumed to be rigid. This means that the full loading must be transferred to the frame itself. Since we will assume the response of the frame is linear, any loading magnitude will be sufficient to calculate the torsional rigidity.

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Loading Conditions

Goal

With the proper boundary and loading conditions, calculate the torsional rigidity: TorqueLoad TorsionalRigidity = -------------------------------------------------AngularDeflection

Remember, the angular deflection result is given as the angle of deflection (in radians) times the radial distance away from the axis. The part for this exercise is located in the Lesson01\Exercises folder.

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PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Exercise 24

Frame Rigidity

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SolidWorks 2012

PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Lesson 11 Design Study

Objectives

Upon successful completion of this lesson, you will be able to: I

Understand and use the Design Study to analyze trends when specific parameters are varied.

I

Find optimum value of some design parameters.

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Lesson 11

SolidWorks 2012

Design Study

Design studies can be conveniently used to analyze an assembly in which the loads, geometry or material constants are to be treated as design variables. Results, such as displacements or stresses, can then be graphed as functions of the design variables. Design studies are used to run multiple studies with the intent of determining trends that can be used to make important design decisions, or to fully optimize the design.

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Design Study

Note that the automatic optimization feature of the Design Study is available in the SolidWorks Simulation Professional module.

Case Study: Suspension Design

The vehicle suspension assembly can be subjected to a multitude of loading variations during its operating conditions. We will use a design scenario to test the assembly under several different conditions so that we optimize the size of the parts.

Project Description

Analyze the suspension assembly when subjected to the following four conditions: 1. 2. 3. 4.

stationary vehicle vehicle moving at constant acceleration on a smooth road vehicle moving on a bumpy road vehicle moving at a constant speed on a smooth road and turning on a banked road All of the suspension components are manufactured from Alloy Steel.

The goal of the analysis is also to adjust the thickness of the lower arm to a value that will result in a Factor of Safety of 1.3 or better.

Stages in the Process

The basic steps of a design scenario are: I

Specify the parameters. Determine which parameters will be varied in each scenario.

I

Create a table defining the values of the variables for the design studies. Analyze the results. Review the available output to determine the necessary changes.

I

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Lesson 11 Design Study

Part 1: Multiple Load Cases

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For the first design study, four sets of loads will be applied to the axle of the suspension. There will be both a vertical and lateral load.

1

Open an assembly file.

Open suspension located in the Lesson11\Case Studies folder.

2

Set SolidWorks Simulation options. Set the global system of units to SI (MKS) and the units of Length and Stress to mm and N/mm^2(MPa), respectively.

3

Create new study. Create a new Static study named Multiple loads.

The spring is missing from the assembly. We will simulate the spring using connectors.

Note

4

Assign the material. Specify Alloy Steel to all the components.

This material has a yield strength of 620 MPa.

5

Define Fixed Hinge fixtures.

Define five Fixed Hinge fixtures as indicated in the figure.

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Lesson 11

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Design Study

Define a spring connector. Define a Spring connector between the two Flat parallel faces of the Front Shock Clamp and the Shock Plunger, as shown in the figure

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6

below.

Specify the Total, Normal stiffness of 105,000 N/m [600 lb/in].

7

Pin connectors.

All of the pin definitions have been defined beforehand. Copy all pin definitions from the study partially completed to this study multiple loads.

Design Studies

Design studies can be conveniently used to analyze an assembly in which the loads, geometry or material constants are to be treated as design variables. Results, such as displacements or stresses, can then be graphed as functions of the design variables. A design study is defined in two steps: 1. A list of the parameters (design variables) must be specified. 2. A design study is created in which scenarios (combinations) of the parameters along with their numerical values are specified.

Where to Find It

Menu: Insert, Design Study, Add. CommandManager: Evaluate > Design Study. Parameters, or design variables, are quantities which can be varied in the design study to investigate the behavior of the assembly. They are also used in the Optimization module to optimize the design with the specified set of the design constraints. (Optimization module is part of the SolidWorks Simulation Professional module.) A multitude of the parameter types is available: loads, geometrical features, material constants, and others. I I

Parameters

Where to Find It

I I

Note

404

Menu: Insert, Design Study, Parameters. CommandManager: Evaluate > Design Study > Parameters.

In some cases, such as when a load or a material constant is used as a parameter, a definition of the load or of the material constant must be linked to the corresponding parameter. This intermediate step will be practiced in this lesson.

SolidWorks 2012

Lesson 11 Design Study

Define the Vertical and Lateral forces.

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8

Apply force on the cylindrical face, as indicated in the figure. Use the assembly Front plane as a reference.

9

Add a parameter..

In the Normal to Plane field, select Link value (see the figure above).

In the Select Parameters dialog window, select Edit/ define to create a parameter for this direction of the force.

10 Specify load parameters.

The design study will consist of multiple loading conditions corresponding to various vehicle travel scenarios. The Parameters window opens automatically.

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Lesson 11

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Design Study

Type Vertical as Name and select Simulation under Category.

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Under Value, enter 225. The Units field displays N automatically as the Force/Torque is being defined in SI units. Define the second parameter named Lateral with 0 N as the Value.

Click OK to close the Parameters dialog window.

Note

Two Force parameters have been defined in this step: Vertical and Lateral.

11 Link values. From the Select Parameters window, select Vertical to

link this parameter to the corresponding component of the force.

Click OK to close the Select Parameters dialog window.

Notice that the user defined value of 225 N is shown in the appropriate field with a distinct background color.

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SolidWorks 2012

Lesson 11 Design Study

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12 Link the other load. Link the Along Plane Dir 2 force component to the parameter Lateral.

Both load components are now linked to the parameters controlling their magnitudes.

Click OK to exit the Force/Torque definition.

13 Refine mesh at higher curvature regions.

Apply mesh controls at the two fillets on the Shock Plunger. and the eight fillets of the lower arm, as shown in the images below. Use an Element size of 0.76 mm and a Ratio of 1.5.

14 Mesh the assembly. Create a High quality mesh with the default settings using the Curvature based mesh. 15 Run static study Multiple loads.

Run the analysis and note that the solver issues a warning about large displacements. Click No. The analysis will then complete.

While running static study is not required at this stage, it is recommended in order to verify the study setup.

16 Create a design study. Click the Design Study

icon on the Evaluate tab of the

CommandManager.

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Lesson 11

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Design Study

Alternatively, select Design Study from the Insert menu.

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Rename the Design Study 1 to Multiple Loads - Design Study.

The Design Study interface opens up on the bottom of the screen. It offers two view styles:

I

Variable View, where parameters can be entered in other than table

form.

I

Table View, where a discrete set of values for each variable is

shown.

17 Select Variables and enter their values. In the Variable View, under Variables, select the parameter Lateral.

From the pull down list specify Discrete Values and enter the values 0 N, 60 N, 72 N and 115 N, separated by commas, as shown in the figure below.

Switch to the Table View and include the second parameter named Vertical. Enter the values of -225 N, 185 N, 385 N and 900 N in the table.

Make sure that all four scenarios are checked. Unchecking a specific scenario excludes this combination of the design parameters from the design study. Uncheck the Optimization check box.

Note

408

Check box for Optimization is available only in the SolidWorks Simulation Professional module.

SolidWorks 2012

Lesson 11 Design Study

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Each Scenario represents a load case corresponding to the specific vehicle travel conditions: I I I I

Design Study Results

Scenario 1 corresponds to the loading when a vehicle is stationary [-225 N Vertical, 0 N Lateral]. Scenario 2 to a vehicle moving at constant acceleration on a smooth road [185 N Vertical, 60 N Lateral]. Scenario 3 to a vehicle moving on a bumpy road [385 N Vertical, 72 N Lateral]. Scenario 4 to a vehicle moving at constant speed on a smooth curving and banking road [900 N Vertical, 115 N Lateral].

The Design Study automatically generates and runs multiple studies corresponding to each Scenario (parameter combination). Full results from all scenarios are saved. As the amount of data can become excessive, attention should be paid to the size of the model and the number of the scenarios. All results are reported at specified sensors.

18 Sensors for the global results.

Result quantities are defined through the sensors. For the global results, monitoring the extremes for the entire model, Model Max sensors will be specified. In the FeatureManager add a Simulation Data sensor for VON:von Mises Stress. Under Properties select N/mm^2 (MPa) and Model Max.

Similarly, add a Model Max sensor for the URES: Resultant Displacement. Select mm for the Units.

19 Sensors for the local results.

Additional sensors must be specified at locations where results need to be reported and graphed. In our case, we will compare hub displacements from each design scenario.

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Lesson 11

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Design Study

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In the FeatureManager add a Simulation Data sensor for VON:von Mises Stress. Under Properties select N/mm^2 (MPa) and Max over Selected Entities. Delete suspension.SLDASM and select the vertex indicated in the figure.

Similarly, add a Max over Selected Entities sensor for the URES: Resultant Displacement. Select mm for the Units.

20 Result quantities.

Selected sensors defining the global and local results must be included in the design study.

Under Constraints, select all specified sensors. For all select Monitor Only and specify study Multiple Loads.

Note

Study selected in the above pull down menu associates our design study Multiple Loads - Design Study with the static study Multiple Loads.

Design Study Options

The design study can be run using two different options, Fast results and High quality. I

I

Where to Find It

410

I

Fast results: Scenarios, algorithmically selected from the active

scenarios are calculated only. The results for the remaining (not calculated) active scenarios are obtained using the interpolation. It is possible to additionally calculate the interpolated scenarios in order to obtain their precise solution. This option is typically used with larger number of scenarios where considerable time would be required otherwise. High quality: In this option all active scenarios are calculated. If the number of the scenarios is significant, this option may lead to a significant computation time. In the Design Study click the Design Study Options button

.

SolidWorks 2012

Lesson 11 Design Study

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21 Design Study options. Click on the Design Study Options button .

Make sure that High quality option is selected.

22 Run Design Study. Click the Run button.

Note

Make sure that the Optimization check box is unchecked.

23 Analyze global extreme results.

Global results are shown in the Design Study dialog when the study completes. Results sliders

We can see that the last study (Scenario 4) reports the largest magnitude for the von Mises stresses 654.35 MPa. The resulting displacements reaching the value of 25.7 mm is also the largest in Scenario 4. Thus, we can conclude that the last study, Scenario 4 (corresponding to the loading when the vehicle travels at a constant speed on a smooth, curved and banked road), represents the most extreme case and the shock assembly will be designed to withstand this loading.

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Design Study

24 Plot stress results.

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The complete results for all scenarios are saved on the disk and can be accessed through the results sliders or by selecting the desired column, as shown in the above figure.

Expand the Results and Graphs folder of the Multiple Loads Design Study study and Show the VON: von Mises Stress plot.

We see that the von Mises stress in the Scenario 4 exceeds the yield strength of Alloy Steel 620 MPa.

The four design scenarios could be easily specified as four unique studies. The advantage of the design study becomes more apparent if the number of scenarios (in this example, load cases) increases.

Part 2: Geometry Modification

Because Scenario 4 was identified as the worst load combination, the assembly geometry will now be modified with the help of design scenarios. A safety factor of 2 on von Mises stresses and the maximum resultant displacement of the hub component equal to 23 mm will be required.

25 Switch to static study. Switch to Multiple loads static study.

Note

412

Note the additional folder Parameters. in the static study FeatureManager. This folder becomes accessible after the initial parameters definition (steps 9 to 12).

SolidWorks 2012

Lesson 11 Design Study

26 Define geometrical parameter.

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Define an additional geometrical parameter that will be used in this study. Go to the View pull-down menu and select All Annotations.

Right-click on the Parameters folder and select Edit/Define.

In the Parameters dialog window, enter Arm_thickness as Name and select Model dimensions as Category.

Click on the 3 mm dimension (in Extrude2) identifying the thickness of the lower arm. The dimension D2@[email protected] will then be shown in the Model dimension field. Click OK to close the Parameters window.

27 Modify the load.

Edit the force definition and unlink the values of the force components from the parameters.

Enter a value of 115 N [25.9 lb] in the Along plane Dir2 field and 900 N [202 lb] in the Normal to plane field. This corresponds to the worst loading case in which the vehicle travels at a constant speed on a smooth, curved and banked road (Scenario 4 in the previous design study). Click OK.

28 Define new Design Study. Follow the steps 16 to 20 and define a design study with a single parameter Arm_length reaching the following values: 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5 and 8 mm.

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Design Study

Use identical sensors for both the global and local results.

29 Design Study options.

Set the design study quality to Fast Results.

Note

The Fast results option calculates only algorithmically selected active scenarios. In our case, only three out of the seven activated scenarios will be solved.

30 Run design scenario.

Note

Make sure that the Optimization check box is unchecked.

31 Review global extremes of the results.

Use the slider to view the results from the last Scenario in the column titled Current.

We observe that the maximum value of the von Mises stresses was reduced to 453.7 MPa. This is still not within our factor of safety. We would want to investigate the design to see what is causing the high stresses. The maximum resultant displacement has reduced to 23.57 mm.

Note

Notice that only three activated scenarios, with results in black font, were calculated. The remaining activated sets with the numbers in gray font show results obtained using the interpolation. If precise results for the interpolated scenario are required, calculation need to be requested.

32 Calculated interpolated scenario.

In the Results View tab right-click on the Scenario 2 column and select Run. The scenarios will then be computed.

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Design Study

The result numbers for this scenario will then change font color from gray to black, indicating the fact that the scenario is now calculated.

Because in this study we want to see all scenarios calculated, the study will be recalculated with High Quality settings.

33 Change properties and re-calculate. Change the study quality to High Quality.

Click the Run button to compute all 14 activated scenarios.

34 Display von Mises plot.

Show the von Mises stress plot for the last scenario (Scenario 14) when the thickness of the lower arm was 8 mm.

We can see that the maximum von Mises stress has decreased to 472.8 MPa. Notice, also, that the location of the maximum stress shifted to the fillet on the plunger. Varying model dimensions caused the stresses to redistribute as the stiffness of the components change relative to each other.

Design Study Graph

Design Scenario results can be shown in a graph form to identify the trends more easily. Multiple results can be shown in the same graph by selecting the different locations established when setting up the scenarios.

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Design Study I

Shortcut Menu: Right-click the Results and Graphs folder and select Define Design History Graph Simulation toolbar: Click Define Graph

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Where to Find It

I

35 Graph the global extreme for von Mises stresses. Right-click on the Results and Graphs folder and select Define Design History Graph.

Under the Y-Axis select Constraint, and the sensor monitoring the model maximum for stresses (in our case this sensor was named Stress1). Under Extra Location leave the field blank. This way the global results will be graphed. Click OK to show the graph.

The above graph shows the variation of the global extreme value of the von Mises stress with the thickness of the lower arm.

We observe that any increase in the thickness of the lower arm above 4 mm does not deliver any substantial decrease in the global von Mises stress magnitude (the maximum value location shifted from the lower arm to the Plunger). We can, therefore, conclude that the thickness of 4 mm is optimal. At Arm_thickness = 4 mm, the global extreme of von Mises stress reached approximately 487 MPa, which is 78.5% of the Alloy Steel yield strength (620 MPa [90 ksi]). Any further increase in the arm thickness does not significantly reduce the maximum stress. If we need to achieve a larger factor of safety, other design modifications must be investigated.

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36 Save and Close the file.

Note

Alternatively, we could analyze the variety of material combinations used for different parts in this assembly. Using the identical procedure that was practiced in this lesson, we would first define the parameters for the material properties (such as Young’s modulus or Yield strength). Then, we would define a design study in which the combinations as well as the numerical values of the material parameters would be specified.

Summary

This lesson introduced and practiced the design study that allows the user to study various trends in the design when specific design parameters are defined. This feature has many practical applications, some of which were practiced in this lesson. Namely, it was used to study load cases simulating various travel conditions of a small vehicle and to find an optimum value of the thickness of one of the suspension components. The design study is defined in two steps:

First, a list of the parameters (design variables) must be specified. A multitude of parameter types is available: loads, geometrical features, material constants, and others. Second, a design study in which scenarios (combinations) of the parameters along with their numerical values are created.

It is apparent that if an optimum combination of a larger number of design parameters is desired, the process may be rather lengthy and cumbersome. In such case, a full automatic Optimization feature of the design study, available in the SolidWorks Simulation Professional module, should be used.

In our model, we saw that with an arm thickness of 4mm, we fall below the yield strength of the material. This is the thinnest we can make the arm without doing any permanent damage.

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Design Study

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SolidWorks 2012

Exercise 25 Design Study

In this exercise, a design scenario will be created to determine the distance between two supports that minimizes the deflection in the plate.

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Exercise 25: Design Study

This exercise reinforces the following skills: I I I I

Project Description

Design Study on page 402. Design Studies on page 404. Design Study Results on page 409. Design Study Graph on page 416.

A rectangular platform made of Nylon 6/10 plastic material, is supported by two steel rods protruding through the platform width.

The rods are suspended by short links, which themselves are pinsupported. The distance between the pins attached to the platform may change when the platform experiences deformation.

This type of support makes it possible to use linear analysis for the study of deflections and stresses of the platform. The platform assembly is subjected to an acceleration of 100 G.

We can assume that the steel rods are rigid and that we are not interested in the contact stresses between the pins and the platform. These assumptions allow us to exclude the rods from the analysis model.

Support

Pin

Rod

Link

Since the rods are represented by properly applied supports, the analysis is conducted using the SolidWorks part file platform, rather than the assembly file platform assembly. Find the distance between the two steel pins that minimizes the platform deflection.

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Design Study

Open a part file. Open platform located in the Lesson11\Exercises folder.

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1 2

Show feature dimensions.

In the FeatureManager design tree, right-click Annotations and select Show Feature Dimensions. In this exercise, we take advantage of platform double symmetry to analyze one quarter of the model.

Note

3

Make symmetry cut.

Unsuppress the feature called double symmetry.

4

Create a study.

Create a static study named 100G.

5

Define parameters.

In the Insert menu, select Design Study, Parameters. (Alternatively, you can click Parameters on the Evaluate tab). Define a distance parameter.

Select the 400 mm dimension that defines the distance between the two hinges.

6

Material.

Specify Nylon 6/10 material from the Plastics folder.

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7

Fixtures.

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Apply symmetry boundary conditions to the two faces created by the cut.

8

Define restraint to simulate rod support. Apply a Fixed Hinge

fixture to the cylindrical face as indicated in the figure.

9

Apply gravity load.

To apply a gravity load, right-click External Loads and select Gravity.

Select the Front plane as the reference to define the direction of gravitational acceleration. Make sure the Unit field is set to SI.

Enter 981 m/s^2 (this value is one hundred times the gravitational acceleration) in the direction normal to the Front plane in negative Z direction. Click OK.

Note

Mass density is a required material property when using gravity loading.

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Design Study

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10 Mesh the model. Create a High quality mesh with the default settings using the Curvature based mesh. 11 Define design study.

Define a design study with 10 scenarios for the following values for the parameter distance: 475, 425, 375, 325, 275, 225, 175, 125, 75, and 25 mm.

12 Results specification.

Monitor the global maximums for the stress and the resultant displacement, and the local results for the same quantities at the two vertices indicated in the figure below.

13 Run design study. Use High Quality. 14 Results.

Examine the global maximums for the von Mises stress and the resultant displacement, and review the local stresses and resultant displacements for the Vertex1 and Vertex2.

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15 Graph results at global max and Vertex1 locations.

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Define design history graphs for the variation of the von Mises stress and the resultant displacement.

We observe that both the von Mises stresses and the resultant displacements are minimized when the distance between the two supporting rods is 275 mm. (Set 5). The corresponding values are 4.7 MPa and 0.36 mm.

16 Save and Close the file.

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Design Study

At the beginning of this exercise, we stated that the platform was suspended by floating links. The links themselves are pin-supported and rotate about supporting pins. For this reason, the distance between the rods may change when the platform experiences deformations under the prescribed load.

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Limitations of Linear Analysis

Consequently, in the assumption of small displacements, a platform suspended by floating links does not develop any tensile stresses. It resists the load only with bending stresses. Link can rotate about this pin

If the links are rigidly supported and the rods are unable to move closer together, tensile stresses develop in addition to bending stresses.

These tensile stresses, also called membrane stresses, are the result of deformation and significantly increase the platform stiffness.

Question:

What does this have to do with linear analysis?

Answer:

Linear analysis assumes that the structure stiffness does not change with deformation, and the solution is based on the original stiffness calculated before any deformations occurred. Therefore, linear analysis cannot account for additional stiffness created by membrane stresses that develop during the deformation process.

Even if we intended to model rigid hinges, the results would still have pertained to floating hinges and the platform stiffness would have been underestimated. To differentiate between floating and rigid hinges we use nonlinear geometry analysis, which is available in SolidWorks Simulation Premium.

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Objectives

Upon successful completion of this lesson, you will be able to: I

Perform a static analysis with a temperature load.

I

Define temperature dependent material properties.

I

Use sensors to retrieve results at desired locations.

I

Use soft springs option in thermal stress analysis.

I

Save the deformed shape of the model.

I

Examine results in local coordinate systems.

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Thermal Stress Analysis

The heating or cooling of bimetallic parts create internal stresses due to the difference in expansion coefficients in different materials. In this lesson we will determine the stress and deformation that results from heating a bimetallic part.

Case Study: Bimetallic Strip

Due to the difference in the coefficients of the thermal expansion of aluminum (200 W/m K) and nickel (43 W/m K), the bimetal will deform with temperature changes. In this case study, the stress will be zero at room temperature.

Project Description

An aluminum strip, glued with a nickel strip into a bimetal assembly, is at room temperature 25°C (77°F). Without any constraints on its deformation, the bimetal strip is then heated to 280°C (536°F).

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Thermal Stress Analysis

Aluminum

Nickel

Determine the deformations that arise due to the different thermal expansions of aluminum and nickel, and the minimum required strength of the bonding glue material.

Also required is that the numerical simulation be followed by an experiment. Six tensometers, oriented along the longitudinal direction, will be attached to the surface of the tested model (three on the top of each part) as shown in the figure to measure the surface deformation. To allow for the correlation between the numerical and experimental data, sensors will be defined in the same locations in the finite element model. The deformed assembly will then be saved as a SolidWorks model for further design applications.

Procedure

Proceed as indicated in the following steps.

1

Open an assembly file. Open bimetal located in the Lesson12\Case Studies folder.

2

Create study.

Create a static study named bonded.

The Ni and Al properties are automatically transferred from the SolidWorks assembly.

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Material Properties

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Because the model is exposed to an elevated temperature, the material constants have to be modified accordingly. The following two tables show the dependence of the material constants on the temperature. Variation of SIGYLD [Pa] on temperature

Room

100°C

204°C

260°C

316°C

Inconel 702 Nickel Alloy

406.9e6

-

356e6

-

326e6

2014 - T6 Aluminum Alloy

378.6e6

330.5e6

210e6

119.8e6

44.4e6

Variation of EX [Pa] on temperature

3

Room

100°C

204°C

260°C

316°C

Inconel 702 Nickel Alloy

229.9e9

-

223.4e9

-

205e9

2014 - T6 Aluminum Alloy

71.9e9

70.6e9

64.1e9

50.8e9

50.5e9

Create custom material properties for Ni strip. Right-click on the body ni-2 (under the folder Parts) and select Apply/ Edit Material.

The material dialog window displays default Ni material constants at room temperature. Because the materials in the default library can not be edited, we will copy the Ni material into a new custom library named Lesson 12 materials.

Right-click on Custom Materials folder and select New Category. Name the new catergory Lesson 12

materials.

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Thermal Stress Analysis

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Copy and Paste Nickel from SolidWorks Materials, Other Metals, into our newly created category Lesson 12 materials.

Edit Nickel, select the Tables & Curves tab and Elastic Modulus in X vs Temperature under Type. Select oC and N/m^2 under the Table data section.

4

Enter data.

Enter the available data points from the table above defining the dependence of the Young’s modulus on temperature for Inconel 702 Nickel Alloy.

To add a new line in the Table data definition, double-click on the last row.

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Enter data from Excel.

In some cases, the number of data points can be excessive. In SolidWorks Simulation, the data can be conveniently copied from other programs such as Excel.

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5

Continue editing Nickel and under Type, select Yield Strength vs Temperature, set the Units to oC and N/m^2 (Pa). Open the Excel file

materialdata.xls located

in the lesson directory, and navigate to the sheet with the Inconel 702 Nickel Alloy data. Right-click on the corresponding data and select Copy.

Paste (CTRL-V) the data into the Table data area of the Material dialog window.

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Make the properties temperature dependant. Select the Properties tab. Under the Value column, click on the corresponding cells for Elastic modulus and Yield strength, and select Temperature dependent.

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6

Notice that the cells for Elastic modulus and Yield strength under the Value column show Temperature Dependent.

Click Apply and Save to confirm the definition of the Inconel 702 Nickel Alloy properties and save the database.

We will assume that the thermal expansion coefficient remains constant in a given temperature range.

Note

7

Assign material to Al strip.

Follow the procedure above and assign the temperature dependent material constants (Yield Strength and Elastic Modulus) for 2014-T6 Aluminum Alloy. The data can be again found in the materialdata.xls Excel file located in the lesson directory.

8

Global Contact.

The default top level assembly contact (Global Contact) condition is set to Bonded. As we analyze glued components, bonded contact is appropriate.

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9

Define sensors on Al strip.

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In the FeatureManager design tree, right-click the Sensors folder and select Add Sensor. For Sensor Type, select Simulation Data.

For Data Quantity, select Workflow Sensitive.

Select the three sketch points on top of the Al strip, then select OK.

Aluminum Sensors

Nickel Sensors

Rename this set of sensors to Al_sensors.

10 Define sensors on Ni strip.

Follow the procedure above to define three sensors on the Ni strip. Name this set of sensors Ni_sensors.

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11 Apply temperature load. Right-click External Loads and select Temperature. Use the

SolidWorks fly-out menu to select both components.

Enter a temperature of 280°C. This definition states that the temperature of both assembly components is uniformly elevated/ lowered to 280°C from the reference temperature at zero strain. Click OK.

12 Define zero strain temperature. Right-click the bonded

study folder and select Properties. Select the Flow/

Thermal Effects tab.

In the Thermal options area, select Input temperature (this is the default choice). The input temperature is the 280°C that we defined earlier.

Enter 25°C as the Reference temperature at zero strain. This temperature corresponds to the room temperature, and we assume that no strain exists in the model at this temperature, due to the structural loads and boundary constraints.

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Temperature loads can be also imported from the SolidWorks Simulation thermal study or directly from the CFD (Computational Fluid Dynamics) simulation in SolidWorks Flow Simulation.

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Importing Temperatures

For the stress analysis it is also possible to import the distributions of the fluid pressures from SolidWorks Flow Simulation.

13 Stabilize the model.

Because the strip’s deformation should be unconstrained, we cannot apply an external boundary condition. Since the model is in the state of thermodynamic equilibrium and is not subjected to any external force loads, we can use the soft spring option to stabilize the model. Select the Options tab.

Select Use soft spring to stabilize model. Click OK.

14 Mesh the model. Create a High quality mesh with

the default settings using the Curvature based mesh.

This element size creates two layers of elements through the thickness of each part.

15 Run the analysis.

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16 Plot displacements.

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Plot the resultant displacements (in 1:1 deformation scale). The maximum displacement at the tip of the bimetallic strip is 0.59 mm [0.023 in].

17 Plot von Mises stress results.

Examine the results. There appears to be very high stress at the junction of the two materials.

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This stress plot can be misleading. As we learned in Lesson 1, the von Mises stresses are obtained by averaging the stress values extrapolated to the nodes from all the adjacent elements. In this case, the stresses at the interface are averaged between two distinct parts. To obtain the correct distribution of the von Mises stresses, we have to disable the averaging across the part boundaries.

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Averaging Stress

18 Edit the plot.

Right-click on the stress plot and select Edit Definition.

In Advanced Options, clear Average results across boundary for parts.

The new von Mises plot above shows the correct distribution. We can see that with the averaging across the boundaries option disabled, the maximum value jumped to approximately 264 MPa [38.2 ksi] in some interface regions.

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19 Stress on individual parts.

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To view the maximums in each of the two parts separately, isolate the components in SolidWorks and plot the distribution of the von Mises stress for the displayed part only.

Display the extreme values for the shown parts. In Chart Options, select Show min annotations, Show max annotations, and Show Min/Max range on shown parts only options.

Aluminum part

Nickel part

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20 Examine the plots.

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We can see that the maximum von Mises stresses in the Aluminum and Nickel Alloy parts are 121 and 264 MPa respectively. The stress in the Aluminum part is well above the corresponding yield strength at 280°C (93 MPa) whereas the Nickel part is below (335 MPa at 280°C ). This indicates that one of the parts is yielding.

The accurate solution to the above problem can, therefore, be obtained using a nonlinear modulus of SolidWorks Simulation Premium, where full stress-strain curves for the given alloys would have to be specified. We will ignore the fact that one of the parts is yielding and continue with the lesson. In the next part, we would like to analyze the interface layer and find the minimum required strength of the bonding material.

21 Show strain results at the sensor locations. Define a new strain plot for the ESPX: X Normal strain component.

Right-click on the newly defined strain plot and select List selected.

Select From sensors under Options and Al sensors under Results. These are the probes for the Aluminum strip. The normal strain values will be listed in the table and shown on the model.

Note that the buttons under Report Options let you graph the results at the sensor locations or save them in.cvs file for further processing. Also, it is possible to include the results at all sensor locations in the study report.

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22 Plot distribution of normal stress SX. Define a new stress plot for the SX: X Normal stress component. In exploded view, analyze the through-thickness variation of the SX

normal stress.

Important

Similarly to the von Mises stress plot, deactivate Average results across boundary for parts option.

23 Graph stress through the thickness.

Use the Probe feature to path plot the variation of the SX stress through the thickness.

Ni (interface)

Al (top)

Ni (bottom)

Al (interface)

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The results and the graph above indicate the following variation of SX.

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Interpret the Results

We observe that at the interface the normal stresses change abruptly from -96 MPa (compression) in Aluminum to 147 MPa (tension) in Nickel. Furthermore, we can observe three neutral axes (planes) where the normal stresses are at zero. Two of these axes (planes) are clearly indicated in the figure. The third axis coincides with the interface plane, where the normal stresses change abruptly from -96 MPa (compression) in Aluminum to 147 MPa (tension) in Nickel. All three locations are accompanied by the local extremes of shear stress that may delaminate the glued strips (see the figure above). Since our main goal is to obtain the required strength of the bonding material, we will focus on the interface location. The bonding material must be capable of resisting the shear stress at the Aluminum/Nickel interface.

Reviewing the Interpretation of FEA Results on page 17 of the Introduction reveals that we must plot the τxy component of the stress. This corresponds to the TXY: Shear stress in the Y dir on YZ plane component.

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24 Plot interface shear stress. Define a new plot of TXY: Shear stress in the Y dir on YZ plane stress. Display the plot in the exploded view and, under Settings, Fringe Options select Discrete.

We can observe that the interface shear stress on the side of Aluminum and Nickel are identical, i.e. the equilibrium is satisfied. The discrete plot conveniently shows that the maximum value of shear stress (ignoring the localized stress concentrations at the tip of the straight section) equals approximately 13 MPa. This would be the minimum required strength of the glue in shear for this application.

Question

We concluded that the minimum required strength of the glue is approximately 10 MPa. Inspection of the τxy plot above shows that the bent part should experience much larger shear stress. Why? For the answer review the following section.

Examining Results in Local Coordinate Systems (Optional)

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τxy

in the previous figure is referencing the global coordinate system. In the bent section, the global x, y and z axes are no longer aligned with the interface geometry. In other words, the τxy distribution in the bent section no longer represents the interface shear stress. For the correct representation of the interface shear stress in the bent section, we have to switch to the appropriate coordinate system aligned with the geometry.

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Lesson 12 Thermal Stress Analysis

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25 Interface shear stress at the bent location. Create a Discrete τxy plot with Axis1 used as a reference. Axis1

defines a local cylindrical coordinate system aligned with the geometry of the bent section.

Shear Stress in Cylindrical Coordinates

In the cylindrical coordinate system, the r, θ , and z sequence of coordinate axes corresponds to the x, y, and z sequence in the Cartesian coordinate system. By specifying τxy in the plot definition dialog with Axis1 specified as a reference, we request a plot of τrθ , which is the interface shear stress. The above plot of the interface shear stress shows that the bent section experiences similar shear. The indicated value is approximately 11 MPa. As this is greater than the value of 10 MPa obtained from the straight section, we conclude that this is the minimum required shear strength of the bonding material.

Since the bonding material will also have to resist the normal stress we would have to verify the interface normal stress in the proper coordinate systems. It can be checked that this stress is significantly smaller in this case (approximately 5MPa) and will not govern.

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Saving Model in its Deformed Shape

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We end this lesson by saving the deformed shape as a new SolidWorks model so that it can be used as an assembly component to check for interference, and so on.

1

Create new body from deformed shape. Right-click on the Results folder and select Create Body from Deformed Shape.

Click the Save as New Part button and enter Deformed bimetal as the Part name. Click OK.

2

Open the new body in the SolidWorks environment. In the options area of the SolidWorks File, Open window and select the saved Deformed bimetal.sldprt file.

Click OK.

The deformed geometry model appears as an imported feature in the SolidWorks FeatureManager. The deformed shape can now be examined with the standard SolidWorks tools.

3

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Save and Close the file.

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Lesson 12 Thermal Stress Analysis

A simple bimetal assembly was analyzed when subjected to the elevated temperature. To eliminate the effect of absent external supports, the Use soft springs to stabilize model option was used.

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Summary

At elevated temperatures, the values of some of the material properties may vary considerably. In this lesson, we practiced the definition of the temperature dependent yield strength and Young’s modulus. The main goal of the lesson was to obtain the minimum required bond strength of the interface glue. To obtain this value, a complex distribution of the normal stress SX was studied, and the definition of the neutral axes (planes) was introduced. Furthermore, the corresponding component of the shear stress was plotted. In the bent section, the curved geometry required the introduction of the local cylindrical coordinate system. The interface shear stress was then plotted with respect to this local coordinate system.

Since the experimental verification of the numerical results was required a set of sensors was defined to extract the deformation results at the specified tensometer locations.

Lastly, exporting of the deformed geometry as a VRML file was shown and discussed.

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Thermal Stress Analysis

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Objectives

Upon successful completion of this lesson, you will be able to: I

Use and understand the h-adaptive solution method.

I

Use and understand the p-adaptive solution method.

I

Compare results obtained using h-adaptive and p-adaptive solution method.

I

Use symmetry boundary conditions.

I

Use the Graph tool.

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Adaptive Meshing

Through the previous lessons, we have manually refined the mesh to improve the accuracy of our results. In this process, we have examined the model and then the results to determine the refinements necessary to get accurate results. Two new solution methods called h-adaptive and p-adaptive will be used in this lesson that will automate the process.

Case Study: Support Bracket

A cantilever bracket will be analyzed using the different meshing techniques.

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Adaptive Meshing

Symmetry boundary conditions will be used to reduce the analysis to only half the model, resulting in a faster solution. First we will create a mesh using the same method used in previous lessons. This will be the standard solution. The results of the standard study will serve as a basis for comparison between the three different solution methods used in this lesson:

1. Standard solution 2. h-adaptive solution 3. p-adaptive solution

Project Description

A cantilever bracket is supported along the face at the back side.

A load of 22,000 N [4,946 lb] is uniformly distributed to the split face that surrounds the cylindrical hole. Determine the location and maximum magnitude of von Mises stresses.

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Load

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Procedure

Proceed as indicated in the following steps. Open a part file. Open support bracket located in the Lesson13\Case Studies

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folder.

2

Activate symmetry configuration. Activate the configuration called symmetry.

Geometry Preparation

The bracket geometry has been defeatured to make meshing easier; the external cosmetic fillets have been suppressed. While these details do not complicate this model to the point of preventing us from meshing or solving it, we use the model with suppressed features to emphasize the fact that defeaturing is often necessary for more complex models.

Symmetry

Due to the symmetry of the bracket geometry, loads, and supports, we can simplify the finite element model by analyzing only one half of its geometry.

3

Define a study.

Define a static study named standard.

This study will provide results that will serve as reference when comparing different solution methods. The study name standard reflects the fact that we use a “regular” solution method where mesh does not change during the solution process. This is how we have solved all previous lessons in this training manual.

The material properties (AISI 304) were defined earlier in SolidWorks and have been transferred automatically to SolidWorks Simulation.

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Adaptive Meshing

Apply load as a force. Apply 11,000 N [2,473 lb.] force

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to the split face around the hole. Note that only one half of the force magnitude must be applied because the model represents only one half of the geometry.

5

Apply Fixed Geometry fixture to the back face.

6

Apply Symmetry Boundary Conditions. Apply Symmetry boundary

conditions on the faces exposed by the cut.

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Mesh the standard study. Create a High quality mesh with the

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default element size using the Curvature based mesh.

Since no local mesh control was defined, the element size is uniform.

8

Run the analysis.

Run the solution for the standard study.

To verify that the symmetry boundary conditions work as expected, animate one of the results plots. While the model deforms, verify that the faces with symmetry boundary conditions applied to them remain flat and there is no movement of these faces in the direction normal to the plane of symmetry.

h-Adaptive Solution Method

Before we explain the h-adaptive solution method, recall that any solution obtained using the Finite Element Analysis depends on how the analyzed model has been meshed. We may re-phrase the above observation to say that the FEA data of interest depends on the choice of discretization. Thus, changing the mesh parameters (global or local mesh controls) will affect the FEA results. This is because different meshes (different choices of discretization) will cause different discretization errors.

Discretization errors can be estimated by making systematic changes to the mesh and studying the impact of these changes in the area of interest. This process is called “convergence process”. One way to make systematic changes to the mesh is to modify the element size through mesh refinement. Because h denotes the characteristic element size, the convergence process through mesh refinement is called “h convergence process”. In this process, the size of the elements is gradually reduced.

h

We have already conducted the h convergence process in Lesson 1 and Lesson 2.

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In Lesson 1, we refined the model uniformly, meaning the entire model was meshed with the same element size. That size was reduced in different studies. In Lesson 2, we used mesh controls to refine the mesh only in areas where we deemed it necessary. The convergence process we conducted in Lesson 1 and Lesson 2 required us to define several studies with different meshes, run the analysis, and summarize the results. These were informative but rather tedious exercises.

Using the h-adaptive solution method we will automate the h convergence process.

h-Adaptivity Study

We will analyze the same bracket, with the same material fixtures and loads using an h-adaptive solution.

1

Create new study for h-adaptive solution.

Duplicate the study standard into a new study and name it h adaptive.

2

Set h-adaptive solution parameters. Right-click h-adaptive study and select Properties.

Select the Adaptive tab.

Note

The Adaptive solution tab is available only for static analysis and solid mesh elements.

Under the Adaptive method option, select hadaptive.

Under the h-Adaptive options, accept the default value for Target accuracy. Also, accept the slider location at the center for Accuracy bias. In the Maximum no. of loops box, enter 5.

Select the Mesh coarsening check box. Click OK.

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What is going to happen when we solve the study with the above settings?

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h-Adaptivity Options

SolidWorks Simulation will solve the same model several times, each time using more refined meshes. The mesh refinements will be performed automatically, no user intervention is required.

How many mesh refinements will be performed?

Considering that we have set the Maximum number of loops to 5, SolidWorks Simulation will solve for the original mesh and then perform several other mesh refinements. Looping will terminate when Target accuracy is obtained or if the Maximum number of loops is reached. Maximum number of loops of 5 means that the solution may consist of a maximum of six steps: the original mesh and five refinements. Target accuracy is the accuracy of strain energy norm (RMS strain

energy) in the model. We set it at 98% which means that looping stops if the difference in the strain energy norm between the two consecutive loops drops below 2%.

Target Accuracy

The Target accuracy is based on the total strain energy in the model. This is a global measure of the discretization error. As such, it is largely insensitive to localized errors, even if those errors are high.

Accuracy Bias

To account for the local errors, looping is also controlled by an Accuracy bias.You can move the Accuracy bias slider to the left (Local) to instruct the program to concentrate on getting accurate peak stress results, meaning that local areas with high strain energy errors will receive “preferential treatment” (mesh will be highly refined in those areas). Or, you can move the slider to the right (Global) to instruct the program to compute overall accurate results with respect to lower strain energy errors. We do not have explicit control over the magnitude of local strain energy error. From Lesson 2 you will recall that stress singularity occur at the locations of concentrated forces and sharp re-entrant corners. The stresses at these locations diverge to infinity as smaller mesh elements are used.

Therefore, for models with such singularity, it is recommended to move the Accuracy bias slider to the right (Global). This way high, but localized, strain energy errors will be ignored; the solver will not adjust mesh refinement pattern to reduce these errors.

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Local Accuracy bias usually produces results faster than Global Accuracy bias. De-refined

Refined

De-refined

Original mesh

Mesh after completion of h-adaptive solution

When h-adaptive solution is used, you can start with a coarser original mesh size. This mesh is a starting point and SolidWorks Simulation refines it as needed during the solution process. Additionally during the mesh refining process, the mesh may be “de-refined” if Mesh coarsening is selected, as it has been in our study.

The mesh may become coarser in some locations if the h-adaptive solver decides that the initial user defined mesh is “too fine”, meaning it is excessively refined giving low stress gradients in these locations.

The mesh is not refined uniformly but only where needed to keep strain energy errors low. We may say that mesh adapts to the stress patterns. This gives the “adaptive” name to h-adaptive solution method.

3

Create mesh for h-adaptive study. Mesh the model with the mesh density slider set to Coarse. Make sure High quality elements are used.

This mesh is not acceptable for standard solution techniques because there are not enough elements to capture the complex stress gradients around the fillets.

4

Run the h-adaptive study. Run the solution for the h-adaptive study. The solution progresses in steps corresponding to the number of mesh refinements.

To help re-visualize the stress results, the regions where the material yields will be plotted in a distinct color.

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Set distinct color for yielding regions. Select Option from the Simulation menu. Select the Default Options tab. Select Color Chart under Plot.

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Select Specify color for values

above yield for von Mises plot

feature. The default color is gray. Click OK.

6

Plot von Mises Stress.

Define a new von Mises stress plot. Under Settings, select Mesh for the Boundary options.

The stress plot shows the maximum von Mises stress of 227 MPa [33 ksi], which slightly exceed the yield strength of AISI 304 steel. Note that the yielding regions are shown in a distinct color.

Displaying mesh superimposed on the plot confirms that the mesh has indeed been refined where stress concentrations are located and derefined in “quiet” portions of the model.

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h-Adaptive Plots

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Any plot (stress, displacement, strain, and so on) in the results folders of the h-adaptive study displays the final result, or the last performed step of the h-adaptive solution process. In addition to displaying the final plot results, we can also access the history of the iterative solution.

Convergence Graph

To visually see how well the solution is converging, we can use a convergence graph.

Where to Find It

I

I

7

Shortcut Menu: Right-click on the Results folder and select Define Adaptive Convergence Graph. Menu: Simulation, Results Tools, Convergence Graph.

Create convergence graph. Right-click on the Results folder and select Define Adaptive Convergence Graph.

Under Options, select Maximum von Misses stress. Clear Target Accuracy. Click OK.

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Review h-adaptive Solution

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Let us review the graph and make a few observations about the hadaptive solution. I

I I

I

The h-adaptive iterations went through all five steps: the first using the original mesh and the next four steps with automatically refined meshes. In each loop the mesh is refined further. The maximum number of loops (5) has been reached. Because no convergence confirmation message was displayed at the end of the process the required strain energy error of 2% was not achieved. The stress units in the graph are N/m^2, regardless of what units are used in the model.

We now wish to continue with the iterative procedure to reduce the strain energy error below the requested 2%.

8

Continue running the analysis. Run the study h-adaptive again.

The last results and mesh from the previous iterations are now the initial configuration for new h-adaptive iterations.

Note

At one point we get the following message:

Analysis has satisfied the current h-Adaptive accuracy of 98.0334 percent. You may increase target accuracy to re-run.

The convergence criteria has now been met.

9

Plot von Mises stress.

The maximum stress increases from 227 to 229.3 MPa [33 ksi to 33.25 ksi]. The difference in stresses is therefore minimal in this case.

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10 Create convergence graph for Maximum von Mises stress.

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Counting the number of data points we see that the h-adaptivity iterations had to go through seven loops to achieve the desired accuracy of 2%.

Strain Energy Error is NOT Stress Error

The 2% strain energy error we specified in the properties of the hadaptive study is not the stress error.

If we are interested in von Mises stress, why can’t we specify the error in terms of von Mises stress? In other words, why don’t we use von Mises stress rather than the total strain energy as a convergence criterion?

The reason why the total strain energy is used as a convergence criterion is because the total strain energy (“total” means in the entire model) always shows monotonic convergence without local “plateaus”, which might lead to premature termination of the convergence process. Also, recall the local stress singularities phenomenon analyzed in Lesson 2. In this case the stress diverges and convergence could not be achieved. Review displacement results of study h-adaptive before proceeding.

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Having obtained a solution with the h-adaptive solution method we now solve the same model using the p-adaptive solution method.

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p-Adaptivity Study

P-adaptive solution requires the use of a different type of finite

element called p-element. Before we begin, we need to explain what pelements are and what they do.

p-Adaptive Solution Method

In Lesson 1, we said that SolidWorks Simulation uses three types of elements: tetrahedral solids, triangular shells, and beams. Each can be defined as either a: I I

First order element (draft quality). Second order element (high quality).

First order elements model a linear (or first order) displacement and constant stress distribution, while second order elements model a parabolic (second order) displacement and linear stress distribution.

We now have to amend the above paragraphs. Besides first and second order solid tetrahedral elements, SolidWorks Simulation also has higher order tetrahedral solid elements (up to the 5th order) meaning that a polynomial of the 5th order can be used to model a displacement field inside the element, along its faces and edges. These elements are available when the p-adaptive solution method is used.

The order of elements used in the p-adaptive solutions is not predefined, but can be upgraded automatically during the iterative solution process without our intervention. These elements with upgradeable order are called p-elements.

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Adaptive Meshing

Create p element study. Duplicate the study h adaptive into a new study named p adaptive.

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Define p-element method and its options.

To utilize p-elements in the analysis, right-click the p elements study folder and select Properties. Select the Adaptive tab, then select the p-adaptive. This option is available only for static analysis and only when using solid elements.

Set Starting p-order to 2, which means that all elements are first defined as second order elements.

Set Maximum p-order to 5. The p-adaptive solution runs in iterations, called loops, and with each new loop, the order of elements increases. The highest order available is the 5th order, but the actual highest order we use can be lower and is defined by Maximum p-order. Set Maximum no. of loops to 4.

Under p-adaptive options, in the change is text box, enter 0.05.

Click OK.

Looping continues until the change in Total Strain Energy between the two consecutive iterations is less than 0.05%, as specified in the p-adaptive options. If this requirement is not satisfied, then looping stops when the elements reach the highest available order, which in our case is the 5th order. Note that it takes four iterative loops to reach a 5th order element. Investigate other choices in the p-adaptive options area.

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Why are we specifying this high accuracy requirement (0.05%) for the total strain energy error? Actually, we do not expect that the solution will satisfy this requirement. We want to force the solver to complete all four steps so we can analyze graphs consisting of four, rather than two or three points.

The p-adaptive solution process is conceptually similar to the already performed h-adaptive iterative process of mesh refinement. Both add degrees of freedom to the model, one by mesh refinement, the other by element order upgrade. The difference between h-adaptive and p-adaptive solution methods is that, in h-adaptive, mesh changes while element order stays the same, while in p-adaptive, mesh stays the same but element order changes.

h vs. p Elements

Let us pause to explain some terminology:

Question:

Why are upgradeable elements called p-elements?

Answer:

The iterative process that we are currently discussing does not involve mesh refinement. While the mesh remains unchanged, the element order changes from the initial 2nd order all the way to 5th order (or less if the convergence criterion is satisfied sooner).

The element order is defined by the order of polynomial functions that describe the displacement field in the element. Because the polynomial (p) order experiences change, the process is called the p convergence process, and the upgradeable elements we use are called p-elements.

Question:

Why is the p convergence process called a p-adaptive solution, and what exactly does “adaptive” mean?

Answer:

Adaptive means that not all p-elements are necessarily upgraded during the solution process.

Indeed, as you see in the p-adaptive options area, Update elements with relative Strain Energy error of _% or more means that only those elements not satisfying the above criterion are upgraded. We say, therefore, that element upgrading is “adaptive”, or driven by the results of consecutive iterations. This is in close analogy to h-adaptive solution (performed earlier in this lesson), where the mesh was refined during consecutive loops.

We are now sufficiently familiarized with p-elements to proceed with

p-adaptive solution.

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Adaptive Meshing

Create mesh. Right-click Mesh and select Create Mesh.

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Under Advanced, select At nodes for Jacobian points.

4

Mesh the model and run the analysis. Create a High quality mesh using the Curvature based mesh intended for

p-elements with the mesh density slider set to Coarse.

Considering that a p-adaptive solution is used, we can manage with a coarser mesh. Select Run (solve) the analysis to combine the mesh and run steps into one.

This mesh would not be acceptable for use in the standard study because there are not enough elements to capture the complex stress field, especially near the rounds. Using higher order p-elements, however, is equivalent to refining an h-element mesh, so that even this coarse mesh delivers accurate results.

Note

5

Run.

When the analysis runs, the solution progresses in steps corresponding to the number of element-order upgrades.

6

Display von Mises stress plot.

Now that we have solved the study with p-elements, we display a von Mises stress plot.

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To set the plot settings, right-click the stress plot and select Settings. Select Discrete for the Fringe options and select Mesh for the Boundary options.

The resulting stress plot shows a maximum von Mises stress of 207 MPa [30.0ksi], which is just above the yield stress of AISI 304.

Note

Any plot (stress, displacement, strain, and so on) in the results folders of the p elements study displays the final result, or the last step of the p-adaptive solution process. In addition to displaying the final plot results, we can also access the history of the iterative solution.

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Create a convergence graph. Right-click the Results folder and select Define Adaptive Convergence Graph.

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Because we are primarily interested in the maximum von Mises stress, select Maximum von Mises stress in the Options.

Click OK.

8

Review the graph.

Let us review the graph and make a few observations about the padaptive solution.: I

I

I

I

9

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The p-adaptive iterations went through all four steps: the first using the second order elements, and the next three with higher order element up to the 5th order. The 0.05% strain energy error we specified in the properties of the p-adaptive study is NOT stress error. The maximum strain energy error of 0.05% has not been achieved and we would have to continue with the iterations further to reduce the error. (The maximum element order is limited by 5, however.)

The stress units in the graph are N/m2. SI units are internally used by SolidWorks Simulation for calculations, regardless of what units are used in the model.

Save and Close the file.

SolidWorks 2012

Lesson 13 Adaptive Meshing

Now, let us summarize the results of all three studies executed in this lesson. Recall that information on the number of degrees of freedom is taken from the OUT file corresponding to the given study in the SolidWorks Simulation data base.

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Method Comparison

Solution type

Max. resultant displacement

Max. von Mises stress [psi]

# D.O.F.

Standard

0.427 mm [0.0168 in]

207.5 MPa [30,094 psi]

37479

h-adaptive

0.428 mm [0.0168 in]

229.3 MPa [33,254 psi]

75225

p-Adaptive

0.428 mm [0.0168 in]

207.9 MPa [30,150 psi]

42801

Displacement results are practically the same. Stress results are within 9%. Considering that a highly concentrated stress is rather difficult to model with any solution technique, this accuracy is satisfactory. Standard solution appears to be the most economical; it had the shortest solution time.

Having completed the exercise with three solution methods, we note that h-adaptive and p-adaptive solution methods are very close, conceptually. Upgrading the element order in the p convergence process adds degrees of freedom to the model, which is a direct analogy to adding degrees of freedom by mesh refinement in the h convergence process. This explains why we can use a coarse mesh for both h-adaptive and p-adaptive solution. The degrees of freedom that are “missing” in the initial mesh are added in the process of iterative solution either by mesh refinement or by element order upgrade, and produce an analogous effect to using a standard solution technique with properly refined mesh.

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The following table summarizes the differences between h-adaptive and p-adaptive solutions.

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h vs. p Elements Summary

Solution type

h-adaptive

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p-adaptive

Element order

2nd order, does not change during the solution.

Changes during the solution process from 2nd to max. 5th to satisfy the accuracy requirements.

Mesh adaptivity

Mesh is changed by refinement (both element size and location of refinement) and adapts to the pattern of stress distribution found in the model. High stress gradients are meshed with more refined mesh.

Mesh does not change.

Global error control

Total Strain Energy (called Target accuracy)

Total Strain Energy, or RMS Resultant Displacement, or RMS von Mises stress

Local error control

Local strain energy (called Accuracy bias)

Local strain energy

Maximum number of loops

Unlimited: The study can re-run repeatedly until the desired accuracy level is reached.

Four: The first one with 2nd order elements, the last one with 5th order elements but, mesh can be refined then re-run.

Element order adapts to the pattern of stress distribution found in the model. High stress gradients are meshed with higher element order.

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The standard solution using h elements? The h-adaptive solution using h elements? The p-adaptive solution using p elements?

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Which Solution Method is Better?

I

Generally, with the standard solution method using second order elements, we obtain a reasonably accurate solution within a reasonably short time.

Experience indicates that the standard solution method utilizing second order elements offers the best combination of accuracy and computational efficiency. For this reason, the automesher in SolidWorks Simulation is tuned to meet the requirements of an h-element mesh intended for the standard solution method.

Both h-adaptive and p-adaptive methods involve iterative solutions that stop either when the accuracy requirement has been satisfied or when the maximum allowed number of iterations has been reached. In this lesson, we requested a very low error to make sure that the solver goes through the maximum number of iterations. This way we obtained solutions with low, but not explicitly known, error. Try running h-adaptive and p-adaptive studies again with relaxed accuracy requirements so that the solver does not use up all available loops. If the convergence graph shows:

less than six iterations have been performed for h-adaptive solution or... I less than four iterations have been performed for p-adaptive solution, I

then this means that the solution has stopped because your accuracy requirements have been satisfied and not because the maximum number of loops has been reached.

Summary

Both h-adaptive and p-adaptive solution methods are significantly more time-consuming. Therefore, these solution methods are reserved for special cases where the solution must have narrowly specified accuracy.

The adaptive solution methods are also great learning tools, leading to a better understanding of element order, the convergence process, and discretization error. For this reason, you are encouraged to repeat some of the lessons presented in this course using the adaptive solution technique of your choice.

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PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Lesson 14 Large Displacement Analysis

Objectives

Upon successful completion of this lesson, you will be able to: I

Understand the difference between geometrically nonlinear (large displacement and geometrically linear (small displacement) analyses.

I

Perform geometrically nonlinear (large displacement) analysis.

I

Assess limitations of the linear material model.

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Large Displacement Analysis

As explained in the beginning of this course, SolidWorks Simulation computations are limited to the small displacement class of problems (geometrically linear analysis). In this lesson, we will show that this limitation is actually not present and SolidWorks Simulation is capable of solving large displacement, nonlinear problems as well.

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Small vs. Large Displacement Analysis

In small displacement analysis, it is assumed that the shape of the model before and after the deformation took place is nearly identical.

Consider a cantilever beam loaded by a pressure, as shown in figure a below. First, let us assume that our load is small in relation to the stiffness of the beam, resulting in deformations that are barely noticeable (figure b). The stiffness of the deformed beam, [ K 1 ] , which is a function of geometry and the material, will be nearly identical to the original stiffness of the undeformed beam, [ K ] . We can conclude that [ K ] ª [ K 1 ] , and that the linear elastic solution [ K ] { u } = { F } is valid as long as the above assumption is acceptable. a.

b.

c.

If the same beam is loaded with a significantly larger pressure, its deformation will become large. Because of the significant change in the geometry, the stiffness of the this beam, [ K 2 ] , is considerably different, and the linear elastic solution is no longer acceptable. Cases b and c are commonly referred to as small displacement and large displacement problems, respectively.

Large displacement problems are of a nonlinear nature. They are significantly more complicated because they require a gradual increase of the load in small increments and elaborate iterational schemes to converge the solution to the equilibrium. They are very sensitive to the selection of the various analysis parameters and their solution requires some experience.

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Case Study: Clamp

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A u-shaped clamp will have a force applied to one side while the other side remains fixed. For small applied forces, the clamp will still retain its u-shape. If the force is larger, the ends of the clamp will get closer together or touch which will require a large displacement analysis. We will analyze the clamp using both small and large displacement methods and compare the results.

Project Description

A clamp is bent with a 14,000 N [3,147 lb.] force applied to one arm while the other arm rests on a rigid support (such as a steel block or concrete foundation).

It is known that this load deforms the clamp significantly and brings both of the arms in contact.

Determine whether this load causes the arms to touch and if the clamp remains permanently bent after removal of the load.

Part 1: Small Displacement Linear Analysis

First, we will attempt to solve this problem as linear, with the assumption of small displacements.

1 2

Open an assembly file. Open clamp located in the Lesson14\Case Studies folder. Define study.

Define a Static study named small displacements.

3

Review material properties.

The material properties of Alloy Steel are automatically transferred from SolidWorks.

4

Apply restraint.

Locate the two faces created by the split lines on the outside of the arms. Apply Fixed Geometry restraint to one face.

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Apply force. Apply a 14,000 N force normal to the other

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5

face.

6

Define surface contact set. Define a No penetration, Node to Surface

contact set between the two small faces at the end of the clamp arms.

7

Mesh assembly.

Mesh the assembly with High quality elements and the default settings using the Curvature based mesh.

8

Specify Direct Sparse solver.

Direct sparse solver is considerably faster for this type and size of problem.

9

Run the analysis.

SolidWorks Simulation solver detects the large displacements in the model and issues a warning.

Excessive displacements were calculated in this model. If your system is properly restrained, consider using the Large Displacement option to improve the accuracy of the calculations. Otherwise, continue with the current settings and review the causes of these displacements.

Click No to complete the analysis as linear with small displacements.

10 Plot resultant displacements. Create a URES: Resultant displacement plot in True deformation

scale.

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11 Examine the model.

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A quick review of displacement results reveals that the loaded arm has overextended the fixed arm. Obviously, this result is incorrect.

Results Discussion

The ignored warning of the solver along with the incorrect displacement results are sufficient reasons to invalidate the produced results. Therefore, we do not have to analyze the stresses.

Contact Solution in Small and Large Displacement Analyses

In small displacement analysis, the normals to the contact areas do not change directions during the loading. This implies that the direction of the normal and friction forces remains fixed as well.

Contrarily, in the large displacement analysis, the directions of the normal and friction forces are updated during the deformation process. Because of the potential significant displacements and sliding in the contact regions during the large displacement analysis, the Node-tonode (No penetration) contact option should not be used. For more information on the contact solution in a geometrically nonlinear analysis, consult the SolidWorks Simulation Premium: Nonlinear training manual.

Part 2: Large Displacement Nonlinear Analysis

To obtain the correct solution, we must use large displacement formulation.

1

Create new study.

Duplicate the study named small displacements into a new study named large displacements.

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Set study properties. Right-click study large displacements and select Properties. Select the Options tab and then select Large displacement.

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2

Click OK.

3

Run the analysis.

Note that the solution takes significantly longer due to the extra time required to increment the load in steps, as discussed earlier.

4

Plot resultant displacements. Plot the distribution of URES: Resultant displacements.

5

Examine the model.

We can observe that the detail of the displacements at the tip location is what we would expect, i.e. the tip edges of the contact surfaces are nearly touching.

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6

Plot von Mises stresses.

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Stress results are also consistent with what we expect to see in a bending problem such as this.

7

Analyze the results.

There is no high stress shows in the contact region because the mesh size is too large to capture these localized contact stresses.

Observing that contact area is very small (in fact, the solution presents it as a line contact) we conclude that our choice Node to surface option in No penetration contact set definition is correct. While stress results obtained using the large-displacement contact option are generally correct, a closer examination reveals some problems. Additionally, the stresses are well above the yield strength of the material, however this lesson is for demonstration purposes only.

8

Permanent Deformation

Save and Close the file.

It is evident that significant portions of the clamp experience stresses above the yield stress. Therefore, after the load is removed, the clamp will not return to its original shape.

This is as far as we can take this problem using a linear material model (the large displacement analysis is geometrically nonlinear, but the material model is linear elastic).

To determine the shape and residual stresses in a permanently deformed clamp after the load has been removed, the analysis must include a nonlinear material model. This option is available in SolidWorks Simulation Nonlinear modulus which is part of the SolidWorks Simulation Premium suite.

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Large Displacement Analysis

The presence of a geometrically nonlinear solver (large displacement option) in SolidWorks Simulation provides the user with the very powerful feature to solve problems out of the scope of the geometrically linear static study. However, the solution of these problems in general requires the correct setup of various parameters and solver options. Because a large displacement option of SolidWorks Simulation uses a predefined set of parameters, its solution success is limited.

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SolidWorks Simulation Premium

All of the features and options of the advanced nonlinear solver are available in SolidWorks Simulation Nonlinear modulus which is part of the SolidWorks Simulation Premium suite. Furthermore, multiple advanced material models are available in SolidWorks Simulation Premium only. Users who wish to take their SolidWorks Simulation expertise to the next level are encouraged to inquire about SolidWorks Simulation Premium suite and to take a SolidWorks Simulation Premium: Nonlinear training course.

Summary

In this lesson, we ventured into the next level of FEA analysis and discussed and practiced the basic characteristics of the geometrically nonlinear (large displacement) analysis. The limitations of the geometrically linear (small displacement) analysis were discussed as well.

We first attempted to solve the problem using a small displacement formulation, but erroneous displacement results indicated the need to consider this analysis as a large displacement problem.

In the large displacement problem, the load was applied in steps and the model stiffness was updated during the deformation process. This process took longer to solve, but was required to obtain accurate results. Stress results indicated that the clamp will remain permanently deformed after the load has been removed, but for a quantitative analysis of this deformation a nonlinear material analysis would be required.

Finally, the significance of a SolidWorks Simulation Premium suite upgrade for users interested in nonlinear FEA was discussed.

Questions

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SolidWorks Simulation suite computations (are / are not) limited to small displacement analyses only.

I

SolidWorks Simulation suite computations (are / are not) limited to models that experience stresses below the material yield strength.

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Meshing, Solvers, and Tips & Tricks

Meshing, more precisely called discretization, is what converts a mathematical model into a finite element model ready for solution.

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Meshing Strategies

As a finite element method, meshing accomplishes two tasks. First, it replaces a continuous model with a discrete one. Meshing, therefore, reduces the problem to one with a finite number of unknowns suitable for solution with an approximate numerical technique. Second, it represents the desired solution (e.g., displacements or temperatures) with an assembly of simple polynomial functions defined individually for elements. See the Introduction to FEA section of the manual for a description of this process.

For the user, meshing is a necessary step towards the problem solution. Many new FEA users expect meshing to be a fully automated process requiring little, in any, input from the user. With experience comes the realization that meshing is often a demanding task.

The history of development of commercial FEA software witnessed many attempts to make meshing invisible to FEA users, but this has not been a successful approach.

While the meshing process has been simplified and automated, it is still not a “hands-off” task that runs in the background. As FEA users, we require a means to interact with the meshing process. SolidWorks Simulation finds the fine balance by isolating us from those issues that are purely meshing-specific, but providing us control over meshing when needed.

Geometry Preparation

Ideally, we use SolidWorks geometry, toggle to SolidWorks Simulation, where we define the type of analysis and material, apply external loads and fixtures, and then we mesh the geometry and obtain the solution.

This approach works well for simple models. More complex geometry requires preparation before it can be meshed. In the process of geometry preparation for FEA, we depart from manufacturing-specific, CAD geometry and construct geometry intended specifically for analysis. We call this geometry FEA geometry.

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We differentiate between CAD geometry and FEA geometry based on their different requirements: CAD Geometry

Must contain all information necessary for manufacturing

FEA Geometry

Must be meshable

Must allow for creation of a mesh that will correctly model the data of interest Must allow for creation of a mesh solvable within a reasonable time

Often CAD geometry does not satisfy the requirements of FEA geometry. CAD geometry serves as a starting point in the process of FE model preparation, but is only seldom used for FEA without modifications. We now describe several actions performed on manufacturing-specific, CAD geometry in order to convert it into FEA-specific geometry.

Defeaturing

CAD geometry contains all the features necessary to make a part. Many of those features are unimportant for analysis and should be suppressed prior to meshing.

At best, leaving such features results in an unnecessarily complicated mesh and a long solution time. At worst, it may prevent the mesher from completing its task.

Of course, determining which features to exclude and which to include in the FE model requires careful engineering judgment. The small size of a feature as compared to the overall size of the model does not always justify its exclusion. For example, very small internal fillets should be retained in the model if the objective of the analysis is to find stresses in the area of the round.

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Idealization modifies CAD geometry more substantially than defeaturing. Idealization may, for example, involve converting 3D, solid-CAD geometry into surface geometry suitable for subsequent meshing with shell elements.

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Idealization

SolidWorks Simulation can automatically create shell elements if the geometry was modeled as sheet metal in SolidWorks. If the part was modeled as a solid body, however, surfaces must be created in the SolidWorks model so that shell elements can be created.

CAD geometry meshed with solid elements

Idealized geometry meshed with shell elements

Note that idealization creates an abstract geometry (zero thickness surface) suitable exclusively for analysis.

Clean-up

Clean-up refers to issues of geometry quality that must be dealt with to enable correct meshing.

Clean up

Geometry that is adequate for manufacturing purposes may contain features that either do not mesh or force the mesher to create a large number of elements or create distorted elements. Examples include very short edges and/or faces. Those small features must be removed or the automesher tries to mesh them.

Mesh creation may also fail because of quality issues, including multiple entities, floating solids, and other quality problems.

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To avoid creating elements with tangent edges (see Mesh Quality later in this appendix), geometry faces may have to be merged.

Before merging

Mesh Quality

After merging

Creating a solid-element mesh can be likened to a process of filling up a volume with tetrahedral elements, while creating a shell-element mesh can be likened to filling up a surface with triangles. Recall from the Introduction to FEA section of this manual, that in the vast majority of problems, the second-order, tetrahedral elements and second-order, triangular elements map to curvilinear geometry and are much easier to work with when meshing and analyzing.

This observation exemplifies the fact that elements experience distortion during meshing, which brings us to the issue of mesh quality. While elements are almost always distorted in the process of mapping to geometry, excessive distortion leads to element degeneration. Mesh degeneration can often be prevented by controlling the default element size or applying local mesh or component controls. We have practiced mesh controls in many lessons. Now we discuss the most important forms of element distortion.

Aspect Ratio Check

Numerical accuracy is best achieved by a mesh with uniform, perfect, tetrahedral or triangular elements whose edges are equal in length. For a general geometry, it is not possible to create a mesh of perfect, tetrahedral elements. Due to small edges, curved geometry, thin features, and sharp corners, some of the generated elements can have some edges much longer than others. When the edges of an element become much different in length, the accuracy of the results deteriorates.

ASPECT RATIO inscribed / circumscribed circles

AR

large radius small radius

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The aspect ratio of a perfect, tetrahedral element is used as the basis for calculating aspect ratios of other elements. The aspect Correct element shape Excessively distorted ratio of an element is elements defined as the ratio between the longest edge and the shortest normal dropped from a vertex to the opposite face normalized with respect to a perfect tetrahedral. By definition, the aspect ratio of a perfect tetrahedral element is 1.0. The aspect-ratio check is automatically used by the program to check the quality of the mesh and assumes straight edges connecting the four corner nodes.

As part of the aspect-ratio check, SolidWorks Simulation performs an edge-length check, a radius of inscribed and circumscribed radius check and a length of normals check. ASPECT RATIO edge length checks

AR

ASPECT RATIO edges/face normal ratio

long edge length short edge length

long edge

short edge

AR

longest normal shortest normal

This aspect-ratio measure does not recognize “flat” elements as bad.

Jacobian Check

Second-order elements map to curved geometry much more accurately than linear elements of the same size. The mid-side nodes of the boundary edges of an element are placed on the actual geometry of the model. In sharp or curved boundaries, placing the mid-side nodes on the actual geometry can result in generating distorted elements with edges overlapping each other. The Jacobian of an extremely distorted element becomes negative. An element with a negative Jacobian causes the analysis program to stop.

The Jacobian check is based on a number of points located within each element. SolidWorks Simulation gives you a choice to base the Jacobian check on 4, 16, or 29 Gaussian points or At Nodes.

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The Jacobian ratio of 1.0 is given to a parabolic, tetrahedral element with all mid-side nodes located exactly at the middle of the straight edges. The Jacobian ratio increases as the curvatures of the edges increase. The Jacobian ratio at a point inside the element provides a measure of the degree of distortion of the element at that location. SolidWorks Simulation calculates the Jacobian ratio at the selected number of Gaussian points for each tetrahedral element. JACOBIAN CHECK

Correct element

Self-intersecting element

It is generally the case that a Jacobian ratio of 40 or less is acceptable. SolidWorks Simulation adjusts the locations of the mid-side nodes of distorted elements automatically to ensure that all elements pass the Jacobian check.

Even if this check of mesh quality does not issue warnings, avoiding elements that are too “concave” is generally good practice. This can be accomplished by using mesh controls or adjusting the global element size.

Note

SolidWorks Simulation tries to place two elements over a 90° arc. This, combined with global elements that are too large, may lead to very small elements placed next to large elements.

Too rapid a transition in element size

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If arc is larger than 90°, one element is placed over the arc leading to the creation of elements with “concave” faces.

Concave elements

Applying mesh controls (here to the round face) allows for the creation of a correct mesh.

Correct mesh

Mesh Controls

We have practiced the use of mesh controls in many lessons. For easy reference, we review them now. Generally, mesh controls can be applied to faces, edges, vertices, and assembly components. Mesh control applied to:

Faces

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Edges

Vertices

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The definition of mesh controls applied to a part consists of specifying the following: I I

Element size on the selected entity Ratio of element size between the layers

Element size ratio between layers = 1.5

Element size ratio between layers = 1.1

The definition of mesh controls applied to a component consists of specifying the Component significance, which instructs the mesher, based on the position of the slider, to use a different element size for each selected component.

The left end of the slider corresponds to using the default globalelement size of the assembly. The right end of the slider corresponds to using the default element size if the component is meshed independently.

Low component significance

High component significance

If the option Use the same element size is selected, then all selected components are meshed with the same element size as specified in Mesh Control window.

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Meshing, Solvers, and Tips & Tricks

Many meshing problems can be solved by using a smaller element size. Using a smaller element size, of course, results in longer solution times.

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Automatic Trials for Solids

To find the largest element size that still meshes, we can use Automatic trials for solids, specified in the advanced meshing options. Automatic looping instructs the mesher to automatically mesh the model again using a smaller, global element size. You control the maximum number of trials allowed and the ratio by which the global element size and tolerance are reduced each time.

Meshing Stages

Meshing proceeds in three steps: I I I

Evaluating the geometry Processing the boundary Creating the mesh

Meshing problems may arise at any step.

During the first step, evaluating the geometry, SolidWorks Simulation checks the geometry imported from SolidWorks. Geometry import is completely transparent to the user.

The actual meshing of a solid component consists of two phases. When processing the boundary, the mesher places nodes on the boundary. This phase is called surface meshing. If this phase is successful, the third phase, creating the mesh, starts as the volume is filled with tetrahedral elements. If meshing fails when evaluating the geometry, the most likely cause is a geometry error. To verify if geometry error is the cause, export the geometry as an IGES to see if the error message, “Failed to process trimmed surface entity” is displayed. If this message appears, send the part to SolidWorks support for diagnosis of the geometry problem.

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Appendix A Meshing, Solvers, and Tips & Tricks

When meshing fails, SolidWorks Simulation displays a message and stops unless the automatic mesh looping is active. A failure diagnostics tool is provided to help you locate and resolve solid-meshing problems.

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Failure Diagnostics

The Failure Diagnostics PropertyManager lists the components, faces, and edges that fail. It also highlights the failed entities in the model window. To review the entities that prevented successful meshing, right-click Mesh and select Failure Diagnostics.

The offending entities are listed in Failure Diagnostics window and highlighted in the graphics window and the study tree.

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Meshing, Solvers, and Tips & Tricks

Check for underdefined sketches. Use SolidWorks Utilities to find sliver faces, knife edges, and so on.

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Tips for Meshing Parts

For meshing failures on faces, create a shell study and select only the failed face. Then try various element sizes until that face meshes.

If the mesh failure diagnostics do not provide enough information to determine the exact location of the problem, successively cut portions off the model to isolate the region of failure, or roll back the SolidWorks models until the model meshes.

Tips for Meshing Assemblies

Select Tools, Interference Detection to determine where parts interfere and where faces touch (coincident). Remember that interference is allowed only if the shrink fit contact condition is defined.

Do not model line contact (such as a cylinder tangent to a plate) or point contact (such as the top of a cone touching a plate) between assembly components. The area of contact should be > 0.

Note that when SolidWorks Simulation meshes an assembly, “imprints” are made on all touching faces, allowing the nodes from both components to align.

If bonded contact conditions have been defined, then the same node is shared by both components. If node to node or surface conditions have been defined, two coincident nodes are created and joined by gap elements. Gap elements remain invisible to the user. Note that the color of the imprint in the following illustration has been modified in a graphics program to make it clearly visible.

Imprint

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Beware of imprints that cause sliver faces, thin annular faces, or faces with multiple “lobes” connected by thin sections.

Thin section

Tips for Using Shell Elements

Sliver face

Shell meshing uses only the surface meshing phase; no volume filling occurs.

Although the use of shell elements results in a simpler model that solves faster than a corresponding solid-element model, preparation of a shell-element mesh is more time consuming as compared to a solidelement mesh. Meshing in mid-planes often results in disjointed meshes.

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Meshing, Solvers, and Tips & Tricks

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If surface geometry is to be meshed, split lines may be used where surfaces meet to ensure alignment of the nodes and, consequently, mesh compatibility. However, incompatible mesh with misaligned nodes is also allowed!

No split lines

Split lines added

Hardware Considerations in Meshing

Incompatible mesh

Compatible mesh

Meshing is the most critical step on the way to obtaining a solution. The maximum mesh size, meaning the smallest, element size that can be used, depends on the amount of random access memory. While the simple rule “the more the better” applies, we recommend 2 GB for working with real-life, complex models.

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Having successfully meshed the model we are only one step away from obtaining a solution.

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Solvers in SolidWorks Simulation

Generally, if a model can be meshed, it will solve; solving is a less critical step than meshing.

However, several problems can arise. The solver may find problems with model definition, such as no definition of material or loads. The kinds of issues that prevent solution depend, of course, on the type of analysis (static, frequency, and so on).

The solver may also detect rigid body motions due to insufficient restraints. Rigid body motions can be dealt with using solver options, such as Use soft spring to stabilize model or Use inertial relief. Available solver options depend on the type of analysis. Static analysis

Frequency analysis

Buckling analysis

Soft springs

Soft springs

Soft springs

In-plane effects

In-plane effects

Inertial relief

The meshed model is presented to the solver in the form of a large number of linear algebraic equations. Those equations can be solved with two classes of solution methods: direct and iterative.

Direct methods solve the equations using exact numerical techniques. Iterative methods solve the equations using approximate techniques where, in each iteration, a solution is assumed and the associated errors are evaluated. The iterations continue until the errors become acceptable. SolidWorks Simulation offers two solvers types:

I I

Choosing a Solver

Direct Sparse solver FFEPlus (iterative)

In general, all solvers give comparable results if the required solver options are supported. While all solvers are efficient for small problems (25,000 degrees of freedom or less), big differences in performance (speed and memory usage) occur in solving large problems.

If a solver requires more memory than available on the computer, the solver uses disk space to store and retrieve temporary data. When this situation occurs, a message appears saying that the solution is going out of core, and the solution progress slows down. If the amount of data to be written to the disk is very large, the solution progress can be extremely slow.

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Meshing, Solvers, and Tips & Tricks

The following factors help you choose the proper solver: Size of the problem

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I

In general, FFEPlus is faster in solving problems with degrees of freedom (DOF) over 100,000. This solver becomes more efficient as the problem gets larger.

I

Computer resources

The Direct Sparse solver, in particular, becomes faster with more memory available on your computer.

I

Analysis options

I

Element type

I

Material properties

When the moduli of elasticity of the materials used in a model are very different (like Steel and Nylon), iterative solvers are less accurate than direct methods. The Direct Sparse solver is recommended in such cases.

A solver can be selected in the study properties. Since the choice of the most suitable solver requires some experience, an automatic selection has been implemented as well. Use this option if you are not sure which solver is best suited for your analysis.

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Customer Help and Assistance

SolidWorks Simulation features extensive apparatus to help you with various information needs.

SolidWorks Simulation Help

Nearly every dialog window contains a help icon. Use this as your initial help option. Here you will find answers to most of the common questions relevant to the desired topic or SolidWorks Simulation function.

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Customer Help and Assistance

The above figures show how to access SolidWorks Simulation help files from the most common dialogs that you may encounter in SolidWorks Simulation.

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Appendix B Customer Help and Assistance

Select Research on the Simulation menu to display the Analysis Research tab in the Task Pane.

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Online Resources

This area contains countless resource information in organized and accessible form. The functionality of some of the links in the Analysis Research dialog is described in the following text.

I

Search Knowledge Base

This database contains numerous targeted, well-organized and maintained articles on various topics in analysis theory, SolidWorks Simulation usage and troubleshooting, licensing, and many other practical areas. We strongly encourage users to use this feature as often as possible. Valid subscription and internet connection are required to access this information database.

I

Search Matweb

A search query in this field will take you directly to the free online material database matweb.com (free Premium membership is also available). Internet connection is required to use this feature.

I

Downloads

The latest upgrades and service packs (SP) can be downloaded from the web download page that can be accessed via this feature.

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Customer Help and Assistance

Complete customer account information and customer service and maintenance links can be accessed via the Customer service portal accessible from www.solidworks.com website. The portal allows you to submit service and enhancement requests, search the knowledge base, view the information on the online seminars and various discussion forums and much more.

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Customer Support Portal

Customer Phone Support

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Subscription customers have access to the dedicated phone and email technical support. Please contact your local reseller for the local technical support telephone number and email address. A customer serial number is always required.

PR Do E no RE t c LE op AS y E or D di RA st F rib T ut e Index

A activate SW configuration 96 adaptive meshing 446 analysis process 24 analysis research 336 animate plot 58 annotating plots 138 artificial restraints 157 aspect ratio 479 aspect ratio plot 262 automatic looping 484 averaging stress 435 axial stiffness 256

B beam elements 363 beam joint types 367 beam joints 367 bearing load 212 bending moment diagram 369, 377 bolt force 203 bolts pre-load 246 tight fit 245 bonded 142 bonded contact 229 bonding shell edge to shell face 339 shell face to shell face 339 shell to solid 340 boundary conditions 102 bulk modulus 338

C CommandManager 27 component local options 141 connector bearing 191 bolt 191 elastic support 191 link 191 pin 191, 195 rigid 190 spot weld 191 spring 190, 198 contact 130 bonded 142 bonding shells and solids 330–331, 378

component options 140 contact set 142, 151 free 142 large displacement contact 471 local contact sets 250 local options 140 no penetration 142–143, 250 shrink fit 142, 158 surface contact 470 virtual wall 142 contact stress 146, 162 convergence 64 convergence graph 454 copy parameters 61 create study 32 Curvature Based Mesh 43 customer support portal 494 cylindrical coordinate system 160

fixtures 34 definition 42 symmetry 280 flow/thermal effects tab 432 force type 38

D defeaturing 155 define force 39 design check plot 266 design scenario 402, 404, 411 graph 416

I idealization 478 importing temperatures 433 inertial relief 165 iso plots 52, 59

E Elastic 191 element types 10 element values 50 elements first order shells 13 first order tetrahedral 11 second order 12 second order shells 14 external loads 38, 42

F failure diagnostics 343, 485 find contact sets 250, 252, 369 fixture type circular symmetry 34 fixed geometry 34 hinge 34 on cylindrical face 35 on flat face 35 on spherical face 35 roller/sliding 34 symmetry 34 use referene geometry 35

G gap analysis 130 gap clearance 254 geometry preparation 476 gravity load 421 H h-adaptive 449 accuracy bias 451 solution parameter 450 target accuracy 451 Hoop Stress 161

J jacobian 264 jacobian check 480

K knowledge base 258, 493 L large displacement 467 local contact options 141 local contact sets 250 Local mesh control 91 local mesh refinement 90

M material 336 material properties 42 assigning 32 thermal 427 materials apply to assemblies 131 Matweb 493 Maximum element size 44 mesh

495

Index

R remote load 242 reports 67 Restraint Type 34 restraint types 34 result folder 28 results 95 rigid body mode 157 rotational stiffness 256 run analysis 47 Run Analysis After Meshing 281

thermal stress analysis 426 thin components 278 treat as solid 307

S saving all plots 164 saving deformed model 442 section plot 52, 59, 144 set mesh options 45 shear force diagram 369, 377 shear modulus 338 shell elements 285, 487 shell meshing automatic surface alignment 292 shell mesh alignment 289, 291 thin/thick shells 287 show plot 47 shrink fit 154 shrink fit contact 142 simulation interface 26 simulation options 28 simulation study tree 26 simulation toolbar 27 singularities 95 soft springs 164 SolidWorks 5 solvers 489 spot weld 191 spring connector options 198 steel identification systems 336 strain plot 59–60 stress averaging 435 contact 146 principal 18 stress singularities 95 studies create 61 multiple studies 52 renaming 31 symbols cylindrical system icon 161 display/hide 35, 41 fixture 37 joint 365, 369, 380 mesh control 91 size and color 41 symmetry 154 symmetry fixtures 280

W-Z zero strain temperature 432

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aspect ratio 262 compatible 231 compatible/incompatible 229–230 control 86, 90 control in an assembly 240 controls 482 details 62 display/hide 46 incompatible 234 jacobian 264 local mesh refinement 90 quality 46, 479 ratio 44 required elements 262 shell elements 285 thin vs. thick elements 287 mesh control 86 mesh control symbols 91 Mesh Density 43 mesh details 62 meshing 43 adaptive 446 automatic looping 484 beam elements 363 h vs. p elements 457, 459 h-adaptive 449 hardware considerations 488 mixed 330, 362 p-adaptive 457 shell elements 487 stages 484 strategies 476 Minimum element size 44 Minimum Number of Elements in a Circle 44 mixed meshing 230, 330, 362 moment load 310 multiple studies 52, 60

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N nodal values 50 nodal vs. element stresses 49 P p-adaptive 457 Parameters 404 permanent deformation 473 pin force 203 plot settings 29 plots bending moment 369, 377 design check 266 editing 48 iso 52, 59 modify result plots 50 result 47 save all 164 section 52, 59, 144 shear force 369, 377 postprocessing 47 preprocessing 31 Pressure Load 281 principal stresses 18, 98 probe 52

496

T tangential stiffness 257 temperature load 431–432, 437 temperatures importing 433 thermal material properties 427

U units 19 UNS index 336

V virtual wall 142 Von Mises Stress 17