NX Nastran 8 Verification Manual
Proprietary & Restricted Rights Notice
© 2011 Siemens Product Lifecycle Management Software Inc. All Rights Reserved. This software and related documentation are proprietary to Siemens Product Lifecycle Management Software Inc. NASTRAN is a registered trademark of the National Aeronautics and Space Administration. NX Nastran is an enhanced proprietary version developed and maintained by Siemens Product Lifecycle Management Software Inc. MSC is a registered trademark of MSC.Software Corporation. MSC.Nastran and MSC.Patran are trademarks of MSC.Software Corporation. All other trademarks are the property of their respective owners.
TAUCS Copyright and License TAUCS Version 2.0, November 29, 2001. Copyright (c) 2001, 2002, 2003 by Sivan Toledo, Tel-Aviv University,
[email protected]. All Rights Reserved. TAUCS License: Your use or distribution of TAUCS or any derivative code implies that you agree to this License. THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. Permission is hereby granted to use or copy this program, provided that the Copyright, this License, and the Availability of the original version is retained on all copies. User documentation of any code that uses this code or any derivative code must cite the Copyright, this License, the Availability note, and "Used by permission." If this code or any derivative code is accessible from within MATLAB, then typing "help taucs" must cite the Copyright, and "type taucs" must also cite this License and the Availability note. Permission to modify the code and to distribute modified code is granted, provided the Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. This software is provided to you free of charge. Availability (TAUCS) As of version 2.1, we distribute the code in 4 formats: zip and tarred-gzipped (tgz), with or without binaries for external libraries. The bundled external libraries should allow you to build the test programs on Linux, Windows, and MacOS X without installing additional software. We recommend that you download the full distributions, and then perhaps replace the bundled libraries by higher performance ones (e.g., with a BLAS library that is specifically optimized for your machine). If you want to conserve bandwidth and you want to install the required libraries yourself, download the lean distributions. The zip and tgz files are identical, except that on Linux, Unix, and MacOS, unpacking the tgz file ensures that the configure script is marked as executable (unpack with tar zxvpf), otherwise you will have to change its permissions manually.
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Contents
Proprietary & Restricted Rights Notice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Part I: Introduction Overview of the Verification Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1 Running the Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1 Part II: Linear Statics Verification Using Theoretical Solutions Overview of Linear Statics Verification Using Theoretical Solutions . . . . . . . . . . . 3-1 Understanding the Test Case Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1 Understanding Comparisons with Theoretical Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 3-2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2 Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1 Point Load on a Cantilever Beam . . . . . . . . . . . . . . . . . . . . . . Axial Distributed Load on a Linear Beam . . . . . . . . . . . . . . . . Distributed Loads on a Cantilever Beam . . . . . . . . . . . . . . . . . Moment Load on a Cantilever Beam . . . . . . . . . . . . . . . . . . . . Edge Pressure on Beam Element - Torque Loading . . . . . . . . . Thermal Strain, Displacement, and Stress on Heated Beam . . . Uniformly Distributed Load on Linear Beam . . . . . . . . . . . . . . Membrane Loads on a Linear Quadrilateral Thin Shell Element Axial Loading on Rod Element . . . . . . . . . . . . . . . . . . . . . . . . Stress on a Beam as It Expands and Closes a Gap . . . . . . . . . . Thin Wall Cylinder in Pure Tension . . . . . . . . . . . . . . . . . . . . Thin Shell Beam Wall in Pure Bending . . . . . . . . . . . . . . . . . . Strain Energy of a Truss . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4-1 4-3 4-4 4-6 4-7 4-9 4-11 4-13 4-15 4-17 4-18 4-20 4-22
Part III: Linear Statics Verification Using Standard NAFEMS Benchmarks Overview of Linear Statics Verification Using Standard NAFEMS Benchmarks . . . 5-1 Understanding the Test Case Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1 Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1 Elliptic Membrane . . . . . . . . . . . . . . . . . . Cylindrical Shell Patch Test . . . . . . . . . . . . Hemisphere-Point Loads . . . . . . . . . . . . . . Z-Section Cantilever . . . . . . . . . . . . . . . . . Skew Plate Normal Pressure . . . . . . . . . . . Thick Plate Pressure . . . . . . . . . . . . . . . . . Solid Cylinder/Taper/Sphere — Temperature
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. 6-1 . 6-5 . 6-8 6-10 6-12 6-14 6-18
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Contents
Part IV: Normal Mode Dynamics Verification Overview of Normal Mode Dynamics Verification Using Theoretical Solutions . . . 7-1 Understanding the Test Case Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1 Understanding Comparisons with Theoretical Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2 Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1 Natural Frequency of Circular Ring with Axisymmetric Model . . . . . . Undamped Free Vibration — Single Degree of Freedom . . . . . . . . . . . Two Degrees of Freedom Undamped Free Vibration — Principle Modes Three Degrees of Freedom Torsional System . . . . . . . . . . . . . . . . . . . Two Degrees of Freedom Vehicle Suspension System . . . . . . . . . . . . . Two Degrees of Freedom Vehicle Suspension System . . . . . . . . . . . . . Cantilever Beam Undamped Free Vibrations . . . . . . . . . . . . . . . . . . . Natural Frequency of a Cantilevered Mass . . . . . . . . . . . . . . . . . . . .
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8-1 8-2 8-4 8-5 8-7 8-8 8-10 8-12
Part V: Normal Mode Dynamics Verification Using Standard NAFEMS Benchmarks Overview of Normal Mode Dynamics Verification Using Standard NAFEMS Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1 Understanding the Test Case Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1 Beam Element Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1 Pin-ended Cross — In-plane Vibration . . . . . . . . . . Pin-ended Double Cross - In-plane Vibration . . . . . . Free Square Frame - In-plane Vibration . . . . . . . . . Cantilever with Off-center Point Masses . . . . . . . . . Deep Simply-Supported Beam . . . . . . . . . . . . . . . . Circular Ring — In-plane and Out-of-plane Vibration Cantilevered Beam . . . . . . . . . . . . . . . . . . . . . . . .
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10-1 10-3 10-6 10-8 10-9 10-11 10-13
Shell Element Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-1 Thin Square Cantilevered Plate — Symmetric Modes . . . . Thin Square Cantilevered Plate — Anti-symmetric Modes Free Thin Square Plate . . . . . . . . . . . . . . . . . . . . . . . . . Simply Supported Thin Square Plate . . . . . . . . . . . . . . . Simply Supported Thin Annular Plate . . . . . . . . . . . . . . Clamped Thin Rhombic Plate . . . . . . . . . . . . . . . . . . . . . Cantilevered Thin Square Plate with Distorted Mesh . . . . Simply Supported Thick Square Plate, Test A . . . . . . . . . Simply Supported Thick Square Plate, Test B . . . . . . . . . Clamped Thick Rhombic Plate . . . . . . . . . . . . . . . . . . . . Simply Supported Thick Annular Plate . . . . . . . . . . . . . . Cantilevered Square Membrane . . . . . . . . . . . . . . . . . . . Cantilevered Tapered Membrane . . . . . . . . . . . . . . . . . . Free Annular Membrane . . . . . . . . . . . . . . . . . . . . . . . . Cantilevered Thin Square Plate . . . . . . . . . . . . . . . . . . .
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11-1 11-3 11-6 11-8 11-10 11-12 11-15 11-19 11-22 11-25 11-27 11-30 11-33 11-35 11-38
Axisymmetric Solid and Solid Element Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . 12-1
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NX Nastran 8 Verification Manual
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Free Cylinder — Axisymmetric Vibration . . . . . . . . . . . . . Thick Hollow Sphere — Uniform Radial Vibration . . . . . . . Simply Supported Annular Plate — Axisymmetric Vibration Deep Simply Supported "Solid" Beam . . . . . . . . . . . . . . . . Simply Supported "Solid" Square Plate . . . . . . . . . . . . . . . Simply Supported "Solid" Annular Plate . . . . . . . . . . . . . . Cantilevered Solid Beam . . . . . . . . . . . . . . . . . . . . . . . . .
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12-1 12-3 12-6 12-8 12-11 12-15 12-19
Part VI: Verification Test Cases from the Societe Francaise des Mecaniciens Overview of Verification Test Cases Provided by the Societe Francaise des Mecaniciens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-1 Understanding the Test Case Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-1 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-2 Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements . . 14-1 Short Beam on Two Articulated Supports . . . . . . . Clamped Beams Linked by a Rigid Element . . . . . Transverse Bending of a Curved Pipe . . . . . . . . . . Plane Bending Load on a Thin Arch . . . . . . . . . . . Grid Point Load on an Articulated CONROD Truss Articulated Plane Truss . . . . . . . . . . . . . . . . . . . . Beam on an Elastic Foundation . . . . . . . . . . . . . .
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14-1 14-2 14-4 14-7 14-9 14-12 14-15
Mechanical Structures — Linear Statics Analysis with Shell Elements . . . . . . . . . 15-1 Plane Shear and Bending Load on a Plate . . . . . . . . . . . . . . . . . . . . . Infinite Plate with a Circular Hole . . . . . . . . . . . . . . . . . . . . . . . . . . Uniformly Distributed Load on a Circular Plate . . . . . . . . . . . . . . . . . Torque Loading on a Square Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . Cylindrical Shell with Internal Pressure . . . . . . . . . . . . . . . . . . . . . . Uniform Axial Load on a Thin Wall Cylinder . . . . . . . . . . . . . . . . . . . Hydrostatic Pressure on a Thin Wall Cylinder . . . . . . . . . . . . . . . . . . Gravity Loading on a Thin Wall Cylinder . . . . . . . . . . . . . . . . . . . . . Pinched Cylindrical Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spherical Shell with a Hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bending Load on a Cylindrical Shell . . . . . . . . . . . . . . . . . . . . . . . . . Uniformly Distributed Load on a Simply-Supported Rectangular Plate Uniformly Distributed Load on a Simply-Supported Rhomboid Plate . . Shear Loading on a Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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15-1 15-3 15-6 15-8 15-10 15-14 15-17 15-20 15-23 15-25 15-28 15-31 15-34 15-37
Mechanical Structures — Linear Statics Analysis with Solid Elements . . . . . . . . . 16-1 Solid Cylinder in Pure Tension . . . . . . . . . . . . . . . . . . . Internal Pressure on a Thick-Walled Spherical Container Internal Pressure on a Thick-Walled Infinite Cylinder . . Prismatic Rod in Pure Bending . . . . . . . . . . . . . . . . . . Thick Plate Clamped at Edges . . . . . . . . . . . . . . . . . . .
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. 16-1 . 16-7 16-12 16-17 16-21
Mechanical Structures — Normal Mode Dynamics Analysis . . . . . . . . . . . . . . . . . 17-1 Lumped Mass-Spring System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1 Short Beam on Simple Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-4 Axial Loading on a Rod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-7
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Cantilever Beam with a Variable Rectangular Section Thin Circular Ring . . . . . . . . . . . . . . . . . . . . . . . . . Thin Circular Ring Clamped at Two Points . . . . . . . . Vibration Modes of a Thin Pipe Elbow . . . . . . . . . . . . Cantilever Beam with Eccentric Lumped Mass . . . . . Thin Square Plate (Clamped or Free) . . . . . . . . . . . . Simply-Supported Rectangular Plate . . . . . . . . . . . . Thin Ring Plate Clamped on a Hub . . . . . . . . . . . . . . Vane of a Compressor - Clamped-free Thin Shell . . . . Bending of a Symmetric Truss . . . . . . . . . . . . . . . . . Hovgaard’s Problem — Pipes with Flexible Elbows . . . Rectangular Plates . . . . . . . . . . . . . . . . . . . . . . . . .
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17-10 17-12 17-15 17-18 17-21 17-24 17-26 17-28 17-31 17-34 17-37 17-40
Mechanical Structures — Normal Mode Dynamics Analysis and Model Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-1 Transient Response of a Spring-Mass System with Acceleration Loading . . . . . . . . . . . . . 18-1 Transient Response of a Clamped-free Post . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-4 Stationary Thermal Tests — Heat Transfer Analysis . . . . . . . . . . . . . . . . . . . . . . . 19-1 Hollow Cylinder - Fixed Temperatures . . . . . . . . Hollow Cylinder - Convection . . . . . . . . . . . . . . . Cylindrical Rod - Flux Density . . . . . . . . . . . . . . Hollow Cylinder with Two Materials - Convection Wall-Convection . . . . . . . . . . . . . . . . . . . . . . . . Wall-Fixed Temperatures . . . . . . . . . . . . . . . . . . L-Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthotropic Square . . . . . . . . . . . . . . . . . . . . . . Hollow Sphere - Fixed Temperatures, Convection . Hollow Sphere with Two Materials - Convection .
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19-1 19-3 19-5 19-7 19-10 19-12 19-14 19-16 19-19 19-22
Thermo-mechanical Tests — Linear Statics Analysis . . . . . . . . . . . . . . . . . . . . . . . 20-1 Orthotropic Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-1 Thermal Gradient on a Thin Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-4 Simply-Supported Arch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-7 Part VII: Material Nonlinear (Plasticity) Verification Using Standard NAFEMS Benchmarks Overview of the Material Nonlinear (Plasticity) Verification Using NAFEMS Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-1 Understanding the Verification Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-1 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-1 Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-1 Plane Strain Elements - Perfect Plasticity Tests . . Plane Strain Elements - Isotropic Hardening Tests Plane Stress Elements - Perfect Plasticity Tests . . Plane Stress Elements - Isotropic Hardening Tests Solid Element - Perfect Plasticity Tests . . . . . . . . Solid Element - Isotropic Hardening Tests . . . . . .
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NX Nastran 8 Verification Manual
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Contents
Part VIII: Geometric Nonlinear Verification Using Standard NAFEMS Benchmarks Overview of the Geometric Nonlinear Verification Using NAFEMS Test Cases . . . 23-1 Understanding the Verification Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-1 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-1 Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-1 Straight Cantilever with End Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-1 Straight Cantilever with Axial End Point Load - Brick Elements . . . . . . . . . . . . . . . . . . . 24-6 Straight Cantilever with Axial End Point Load - BEAM Elements . . . . . . . . . . . . . . . . . 24-11 Lee’s Frame Buckling Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-15 Large Displacement Elastic Response of a Hinged Spherical Shell Under Uniform Pressure Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-18 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-21 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-21
NX Nastran 8 Verification Manual
7
Part
I
Introduction
NX Nastran 8 Verification Manual
Chapter
1 Overview of the Verification Manual
This guide contains verification test cases for NX Nastran. These test cases verify the function of the different NX Nastran analysis types using theoretical and benchmark solutions from well-known engineering test cases. Each test case contains test case data and information, such as element type and material properties, results, and references. The guide contains test cases for: •
Linear Statics verification using theoretical solutions
•
Linear Statics verification using standard NAFEMS benchmarks
•
Normal Mode Dynamics verification using theoretical solutions
•
Normal Mode Dynamics verification using standard NAFEMS benchmarks
•
Verification Test Cases from the Societe Francaise des Mecaniciens
•
Material Nonlinear (Plasticity) verification using standard NAFEMS benchmarks (NX Nastran only)
•
Geometric Nonlinear verification using standard NAFEMS benchmarks
NX Nastran 8 Verification Manual
1-1
Chapter
2
Running the Test Cases
All verification test cases are available as *.dat files and are included in the NX Nastran installation in the directory path install_dir/NXr/nast/demo. The test cases are relatively simple, and most have closed-form theoretical solutions. Differences between finite element and theoretical solutions are in most cases negligible. Some tests would require an infinite number of elements to achieve an exact solution. Elements are chosen to achieve reasonable engineering accuracy with reasonable computing times. Note Actual results from NX Nastran may vary insignificantly from the results presented in this document. This variation is generally due to different methods of performing real number algorithms on different systems.
NX Nastran 8 Verification Manual
2-1
Part
II Linear Statics Verification Using Theoretical Solutions
NX Nastran 8 Verification Manual
Chapter
3 Overview of Linear Statics Verification Using Theoretical Solutions
The purpose of these linear statics test cases is to verify the function of the NX Nastran software using theoretical solutions. The test cases are relatively simple in form and most of them have closed-form theoretical solutions. The theoretical solutions shown in these examples are from well-known engineering texts. For each test case, a specific reference is cited. All theoretical reference texts are listed at the end of this topic. The finite element method is very flexible in the types of physical problems represented. The verification tests provided are not exhaustive in exploring all possible problems, but represent common types of applications. This overview provides information on the following: •
Understanding the test case format
•
Understanding comparisons with theoretical solutions
•
References
3.1
Understanding the Test Case Format
Each test case is structured with the following information. •
•
Test case data and information: o
Physical and material properties
o
Finite element modeling (modeling procedure or hints)
o
Units
o
Solution type
o
Element type
o
Boundary conditions (loads, restraints)
Results
NX Nastran 8 Verification Manual
3-1
Chapter 3
•
Overview of Linear Statics Verification Using Theoretical Solutions
References (text from which a closed-form or theoretical solution was taken)
In addition to these example problems, test cases from NAFEMS (National Agency for Finite Element Methods and Standards, National Engineering Laboratory, Glasgow, U.K.) have been executed. Results for these test cases can be found in the next section, Linear Statics Analysis Verification Using NAFEMS Standard Benchmarks.
3.2
Understanding Comparisons with Theoretical Solutions
While differences in finite element and theoretical results are, in most cases, negligible, some tests would require an infinite number of elements to achieve the exact solution. Elements are chosen to achieve reasonable engineering accuracy with reasonable computing times. Results reported here are results which you can compare to the referenced theoretical solution. Other results available from the analyses are not reported here. Results for both theoretical and finite element solutions are carried out with the same significant digits of accuracy. The closed-form theoretical solution may have restrictions, such as rigid connections, that do not exist in the real world. These limiting restrictions are not necessary for the finite element model, but are used for comparison purposes. Verification to real world problems is more difficult but should be done when possible. The actual results from the NX Nastran software may vary insignificantly from the results presented in this document. This variation is due to different methods of performing real numerical arithmetic on different systems. In addition, it is due to changes in element formulations which have been made to improve results under certain circumstances.
3.3 References The following references have been used in the Linear Statics Analysis verification problems presented: 1. Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. 2. Harris, C. O. Introduction to Stress Analysis. New York Macmillan1959. 3. Roark, R. and Young, W. Formulas for Stress and Strain, 5th Edition. New York: McGraw-Hill Book Company, 1975. 4. Shigley, J. and Mitchel L. Mechanical Engineering Design, 4th Edition. New York: McGraw-Hill Book Company, 1983. 5. Timoshenko, S. Strength of Materials, Part I, Elementary Theory and Problems. New YorK: Van Norstrand Reinhold Company, 1955.
3-2
NX Nastran 8 Verification Manual
Chapter
4
Test Cases
4.1 Point Load on a Cantilever Beam Determine the deflection of a beam at the free end. Determine the stress at the midpoint of the
beam.
Test Case Data and Information Input Files mstvl001.dat
Units Inch
NX Nastran 8 Verification Manual
4-1
Chapter 4
Test Cases
Model Geometry Length = 480 in.
Cross Sectional Properties •
Area = 30 x 30 in.
•
Iy = Iz = 67500 in.4
Material Properties •
E = 30E06 psi
Finite Element Modeling Create four successive linear beam (CBAR) elements along the X axis.
Boundary Conditions •
Restraints o
•
Restrain the left end of the beam in all six degrees.
Loads o
Set grid force to 50,000 lb in. the -Y direction.
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
Von Mises Stress, grid point 1 (psi)
5333.
5333.
Y Deflection, grid point 5 (in)
0.9102
0.9130
References Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. p. 716.
4-2
NX Nastran 8 Verification Manual
Test Cases
4.2 Axial Distributed Load on a Linear Beam Determine the stress, elongation and resultant force due to an axial loading along a linear beam
element.
Test Case Data and Information Input Files mstvl002.dat
Units Inch
Model Geometry •
Length = 300 in.
Cross Sectional Properties •
Area = 9 in.2
•
square cross section (3 in. x 3 in.)
•
I = 6.75 in.4
Material Properties •
E = 30E+6 psi
Finite Element Modeling Create 30 beam element along the X axis, each 10 inches long.
Boundary Conditions •
Restraints o
•
Restrain one end of the beam in all six degrees.
Loads o
Set the axial distributed load (force per unit length) to 1000 lb/in. for the 10-inch long element furthest from the restrained end in the X direction.
NX Nastran 8 Verification Manual
4-3
Chapter 4
Test Cases
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
Von Mises Stress, grid point 1 (psi)
1111.
1111.
Deflection in X, grid point 2 (in)
0.01111
0.01093
Reaction in X, grid point 1 (lb)
–1.000E4
–1.000E4
References Beer and Johnston. Mechanics of Materials.. New York: McGraw-Hill, Inc., 1992. p. 76.
4.3 Distributed Loads on a Cantilever Beam Determine the deflection of a beam at the free end. Determine the stress at the midpoint of the beam and the reaction force at the restrained end.
4-4
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input Files mstvl003.dat
Units Inch
Model Geometry Length = 480 in.
Cross Sectional Properties •
Area = 900 in.2
•
Square cross section (30 in. x 30 in.)
•
Iy = Iz = 67500 in.4
Material Properties •
E = 30E06 psi
Finite Element Modeling Create eight successive linear beam (CBAR) elements along the X axis.
Boundary Conditions •
Restraints o
•
Restrain the left end of the beam in all six degrees.
Loads o
Define a distributed load of 250 lb/in. in the –Y direction.
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
X Stress at grid point 1 (psi)
6,400.
6,383.
Deflection Magnitude at grid point 5 (in)
0.8190
0.8225 *
Reaction Force Magnitude at grid point 1 (lb)
1.200E5
1.200E5
* Includes shear deformation which is neglected in theoretical value.
NX Nastran 8 Verification Manual
4-5
Chapter 4
Test Cases
References Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. p. 716.
4.4 Moment Load on a Cantilever Beam Determine the deflection of a beam at the free end. Determine the bending stress of the beam and the reaction force at the restrained end.
Test Case Data and Information Input Files mstvl004.dat
Units Inch
Model Geometry Length = 480 in.
Cross Sectional Properties •
Area = 900 in.2
•
Iy = Iz = 67500 in.4
•
Square cross section 30” x 30” inches
Material Properties •
4-6
E = 30 E+06 psi
NX Nastran 8 Verification Manual
Test Cases
Finite Element Modeling Create eight successive linear beam (CBAR) elements along the X axis.
Boundary Conditions •
Restraints o
•
Restrain the left end of the beam in all six degrees.
Loads o
Set the Z-moment of the end grid point to 2.5E06 in.-lb.
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
Von Mises Stress at grid point 1 (psi)
555.6
555.6
Deflection Magnitude at grid point 5 (in)
0.1422
0.1422
Reaction Force Z Direction at grid point 1 (lb)
2.500E6
2.499E6
* Includes shear deformation which is neglected in theoretical value.
References Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. p. 716.
4.5 Edge Pressure on Beam Element - Torque Loading Determine the stress, elongation and resultant force due to a torque applied to a hollow cylinder at the free end.
NX Nastran 8 Verification Manual
4-7
Chapter 4
Test Cases
Test Case Data and Information Input Files mstvl005.dat
Units SI - meter
Model Geometry Length = 1.5 m
Cross Sectional Properties •
Radius1 = 0.02 m
•
Radius2 = .03 m
Material Properties •
E = 208.6 GPa
Finite Element Modeling •
Create a CBAR element along the X axis.
•
To find the maximum shearing stress, set the effective radius in torsion to 0.03 m.
•
The minimum shearing stress is located at a radius equal to 0.02 m.
4-8
NX Nastran 8 Verification Manual
Test Cases
Boundary Conditions •
Restraints o
•
Restrain the left end of the beam in all six degrees.
Loads o
Apply an edge torque equal to 4.08 kN-m along the 10 cm linear beam (CBAR) element furthest from the restrained end.
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
Max Torsional Shear Stress (MPa)
120.0
120.0
Min Torsional Shear Stress (MPa)
80.00
80.00
Post Processing To obtain the minimum and maximum shear stress values, a post processor which supports contour plots of the torsional shear stress on the cross section using the linear beam (CBAR) element forces must be used. The cross section location can be anywhere except the free end of the beam.
References Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. p. 122.
4.6 Thermal Strain, Displacement, and Stress on Heated Beam A beam originally 1 meter long and at –50° C is heated to 25° C. First, determine the displacement and thermal strain on a cantilever beam. Fix the beam at the free end and then determine the displacement, reaction forces, and stresses along the beam. Next, fix the beam at both ends.
NX Nastran 8 Verification Manual
4-9
Chapter 4
Test Cases
Test Case Data and Information Input Files mstvl007.dat
Units SI - meter
Model Geometry Length = 1 m
Cross Sectional Properties •
Area = 0.01 m2
Material Properties •
E = 2.068E11 Pa
•
Coefficient of thermal expansion = 1.2E–05
•
v = 0.3
Finite Element Modeling •
Create 10 linear beam (CBAR) elements on the X axis and restrain the end grids in all directions.
•
Apply a temperature on all grid points.
4-10
NX Nastran 8 Verification Manual
Test Cases
Boundary Conditions •
•
Restraints o
Case 1: Restrain one end of the beam in all six directions.
o
Case 2: Restrain both ends of the beam in all six directions.
Loads o
Set grid temperatures to 25°C. Set the reference temperature to –50°C.
Solution Type SOL 101 — Linear Statics
Results Case 1 Result
Bench Value
NX Nastran
X Displacement at grid 11 (m)
.0009000
.0009000
Axial Thermal Strain
.0009000
.0009000
Case 2 Result
Bench Value
NX Nastran
X Displacement (m)
0
0
Axial Stress (Pa)
1.860E8
1.861E8
X Reaction Force (N)
1.860E6
1.861E6
References Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. p. 65.
4.7 Uniformly Distributed Load on Linear Beam A beam 40 feet long is restrained and loaded as shown with a distributed load of –833 lbs. per foot. Determine the bending stress and the deflection at the middle of the beam.
NX Nastran 8 Verification Manual
4-11
Chapter 4
Test Cases
Test Case Data and Information Input Files mstvl008.dat
Units Inch
Model Geometry Length = 480 in.
Cross Sectional Properties •
Rectangular cross section (1.17 in. x 43.24 in.)
•
Iz = 7892 in.4
4-12
NX Nastran 8 Verification Manual
Test Cases
Material Properties •
E = 30E06 psi
Finite Element Modeling Create 4 successive linear beam (CBAR) elements that are each 10 feet long.
Boundary Conditions •
Restraints o
•
Restrain the second and the fourth grids in five degrees of freedom. Do not restrain rotation about Z.
Loads o
Define a distributed load (force per unit length) of –833 lb/foot (global negative Y direction) on the end elements.
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
Y Displacement at grid 3 (in.)
0.1820
0.182
Max bending stress (psi)
1.644E4
1.644E4
References Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. p. 98.
4.8 Membrane Loads on a Linear Quadrilateral Thin Shell Element A circle is scribed on an unstressed aluminum plate. Forces acting in the plane of the plate cause normal stresses. Determine the change in the length of diameter AB and of diameter CD.
NX Nastran 8 Verification Manual
4-13
Chapter 4
Test Cases
Test Case Data and Information Element Types cquad4
Input Files mstvl009.dat
Units Inch
Model Geometry •
Length = 15 in.
•
Diameter = 9 in.
•
Thickness = 3/4 in.
4-14
NX Nastran 8 Verification Manual
Test Cases
Material Properties •
E = 10E06 psi
•
Poisson’s ratio = 1/3
•
F(x)/L = 9,000 lb/in.
•
F(z)/L = 15,000 lb/in.
Finite Element Modeling Create 1/4 of the model and apply symmetry boundary conditions. Then multiply the answer by 2 for correct results. Remember to account for the ratio of the circle diameter to plate length.
Boundary Conditions •
Restraints o
•
Restrain the left end of the beam in all six degrees.
Loads o
Set the edge pressure to 9,000 lb/in. in the X direction and 15,000 lb/in. in the Z direction.
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
X Diameter Change (in.)
–4.800E3
–4.800E3
Z Diameter Change (in.)
–14.40E3
–14.40E3
Post Processing Deflection •
(dx at grid point 7 – dx at grid point 10) x 2 = (0.004 – 0.0016) x 2 = 0.0048
•
(dz at grid point 7 – dz at grid point 24) x 2 = (0.012 –0.0048) x 2 = 0.0144
References Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. p. 85.
4.9 Axial Loading on Rod Element Determine the stress, elongation, and strain due to an axial load on a rod element.
NX Nastran 8 Verification Manual
4-15
Chapter 4
Test Cases
Test Case Data and Information Input Files mstvl011.dat
Units SI - meters
Model Geometry Length = 10 m
Cross Sectional Properties •
Area = 0.01 m2
Material Properties •
E = 200.0 GPa
Finite Element Modeling Create a rod (CROD) element along the X axis.
Boundary Conditions •
Restraints o
•
Restrain an end of the rod in the 3 translational degrees.
Loads o
Apply a grid point force in the positive X-direction of 500 kN.
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
Axial Stress (MPa)
50.00
50.00
Axial Strain
0.0002500
0.0002500
Elongation (mm)
2.500
2.500
References Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. p. 716.
4-16
NX Nastran 8 Verification Manual
Test Cases
4.10 Stress on a Beam as It Expands and Closes a Gap Determine the stress on a beam as it expands thermally and closes a 0.002 inch gap. It is initially at 70 °F and is heated to 170 °F.
Test Case Data and Information Input Files mstvl013.dat
Units Inch
Model Geometry Length = 3 in.
Material Properties • •
E = 1.05E07 psi Coefficient of thermal expansion = 1.25E–05 in./(in.–°F)
Finite Element Modeling •
Create a single linear beam (CBAR) element on the X axis.
NX Nastran 8 Verification Manual
4-17
Chapter 4
•
Test Cases
Create an MPC to define the closing of the gap.
Boundary Conditions •
Restraints o
•
Restrain the free end of the beam in all six degrees.
Loads o
Set grid temperature to 170 °F.
o
Set the reference temperature to 70 °F.
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
Axial Stress (psi)
–6.125E3
–6.125E3
References Harris, C. O. Introduction to Stress Analysis 1959. p. 58.
4.11 Thin Wall Cylinder in Pure Tension Determine the stress and deflection of a thin wall cylinder with a uniform axial load.
4-18
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input Files mstvl014.dat
Units Inch
Model Geometry •
R = 0.5 in.
•
Thickness = 0.01 in.
•
y = 1.0 in.
Material Properties •
E = 10,000 psi
NX Nastran 8 Verification Manual
4-19
Chapter 4
•
Test Cases
n = 0.3
Finite Element Modeling Create 1/4 model of the cylinder with thin shell linear quadrilateral (CQUAD4) elements and symmetry boundary conditions.
Boundary Conditions •
Restraints o
Restrain edges of symmetry, in translation, in hoop direction, and rotation about Z axis.
o
Restrain one end in Y direction.
Loads o
Apply membrane edge pressure of p / (pi)D = 3.1831 where p = 10 psi
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
Axial (Z) Stress (psi)
1.000E3
1.000E3
Axial (Z) Deflection (in.)
1.000
1.000
Radial Deflection (in.)
–0.01500
–0.01500
References Roark, R. and Young, W. Formulas for Stress and Strain, 6th Edition. New York: McGraw-Hill Book Company, 1989. p. 518, Case 1a.
4.12 Thin Shell Beam Wall in Pure Bending Determine the maximum stress, maximum deflection, and strain energy of a thin shell beam wall with a uniform bending load.
4-20
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input Files mstvl015.dat
Units Inch
Model Geometry •
Length = 30 in.
•
Width = 5 in.
•
Thickness = 0.1 in.
Material Properties •
E = 30E06 psi
•
n = 0.03
NX Nastran 8 Verification Manual
4-21
Chapter 4
Test Cases
Finite Element Modeling Create a 30 in. x 5 in. plate with thing shell (CQUAD4) elements.
Boundary Conditions •
Restraints o
•
Restrain at one of the ends in all directions.
Loads o
Apply edge pressure of p/w = 1.2 lbs/in. where p = 6.0 lb.
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
Max Z Deflection (in.)
4.320
4.264
Max Z Stress (psi)
2.160E4
1.980E4
Total Strain Energy (lb in.)
12.96
12.79
References Shigley, J. and Mitchel L. Mechanical Engineering Design, 4th Edition. New York: McGraw-Hill, Inc., 1983. pp. 134, 804.
4.13 Strain Energy of a Truss Determine the strain energy of a truss. The cross-sectional area of the diagonal members is twice the cross-sectional area of the horizontal and vertical members.
4-22
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input Files mstvl016.dat
Units Inch
Model Geometry •
Length = 10 in.
Cross Sectional Properties •
Cross-sectional area (A) = 0.01 in.2
Material Properties •
E = 30E06 psi
Finite Element Modeling Create truss shown using rod (CROD) elements.
Boundary Conditions •
Restraints o
Restrain far left grid in directions: X, Y, Z, RX, RY.
o
Restrain far right grid in directions: Y, Z, RX, RY.
NX Nastran 8 Verification Manual
4-23
Chapter 4
•
Test Cases
Loads o
Apply grid force in Y direction on lower center grid; F= 300 lb.
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
Total Strain Energy (lb in.)
5.846
5.846
References Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. p. 588.
4-24
NX Nastran 8 Verification Manual
Part
III Linear Statics Verification Using Standard NAFEMS Benchmarks
NX Nastran 8 Verification Manual
Chapter
5 Overview of Linear Statics Verification Using Standard NAFEMS Benchmarks
The purpose of these linear statics test cases is to verify the function of NX Nastran using standard benchmarks published by NAFEMS (National Agency for Finite Element Methods and Standards, National Engineering Laboratory, Glasgow, U.K.). These standard benchmark tests were created by NAFEMS to stretch the limits of the finite elements in commercial software. All results obtained using NX Nastran compare favorably with other commercial finite element analysis software.
5.1 Understanding the Test Case Format Each test case is structured with the following information: •
Test case data and information o
Physical and material properties
o
Finite element modeling (modeling procedure or hints)
o
Units
o
Finite element modeling information
o
Boundary conditions (loads and restraints)
o
Solution type
•
Results
•
Reference
5.2 Reference The following reference has been used in these test cases: NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks. Glasgow: NAFEMS, Rev. 3, 1990.
NX Nastran 8 Verification Manual
5-1
Chapter
6
Test Cases
6.1 Elliptic Membrane This test is a linear elastic analysis of an elliptic membrane (shown below) using coarse and fine meshes of plane stress elements and thin shell elements. It provides the input data and results for NAFEMS Standard Benchmark Test LE1.
Ellipses:
Test Case Data and Information Input Files le101.dat (plane stress quadrilateral) le102.dat (plane stress triangle) le103.dat (thin shell)
NX Nastran 8 Verification Manual
6-1
Chapter 6
Test Cases
Physical and Material Properties •
Thickness = 0.1 m
•
Isotropic material
•
E = 210E3 MPa
•
v = 0.3
Units SI
Finite Element Modeling •
Plane stress (only MID1 defined on PSHELL) linear (CQUAD4) and parabolic (CQUAD8) quadrilaterals — coarse and fine mesh.
•
Plane stress (only MID1 defined on PSHELL) linear (CTRI3) and parabolic (CTRI6) triangles — coarse and fine mesh.
•
Thin shell (MID1, MID2 and MID3 defined on PSHELL) linear (CQUAD4) and parabolic (CQUAD8) quadrilaterals — coarse and fine mesh.
•
The fine mesh is created by approximately halving the coarse mesh.
6-2
NX Nastran 8 Verification Manual
Test Cases
Boundary Conditions •
Uniform outward pressure at outer edge BC = 10 MPa
•
Inner curved edge AD unloaded
•
X displacement (edge AB) = 0
NX Nastran 8 Verification Manual
6-3
Chapter 6
•
Test Cases
Y displacement (edge CD) = 0
Solution Type SOL 101 — Linear Statics
Results Output — tangential edge stress at D (stress in Y direction)
Plane Stress Elements Test case
Grid point #
Bench Value
NX Nastran
Linear quad — coarse mesh
4
92.7
62.1
Linear quad — fine mesh
204
92.7
79.6
Parabolic quad — coarse mesh
104
92.7
82.1
Parabolic quad — fine mesh
304
92.7
89.9
Linear triangle — coarse mesh
4
92.7
52.9
Linear triangle — fine mesh
204
92.7
70.8
Parabolic triangle — coarse mesh
104
92.7
76.8
Parabolic triangle — fine mesh
304
92.7
93.6
Test case
Grid point #
Bench Value
NX Nastran
Linear quad — coarse mesh
4
92.7
62.1
Linear quad — fine mesh
204
92.7
79.6
Parabolic quad — coarse mesh
104
92.7
82.1
Parabolic quad — fine mesh
304
92.7
89.9
Thin Shell Elements
6-4
NX Nastran 8 Verification Manual
Test Cases
References NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, Test No. LE1. Glasgow: NAFEMS, Rev. 3, 1990.
6.2 Cylindrical Shell Patch Test This test is a linear elastic analysis of a cylindrical shell (shown below) using thin shell elements and two different loadings. It provides the input data and results for NAFEMS Standard Benchmark Test LE2.
Test Case Data and Information Input Files •
le201a.dat (linear shell, case 1)
•
le201b.dat (parabolic shell, case 1)
•
le202a.dat (linear shell, case 2)
•
le202b.dat (parabolic shell, case 2)
Physical and Material Properties •
Thickness = 0.1 m
NX Nastran 8 Verification Manual
6-5
Chapter 6
Test Cases
•
Isotropic material
•
E = 210E3 MPa
•
v = 0.3
Units SI
Finite Element Modeling •
Thin shell linear (CQUAD4) and parabolic (CQUAD8) quadrilaterals
Boundary Conditions •
Translations and rotations (edge AB) = 0
•
Z translations and normal rotations (edge AD and edge BC) = 0
Case 1 loading: •
Uniform normal edge moment on DC = 1.0 kNm/m
Case 2 loading: •
Uniform outward normal pressure at mid-surface ABCD = 0.6 MPa
•
Tangential outward normal pressure on edge DC = 60.0 MPa
6-6
NX Nastran 8 Verification Manual
Test Cases
Solution Type SOL 101 — Linear Statics
Results Output — outer (convex) surface (top shell surface) tangential stress at point E (grid point 2): Test case
Filename
Bench Value
NX Nastran
Linear quad – case 1
le201a
60.00
51.8
Linear quad – case 2
le202a
60.00
51.1*
Parabolic quad – case 1
le201b
60.00
56.4
Parabolic quad – case 2
le202b
60.00
56.4*
* Since the shapes of the shells are an approximation to a cylindrical surface, an edge load will not be in the correct direction. To get this result, the edge load must be input as grid forces in the tangential direction.
Post Processing •
Stress component: Y
NX Nastran 8 Verification Manual
6-7
Chapter 6
•
Test Cases
Results obtained on the element top surface in cylindrical coordinate system
References NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, Test No. LE2. Glasgow: NAFEMS, Rev. 3, 1990.
6.3 Hemisphere-Point Loads This test is a linear elastic analysis of hemisphere point loads (shown below) using coarse and fine meshes of thin shell elements. It provides the input data and results for NAFEMS Standard Benchmark Test LE3.
Test Case Data and Information Input Files •
le301.dat (linear quad, coarse mesh)
•
le302.dat (linear quad, fine mesh)
•
le303.dat (parabolic quad, coarse mesh)
Physical and Material Properties •
6-8
Thickness = 0.04 m
NX Nastran 8 Verification Manual
Test Cases
•
Isotropic material
•
E = 68.25 × 103 MPa
•
v = 0.3
Units SI
Finite Element Modeling •
Thin shell linear (CQUAD4) and parabolic (CQUAD8) quadrilaterals — coarse and fine mesh
•
Equally spaced grid points on AC, CE, EA
•
Point G at X = Y = Z = 10 /( 31/2) grid point 7
Boundary Conditions •
Edge AE symmetry about XZ plane (y = rotation x = rotation z = 0)
•
Edge CE symmetry about YZ plane (x = rotation y = rotation z = 0)
•
Point E (x = y = z = 0)
•
All other displacements on edge AC are free.
•
Concentrated radial load outward at A = 2KN
•
Concentrated radial load inward at C = 2KN
NX Nastran 8 Verification Manual
6-9
Chapter 6
Test Cases
Solution Type SOL 101 — Linear Statics
Results Output — X displacement at point A Mesh
Test Case
Bench Value NX Nastran
linear quad — coarse mesh
le301
0.185
0.1848
linear quad — fine mesh
le302
0.185
0.1865
parabolic quad — coarse mesh
le303
0.185
0.1416
References NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, Test No. LE3. Glasgow: NAFEMS, Rev. 3, 1990.
6.4 Z-Section Cantilever This test is a linear elastic analysis of a Z-section cantilever (shown below) using thin shell elements. It provides the input data and results for NAFEMS Standard Benchmark Test LE5.
6-10
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input Files •
le501.dat (linear quadrilateral)
•
le502.dat (parabolic quadrilateral)
Physical and Material Properties •
Thickness = 0.1 m
•
Isotropic material
•
E = 210E3 MPa
•
v = 0.3
Units SI
Finite Element Modeling •
Thin shell linear (CQUAD4) and parabolic (CQUAD8) quadrilaterals
Boundary Conditions •
All displacements on edges B1, B2, B3 = 0
•
Torque of 1.2MN applied at end C by two edge shears (at C1 & C3) of 0.6 MN
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6-11
Chapter 6
Test Cases
Solution Type SOL 101 — Linear Statics
Results Output — averaged axial stress at mid-surface, point A, grid point 30 (compression) Result
Bench Value
NX Nastran
Linear quad - point A/grid point 30
–108.0
–111.0
Parabolic quad - point A/grid point 30
–108.0
–110.3
References NAFEMS Finite Element Methods & Standards. The Standard NAFEMS Benchmarks, Test No. LE5. Glasgow: NAFEMS, Rev. 3, 1990.
6.5 Skew Plate Normal Pressure This test is a linear elastic analysis of a plate (shown below) using thin shell elements. It provides the input data and results for NAFEMS Standard Benchmark Test LE6.
6-12
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input Files •
le601.dat (linear and parabolic quad)
•
le602.dat (linear and parabolic triangle)
Physical and Material Properties •
Thickness = 0.01 m
•
Isotropic material
•
E = 210E3 MPa
•
v = 0.3
Units SI
Finite Element Modeling •
Thin shelllinear (CQUAD4) and parabolic (CQUAD8) quadrilaterals — coarse and fine mesh
•
Thin shell linear (CTRI3) and parabolic (CTRI6) triangles — coarse and fine mesh
Boundary Conditions •
Simple supports
•
Z displacement = 0
•
Normal pressure = –0.7KPa in the Z direction
Solution Type SOL 101 — Linear Statics
Results Output — maximum principal stress on the bottom surface at the plate center.
NX Nastran 8 Verification Manual
6-13
Chapter 6
Test Cases
Case le601 Mesh
Grid point #
Bench Value NX Nastran
Linear quad coarse mesh
9
0.802
0.325
Linear quad fine mesh
18
0.802
0.683
Parabolic quad coarse mesh
43
0.802
0.625
Parabolic quad fine mesh
52
0.802
0.719
Mresh
Grid point #
Bench Value
NX Nastran
Linear triangle coarse mesh
9
0.802
0.396
Linear triangle fine mesh
18
0.802
0.720
Parabolic triangle coarse mesh
43
0.802
0.926
Parabolic triangle fine mesh
52
0.802
0.857
Case le602
References NAFEMS Finite Element Methods & Standards. The Standard NAFEMS Benchmarks, Test No. LE6. Glasgow: NAFEMS, Rev. 3, 1990.
6.6 Thick Plate Pressure This article provides the input data and results for NAFEMS Standard Benchmark Test LE10. This test is a linear elastic analysis of a thick (shown below) using coarse and fine meshes of solid elements.
Ellipses:
6-14
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input Files •
le1001.dat (linear and parabolic brick)
•
le1002.dat (linear and parabolic wedge)
•
le1003.dat (linear and parabolic tetrahedron)
•
le1004.dat (linear and parabolic pyramid)
Physical and Material Properties •
Isotropic material
•
E = 210E3 MPa
•
v = 0.3
Units SI
Finite Element Modeling •
Solid brick (CHEXA) linear and parabolic - coarse and fine mesh
•
Solid wedge (CPENTA) linear and parabolic - coarse and fine mesh
•
Solid tetrahedron (CTETRA) - linear and parabolic - coarse and fine mesh
•
Solid pyramid (CPYRAM) linear and parabolic - coarse and fine mesh (created by dividing each linear and parabolic brick element into 6 pyramid elements)
NX Nastran 8 Verification Manual
6-15
Chapter 6
Test Cases
Solid Brick
Solid Wedge
6-16
NX Nastran 8 Verification Manual
Test Cases
Solid Tetrahedron — fine mesh only
Boundary Conditions •
Uniform normal pressure on the upper surface of the plate = 1 MPa
•
Inner curved edge AD unloaded
•
X and Y displacements on faces DCD’C¢ and ABA¢B¢ = 0
•
X and Y displacements on face BCB¢C¢ are fixed
•
Z displacements along mid-plane are fixed
Solution Type SOL 101 — Linear Statics
Results Output — direct stress at point Dsyy
NX Nastran 8 Verification Manual
6-17
Chapter 6
Test Cases
Test Case le1001 Mesh
Grid point #
Bench Value
NX Nastran
Linear brick — coarse mesh
4
–5.50
–5.41
Linear brick — fine mesh
204
–5.50
–5.67
Parabolic brick — coarse mesh
104
–5.50
–6.13
Parabolic brick — fine mesh
304
–5.50
–6.04
Test Case le1002 Mesh
Grid point #
Bench Value
NX Nastran
Linear wedge — coarse mesh
4
–5.50
–5.94
Linear wedge — fine mesh
204
–5.50
–5.83
Parabolic wedge — coarse mesh
104
–5.50
–5.32
Parabolic wedge — fine mesh
304
–5.50
–6.01
Test Case le1003 Result
Grid point #
Bench Value
NX Nastran
Linear tetra — fine mesh
40
–5.50
–2.41
Parabolic tetra — fine mesh
171
–5.50
–5.28
Test Case le1004 Mesh
Grid point #
Bench Value
NX Nastran
Linear pyramid — coarse mesh
4
–5.50
–2.85
Linear pyramid — fine mesh
204
–5.50
–3.83
Parabolic pyramid — coarse mesh
104
–5.50
–5.60
Parabolic pyramid — fine mesh
304
–5.50
–5.72
References NAFEMS Finite Element Methods & Standards. The Standard NAFEMS Benchmarks, Test No. LE10. Glasgow: NAFEMS, Rev. 3, 1990.
6.7 Solid Cylinder/Taper/Sphere — Temperature This test is a linear elastic analysis of a solid cylinder with a temperature gradient (shown below) using coarse and fine meshes of solid elements. It provides the input data and results for NAFEMS Standard Benchmark Test LE11.
6-18
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input Files •
le1101a.dat (linear brick — coarse mesh)
•
le1101b.dat (linear brick — fine mesh)
•
le1102a.dat (parabolic brick — coarse mesh)
•
le1102b.dat (parabolic brick — fine mesh)
•
le1103a.dat (linear wedge — coarse mesh)
•
le1103b.dat (linear wedge — fine mesh)
•
le1104a.dat (parabolic wedge — coarse mesh)
•
le1104b.dat (parabolic wedge — fine mesh)
•
le1105a.dat (linear tetra — coarse mesh)
•
le1105b.dat (linear tetra — fine mesh)
•
le1106a.dat (parabolic tetra — coarse mesh)
•
le1106b.dat (parabolic tetra — fine mesh)
NX Nastran 8 Verification Manual
6-19
Chapter 6
Test Cases
•
le1107a.dat (linear pyramid — coarse mesh)
•
le1107b.dat (linear pyramid — fine mesh)
•
le1108a.dat (parabolic pyramid — coarse mesh)
•
le1108b.dat (parabolic pyramid — fine mesh)
Physical and Material Properties •
Isotropic material
•
E = 210E3 MPa
•
v = 0.3
•
a = 2.3E–4 °C
Units SI
Finite Element Modeling •
Solid brick (CHEXA) linear and parabolic — coarse and fine mesh
•
Solid wedge (CPENTA) linear (6 grid point) and parabolic (15 grid point) — coarse and fine mesh
•
Solid tetrahedron (CTETRA) linear and parabolic — coarse and fine mesh
•
Solid pyramid (CPYRAM) linear and parabolic — coarse and fine mesh (created by dividing each linear and parabolic brick element into 6 pyramid elements)
6-20
NX Nastran 8 Verification Manual
Test Cases
Solid Brick
Solid Tetrahedron
NX Nastran 8 Verification Manual
6-21
Chapter 6
Test Cases
Boundary Conditions •
Linear temperature gradient in the radial and axial direction T° C = (X2 + Y2)1/2 + Z
•
X, Y, and Z displacements = 0
•
X and Y displacements on face BCB¢C¢ are fixed
•
Z displacements on XY-plane face and HIH¢I¢ face = 0
Solution Type SOL 101 — Linear Statics
Results Output - direct stress syy at point A File Name
Result
Grid point at Point A
Bench Value
NX Nastran
le1101a
Linear brick — coarse mesh
30
–105.0
–88.50
le1101b
Linear brick — fine mesh
71
–105.0
–98.3
le1102a
Parabolic brick — coarse mesh
67
–105.0
–100.4
le1102b
Parabolic brick — fine mesh
159
–105.0
–111.2
le1103a
Linear wedge — coarse mesh
33
–105.0
–10.0
le1103b
Linear wedge — fine mesh
74
–105.0
–48.3
le1104a
Parabolic wedge — coarse mesh
71
–105.0
–87.2
le1104b
Parabolic wedge — fine mesh
187
–105.0
–96.2
le1105a
Linear tetra — coarse mesh
8
–105.0
–31.4
6-22
NX Nastran 8 Verification Manual
Test Cases
File Name
Result
Grid point at Point A
Bench Value
NX Nastran
le1105b
Linear tetra — fine mesh
8
–105.0
–65.2
le1106a
Parabolic tetra — coarse mesh
8
–105.0
–89.6
le1106b
Parabolic tetra — fine mesh
8
–105.0
–97.3
le1107a
Linear pyramid — coarse mesh
30
–105.0
–57.0
le1107b
Linear pyramid — fine mesh
71
–105.0
–79.8
le1108a
Parabolic pyramid — coarse mesh
67
–105.0
–65.8
le1108b
Parabolic pyramid — fine mesh
159
–105.0
–108.8
References NAFEMS Finite Element Methods & Standards. The Standard NAFEMS Benchmarks, Test No. LE11. Glasgow: NAFEMS, Rev. 3, 1990.
NX Nastran 8 Verification Manual
6-23
Part
IV Normal Mode Dynamics Verification
NX Nastran 8 Verification Manual
Chapter
7 Overview of Normal Mode Dynamics Verification Using Theoretical Solutions
The purpose of these normal mode dynamics test cases is to verify the function of NX Nastran using theoretical solutions. The test cases are relatively simple in form and most of them have closed-form theoretical solutions. The theoretical solutions shown in these examples are from well known engineering texts. For each test case, a specific reference is cited. All theoretical reference texts are listed at the end of this topic. The finite element method is very flexible in the types of physical problems represented. The verification tests provided are not exhaustive in exploring all possible problems, but represent common types of applications. This overview provides information on the following: •
Understanding the test case format
•
Understanding comparisons with theoretical solutions
•
References
7.1 Understanding the Test Case Format Each test case is structured with the following information. •
Test case data and information: o
Physical and material properties
o
Finite element modeling (modeling procedure or hints)
o
Units
o
Solution type
o
Boundary conditions (loads and restraints/constraints)
•
Results
•
Reference
NX Nastran 8 Verification Manual
7-1
Chapter 7
Overview of Normal Mode Dynamics Verification Using Theoretical Solutions
7.2 Understanding Comparisons with Theoretical Solutions While differences in finite element and theoretical results are, in most cases, negligible, some tests would require an infinite number of elements to achieve the exact solution. Elements are chosen to achieve reasonable engineering accuracy with reasonable computing times. Results reported here are results which you can compare to the referenced theoretical solution. Other results available from the analyses are not reported here. Results for both theoretical and finite element solutions are carried out with the same significant digits of accuracy. The closed-form theoretical solution may have restrictions, such as rigid connections, that do not exist in the real world. These limiting restrictions are not necessary for the finite element model, but are used for comparison purposes. Verification to real world problems is more difficult but should be done when possible. The actual results from NX Nastran may vary insignificantly from the results presented in this document. This variation is due to different methods of performing real numerical arithmetic on different systems. In addition, it is due to changes in element formulations which have been made to improve results under certain circumstances.
7.3 Reference The following references have been used in the normal mode dynamics analysis verification problems presented: 1. Blevins, R. Formulas For Natural Frequency and Mode Shape, 1st Edition. New York: Van Norstrand Reinhold Company, 1979. 2. Timoshenko and Young. Vibration Problems in Engineering. New York: Van Norstrand Reinhold Company, 1955. 3. Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, Theory and Applications. Boston: Allyn and Bacon, Inc., 1978. 4. Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, 2nd Edition. Boston: Allyn and Bacon, Inc., 1978.
7-2
NX Nastran 8 Verification Manual
Chapter
8
Test Cases
8.1 Natural Frequency of Circular Ring with Axisymmetric Model Determine the frequency of radial vibration of an axisymmetric ring.
Test Case Data and Information Input File mstvn001.dat
Units Inch
Model Geometry •
Thickness = 0.05 in.
•
Radius = 100 in.
Material Properties •
Density = 0.00073 lb-sec2/in.4
•
E = 30E6 psi
NX Nastran 8 Verification Manual
8-1
Chapter 8
Test Cases
Finite Element Modeling Create a linear axisymmetric thin shell element (CCONEAX) .05 inches long at a radius of 100 inches from the center.
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method
Results Result
Bench Value
NX Nastran
Frequency (Hz)
322.6
322.6
References Timoshenko and Young. Vibration Problems in Engineering, p. 425. New York: Van Norstrand Reinhold Company, 1955.
8.2 Undamped Free Vibration — Single Degree of Freedom Determine the natural frequency of the system shown.
8-2
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input File mstvn002.dat
Units SI - meter
Model Geometry •
Length = 0.5 m
•
a = 0.3 m
Physical Properties •
mass = 20 Kg
•
k = 8 KN/m
Finite Element Modeling •
Create 5 rigid bar (RBAR) elements along the X axis. Each bar should be 0.1 m long.
•
A lumped mass (CONM2) element is applied on the end grid point.
•
A grid point-to-ground spring element (CELAS1) is applied 0.2 m from the lumped mass.
Boundary Conditions •
Restrain the first grid point to allow rotation only in the Z direction.
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method
Results Result
Bench Value
NX Nastran
Frequency (Hz)
1.910
1.910
References Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, Theory and Applications, p. 75. Boston: Allyn and Bacon, Inc., 1978.
NX Nastran 8 Verification Manual
8-3
Chapter 8
Test Cases
8.3 Two Degrees of Freedom Undamped Free Vibration — Principle Modes Determine the natural frequencies of a dynamic system with two degrees of freedom.
Test Case Data and Information Input File mstvn003.dat
Units SI- meter
8-4
NX Nastran 8 Verification Manual
Test Cases
Element Types •
Translational springs (CELAS1)
•
Lumped mass (CONM2)
Physical Properties •
Mass = 1 kg
•
k = 1 N/m
Finite Element Modeling •
Create four grid points on the Y axis.
•
Create three linear springs (CELAS1) with stiffness of 1 N/m and with a uniaxial stiffness reference coordinate system.
•
Create two lumped mass elements (CONM2) with a mass of 1 kg.
Boundary Conditions •
Restrain ends in all directions.
•
Restrain other grid points in all directions but Y.
Solution Type Normal Mode Dynamics - SOL 103, Lanczos method
Results Result
Bench Value
NX Nastran
Frequency of Mode 1 (Hz)
0.1592
0.1592
Frequency of Mode 2 (Hz)
0.2757
0.2757
References Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, 2nd Edition, pp. 145-149. Boston: Allyn and Bacon, Inc., 1978.
8.4 Three Degrees of Freedom Torsional System Determine the natural frequencies of a dynamic system with three degrees of freedom.
NX Nastran 8 Verification Manual
8-5
Chapter 8
Test Cases
Test Case Data and Information Input File mstvn004.dat
Element Types •
Rotational springs (CELAS1)
•
Lumped mass (CONM2)
Units SI — meter
Physical Properties •
J = J1 = J2 = J3 = 0.1
•
k = k1 = k2 = k3 = 1 N*m
Finite Element Modeling •
Create four grid points on the X axis.
•
Create three linear torsional springs (CELAS1) with stiffness of 1 N*m and with a stiffness reference coordinate system being uniaxial.
•
Create three lumped mass elements (CONM2) with a mass coordinate system = 1 and with mass inertia system of: 0.1, 0.0, 0.0, 0.0, 0.0, 0.0.
Boundary Conditions •
Restrain one end in all directions.
•
Restrain the other grid points in all directions but RX.
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos method
8-6
NX Nastran 8 Verification Manual
Test Cases
Results Result
Bench Value
NX Nastran
Frequency of Mode 1 (Hz)
0.2240
0.2240
Frequency of Mode 2 (Hz)
0.6276
0.6276
Frequency of Mode 3 (Hz)
0.9069
0.9069
References Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, 2nd Edition, pp. 153-155. Boston: Allyn and Bacon, Inc., 1978.
8.5 Two Degrees of Freedom Vehicle Suspension System Determine the natural frequencies of dynamic system with two degrees of freedom. Degrees of freedom are one translational and one rotational.
Test Case Data and Information Input Files mstvn005.dat
Units SI - meter
NX Nastran 8 Verification Manual
8-7
Chapter 8
Test Cases
Physical Properties •
Mass = 1800 kg
•
K1 = 42000 N/m
•
K2 = 48000 N/m
Finite Element Modeling •
Create a linear translation spring (CELAS1) with stiffness of K1
•
Create a linear translation spring (CELAS1) with stiffness of K2
•
Create a lumped mass element (CONM2) with a mass coordinate system = 1 and mass inertia system of: 0.0, 0.0, 3528, 0.0, 0.0, 0.0.
•
Create a three-noded rigid element (RBE2)
Boundary Conditions •
Nodal displacement restraints o
Restrain grid points 4 and 5 in all directions.
o
Restrain the other grid points in all directions but Y and RZ.
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method
Results Result
Bench Value
NX Nastran
Frequency of Mode 1 (Hz)
1.086
1.086
Frequency of Mode 2(Hz)
1.496
1.496
References Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations. Boston: Allyn and Bacon, Inc., 1978. pp. 150-153.
8.6 Two Degrees of Freedom Vehicle Suspension System Determine the natural frequencies of dynamic system with two degrees of freedom. Degrees of freedom are one translational and one rotational.
8-8
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input File mstvn005.dat
Element Types •
Translational springs (CELAS1)
•
Lumped mass (CONM2)
•
Rigid (RBE2)
Units SI — meter
Model Geometry •
Length1 = 1.6 m
•
Length2 = 2.0 m
•
r = 1.4 m (gyration radius; J = m*r*r)
Physical Properties •
mass = 1800 kg
•
K1 = 42000 N/m
NX Nastran 8 Verification Manual
8-9
Chapter 8
•
Test Cases
K2 = 48000 N/m
Finite Element Modeling •
Create five grid points in the XY plane with the following coordinates: o
Grid point 1 = (0,0)
o
Grid point 2 = (12,0)
o
Grid point 3 = (–L1,0)
o
Grid point 4 = (L2,–1)
o
Grid point 5 = (–L1,–1)
•
Create a linear translation spring (CELAS1) with stiffness of K1 between grid point 1 and grid point 5.
•
Create a linear translation spring (CELAS1) with stiffness of K2 between grid point 2 and grid point 4.
•
Create a lumped mass element (CONM2) with a mass coordinate system = 1 and mass inertia system of: 0.0, 0.0, 3528, 0.0, 0.0, 0.0.
•
Create a three-grid-point rigid element (RBE2) using grid point 1, grid point 2, and grid point 3.
Boundary Conditions •
Restrain grid points 4 and 5 in all directions.
•
Restrain the other grid points in all directions but Y and RZ.
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method
Results Result
Bench Value
NX Nastran
Frequency of Mode 1 (Hz)
1.086
1.086
Frequency of Mode 2(Hz)
1.496
1.496
References Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, pp. 150-153. Boston: Allyn and Bacon, Inc., 1978.
8.7 Cantilever Beam Undamped Free Vibrations Determine the natural frequencies of a cantilever beam.
8-10
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input File mstvn006.dat
Element Type Linear beam (CBEAM)
Units Inch
Model Geometry •
Length = 100 in.
•
Height = 2 in.
Physical and Material Properties •
w = 1 lb/in.
•
J = .10
•
Poisson’s ratio = .3
Calculated Data •
A = h2 = 4 in2
•
I = h4/12 = 1.33333
•
G = E/2 × 1/1 + nu = 11538461.54
•
m = w/g = 2.59067375E–3
•
Ip = Ixx + Iyy = 2.66666
Finite Element Modeling •
Create 11 grid points on X axis.
NX Nastran 8 Verification Manual
8-11
Chapter 8
•
Test Cases
Create 10 linear beams (CBEAM) between grid points.
Boundary Conditions •
Restrain one end grid point in all directions.
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method
Results Result
Bench Value
NX Nastran
Frequency of Modes 1 & 2 (Transverse Vibration)
6.953
6.953
Frequency of Modes 3 & 4 (Transverse Vibration)
43.58
43.58
Frequency of Mode 5 (Torsional Vibration)
64.68
64.68
Frequency of Modes 6 & 7 (Transverse Vibration)
122.0
122.0
Frequency of Mode 8 (Torsional Vibration)
193.9
195.7
Frequency of Modes 9 & 10 (Transverse Vibration)
238.8
239.3
References Blevins, R. Formulas For Natural Frequency and Mode Shape, 1st Edition, pp. 108,193. New York: Van Norstrand Reinhold Company, 1979.
8.8 Natural Frequency of a Cantilevered Mass Determine the natural frequencies of a dynamic system consisting of a massless beam and a lumped mass at the end.
8-12
NX Nastran 8 Verification Manual
Test Cases
Test Case Data and Information Input File mstvn007.dat
Element Types •
Linear beam (CBAR)
•
Lumped mass (CONM2)
Units Inch
Model Geometry Length = 30 in.
Physical and Material Properties •
Mass = 0.5 lbm
•
E = 30E6 psi
•
Density = 1.0E–6
•
I = 1.5 in.4
Finite Element Modeling •
Create 2 grid points on the X axis with coordinates (0,0,0) and (30,0,0).
•
Create a linear beam (CBAR) element between grid points with shear area ratio = 0.
•
Create a lumped mass (CONM2) on one grid point with mass of 0.5 lbm.
Boundary Conditions •
Restrain wall end in all directions.
•
Restrain mass end in directions of Z, RX, and RY.
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos method
Results Result
Bench Value
NX Nastran
Mode 2 Frequency (Hz)
15.92
15.92
NX Nastran 8 Verification Manual
8-13
Chapter 8
Test Cases
References Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, 2nd Edition, p. 72. Boston: Allyn and Bacon, Inc., 1978.
8-14
NX Nastran 8 Verification Manual
Part
V Normal Mode Dynamics Verification Using Standard NAFEMS Benchmarks
NX Nastran 8 Verification Manual
Chapter
9 Overview of Normal Mode Dynamics Verification Using Standard NAFEMS Benchmarks
The purpose of these normal mode dynamics test cases is to verify the function of NX Nastran using standard benchmarks published by NAFEMS (National Agency for Finite Element Methods and Standards, National Engineering Laboratory, Glasgow, U.K.). These standard benchmark tests were created by NAFEMS to stretch the limits of the finite elements in commercial software. All results obtained using NX Nastran compare favorably with other commercial finite element analysis software. Results of these test cases using other commercial finite element analysis software programs are available from NAFEMS.
9.1 Understanding the Test Case Format Each test case is structured with the following information. •
Test case data and information: o
Units
o
Physical and material properties
o
Finite element modeling information
o
Boundary conditions (loads and restraints/constraints)
o
Solution type
•
Results
•
Reference
9.2 Reference The following reference has been used in these test cases: NAFEMS Finite Element Methods & Standards. Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis. Glasgow: NAFEMS, Nov., 1987.
NX Nastran 8 Verification Manual
9-1
Chapter
10
Beam Element Test Cases
10.1 Pin-ended Cross — In-plane Vibration This test is a normal mode dynamic analysis of a pin-ended cross (shown below) using beam elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 1.
Attributes of this test are: •
Coupling between flexural and extensional behavior
•
Repeated and close eigenvalues
Test Case Data and Information Input Files •
nf001ac.dat (linear consistent)
•
nf001al.dat (linear lumped)
NX Nastran 8 Verification Manual
10-1
Chapter 10
Beam Element Test Cases
Units SI
Cross Sectional Properties •
Area = .015625 m2
Shear ratio: •
Y=0
•
Z=0
Material Properties •
E = 200E09 N/m2
•
r=8000 kg/m3
•
n = 0.29 (Poisson’s ratio)
•
G = 8.01E10
Finite Element Modeling •
Four linear beam (CBAR) elements per arm
Boundary Conditions •
X = Y = 0 at A, B, C, D
•
Z = Rx = Ry = 0 at all grid points
10-2
NX Nastran 8 Verification Manual
Beam Element Test Cases
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method NX Nastran results were obtained in two different ways: •
Using lumped mass (lumped mass on, param coupmass = –1)
•
Using coupled mass (lumped mass off, param coupmass = 1)
Results Mode
Reference Value (Hz)
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
11.34
11.34
11.33
11.34
2, 3
17.71
17.69
17.66
17.69
4
17.71
17.72
17.69
17.72
5
45.35
45.48
45.02
45.52
6, 7
57.39
57.36
56.06
57.43
8
57.39
57.68
56.34
57.75
References NAFEMS Finite Element Methods & Standards. Abbassian, F., Dawswell, D. J., and Knowles, N. C.Selected Benchmarks for Natural Frequency Analysis Test No. 1. Glasgow: NAFEMS, Nov., 1987.
10.2 Pin-ended Double Cross - In-plane Vibration This test is a normal mode dynamic analysis of a pin-ended double cross (shown below) using beam elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 2.
NX Nastran 8 Verification Manual
10-3
Chapter 10
Beam Element Test Cases
Attributes of this test are: •
Coupling between flexural and extensional behavior
•
Repeated and close eigenvalues
Test Case Data and Information Input Files •
nf002ac.dat (linear consistent)
•
nf002al.dat (linear lumped)
Units SI
Cross Sectional Properties Key-in section: •
Area = .015625 m2
Shear ratio: •
Y=0
•
Z=0
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
10-4
NX Nastran 8 Verification Manual
Beam Element Test Cases
Finite Element Modeling •
Four linear beam (CBAR) elements per arm
Boundary Conditions •
X = Y = 0 at A, B, C, D, E, F, G, H
•
Z = Rx= Ry = 0 at all grid points
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method NX Nastran results were obtained in two different ways: •
Using lumped mass (lumped mass toggle on, param coupmass = –1)
•
Using coupled mass (lumped mass toggle off, param coupmass = 1)
Results Mode
Reference Value (Hz)
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
11.34
11.34
11.33
11.34
2, 3
17.71
17.69
17.66
17.69
4, 5, 6, 7,8
17.71
17.72
17.69
17.72
9
45.35
45.48
45.02
45.52
10, 11
57.39
57.36
56.06
57.43
12, 13, 14, 15, 16
57.39
57.68
56.34
57.75
NX Nastran 8 Verification Manual
10-5
Chapter 10
Beam Element Test Cases
References NAFEMS Finite Element Methods & Standards. Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 2. Glasgow: NAFEMS, Nov., 1987.
10.3 Free Square Frame - In-plane Vibration This test is a normal mode dynamic analysis of a free square frame (shown below) using beam elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 3.
Attributes of this test are: •
Coupling between flexural and extensional behavior
•
Rigid body modes (3 modes)
•
Repeated and close eigenvalues
Test Case Data and Information Input Files •
nf003ac.dat (linear consistent)
•
nf003al.dat (linear lumped)
Units SI
Cross Sectional Properties Shear ratio: •
Y = 1.0
•
Z = 1.0
10-6
NX Nastran 8 Verification Manual
Beam Element Test Cases
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
Finite Element Modeling •
Four linear beam (CBAR) elements per arm
Boundary Conditions •
Rotations fixed, translations free
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method NX Nastran results were obtained in two different ways: •
Using lumped mass (lumped mass toggle on, param coupmass = –1)
•
Using coupled mass (lumped mass toggle off, param coupmass = 1)
Results Mode
Reference Value (Hz)
NAFEMS Target Value (Hz)
NX Nastran NX Nastran Result (lumped Result (coupled mass) (Hz) mass) (Hz)
4
3.261
3.262
3.259
3.259
5
5.668
5.665
5.660
5.663
6, 7
11.14
11.15
10.89
11.13
8
12.85
12.83
12.74
12.80
9
24.57
24.66
23.53
24.64
10, 11
28.70
28.81
28.13
28.73
NX Nastran 8 Verification Manual
10-7
Chapter 10
Beam Element Test Cases
References NAFEMS Finite Element Methods & Standards. Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 3. Glasgow: NAFEMS, Nov., 1987.
10.4 Cantilever with Off-center Point Masses This test is a normal mode dynamic analysis of a cantilever with off-center point masses (shown below) using beam elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis,Test 4.
Attributes of this test are: •
Coupling between torsional and flexural behavior
•
Inertial axis non-coincident with flexibility axis
•
Discrete lumped mass, rigid links
•
Close eigenvalues
Test Case Data and Information Input Files •
nf004a.dat
Units SI
Cross Sectional Properties Shear ratio: •
Y = 1.128
•
Z = 1.128
Material Properties •
10-8
E = 200E09 N/m
2
NX Nastran 8 Verification Manual
Beam Element Test Cases
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling •
Five linear beam (CBAR) elements along cantilever
Boundary Conditions •
X = Y = Z = Rx = Ry = Rz = 0 at A
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos (Parameter COUPMASS = –1)
Results Mode
Reference Value (Hz)
NAFEMS Target Value (Hz)
NX Nastran Result (Hz)
1
1.723
1.723
1.714
2
1.727
1.727
1.720
3
7.413
7.413
7.554
4
9.972
9.972
9.954
5
18.16
18.16
17.68
6
26.96
26.97
26.78
References NAFEMS Finite Element Methods & Standards. Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 4. Glasgow: NAFEMS, Nov., 1987.
10.5 Deep Simply-Supported Beam This test is a normal mode dynamic analysis of a deep simply supported beam (shown below). This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 5.
NX Nastran 8 Verification Manual
10-9
Chapter 10
Beam Element Test Cases
Attributes of this test are: •
Shear deformation and rotary inertial (Timoshenko beam)
•
Possibility of missing extensional modes when using iteration solution methods
•
Repeated eigenvalues
Test Case Data and Information Input Files •
nf005ac.dat (linear consistent, param coupmass = 1)
•
nf005al.dat (linear lumped, param coupmass = –1)
Units SI
Cross Sectional Properties Shear ratio: •
Y = 1.176923
•
Z = 1.176923
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling •
Five linear beam elements (CBEAM)
Boundary Conditions •
X = Y = Z = Rx =0 at A
10-10
NX Nastran 8 Verification Manual
Beam Element Test Cases
•
Y = Z = 0 at B
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method NX Nastran results were obtained in two different ways: •
Using lumped mass (lumped mass on, param coupmass = –1)
•
Using coupled mass (lumped mass off, param coupmass = 1)
Results Mode
Reference Value (Hz)
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1, 2 (flexural)
42.65
42.57
43.15
43.26
3 (torsional)
77.54
77.84
77.20
77.84
4 (extensional)
125.0
125.5
124.5
125.5
5, 6 (flexural)
148.3
145.5
149.8
154.9
7 (torsional)
233.1
241.2
224.1
241.2
8, 9 (flexural)
284.6
267.0
271.0
306.7
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 5. Glasgow: NAFEMS, Nov., 1987.
10.6 Circular Ring — In-plane and Out-of-plane Vibration This test is a normal mode dynamic analysis of a circular ring (shown below) using beam elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 6.
NX Nastran 8 Verification Manual
10-11
Chapter 10
Beam Element Test Cases
Attributes of this test are: •
Rigid body modes (six modes)
•
Repeated eigenvalues
Test Case Data and Information Input Files •
nf006ac.dat (param coupmass = 1)
•
nf006al.dat (param coupmass = –1)
Units SI
Cross Sectional Properties Shear ratio: •
Y = 1.128205
•
Z = 1.128205
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling •
20 linear beam (CBAR) elements
10-12
NX Nastran 8 Verification Manual
Beam Element Test Cases
Boundary Conditions •
X = Y = Z = Rx = Ry = Rz active
•
Model is unsupported.
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method NX Nastran results were obtained two different ways: •
Using coupled mass (param coupmass = –1)
•
Using lumped mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
7, 8 (out of plane)
51.85
52.29
51.62
52.38
9, 10 (in plane)
53.38
53.97
54.05
53.80
11, 12 (out of plane)
148.8
149.7
146.9
149.7
13, 14 (in plane) 151.0
152.4
152.2
151.5
15 (out of plane) 287.0
288.3
280.4
287.3
289.5
288.3
289.2
289.1
16 (in plane)
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 6. Glasgow: NAFEMS, Nov., 1987.
10.7 Cantilevered Beam This test is a normal mode dynamic analysis of a cantilevered beam (shown below). This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 71.
NX Nastran 8 Verification Manual
10-13
Chapter 10
Beam Element Test Cases
Attributes of this test are: •
Ill-conditioned stiffness matrix
Test Case Data and Information Input Files •
nf071a.dat (Test 1)
•
nf071b.dat (Test 2)
•
nf071c.dat (Test 3)
Units SI
Material Properties •
E = 200E09 N/m2
•
r=8000 kg/m3
Finite Element Modeling Three tests — all use linear beam (CBAR) elements •
Test 1: a = b
•
Test 2: a = 10b
•
Test3: a = 100b
Boundary Conditions •
X = Y = Rz = 0 at A
•
Z = 0 at all grid points
•
Rx = Ry = 0 at all grid points
10-14
NX Nastran 8 Verification Manual
Beam Element Test Cases
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method Beams always use a coupled mass formulation (param coupmass = 1).
Results Mode
Reference Value (Hz)
Mesh
NX Nastran Result (Hz)
1
1.010
a=b
1.010
a = 10b
1.010
a = 100b
1.010
a=b
6.324
a = 10b
6.327
a = 100b
6.330
a=b
17.70
a = 10b
17.80
a = 100b
17.83
a=b
34.70
a = 10b
34.86
a = 100b
35.07
a=b
57.48
a = 10b
60.64
a = 100b
64.82
a=b
86.24
a = 10b
101.86
a = 100b
104.74
2
3
4
5
6
6.327
17.72
34.72
57.39
85.73
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis Test No. 71. Glasgow: NAFEMS, Nov., 1987.
NX Nastran 8 Verification Manual
10-15
Chapter
11
Shell Element Test Cases
11.1 Thin Square Cantilevered Plate — Symmetric Modes This test is a normal mode dynamic analysis of a thin, square, cantilevered plate meshed with NX Nastran shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 11a.
Attributes of this test are: •
Symmetric modes, symmetric boundary conditions along the cutting plane
Test Case Data and Information Input Files •
nf011a_l.dat (4-noded quadrilateral, lumped mass)
•
nf011a_c.dat (4-noded quadrilateral, coupled mass)
•
nf011ha_l.dat (8-noded quadrilateral, lumped mass)
•
nf011ha_c.dat (8-noded quadrilateral, coupled mass)
Units SI
NX Nastran 8 Verification Manual
11-1
Chapter 11
Shell Element Test Cases
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Two tests: •
32 linear quadrilateral thin shell (CQUAD4) elements — thickness = 0.05m
•
8 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.05m
Boundary Conditions •
X = Y = Rz = 0 at all grid points
•
Z = Ry = Rx = 0 along Y-axis
•
Rx = 0 along Y = 5m
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method Results were obtained in two different ways: •
11-2
Using lumped mass (param coupmass = –1)
NX Nastran 8 Verification Manual
Shell Element Test Cases
•
Using coupled mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
Mesh
NX Nastran Result (lumped mass)(Hz)
NX Nastran Result (coupled mass(Hz)
1
0.4210
Linear
0.4150
0.4180
Parabolic
0.4150
0.4180
Linear
2.490
2.604
Parabolic
2.478
2.567
Linear
3.115
3.314
Parabolic
3.134
3.271
Linear
6.044
6.538
Parabolic
6.163
6.539
Linear
7.094
7.808
Parabolic
7.099
7.495
Linear
10.57
12.34
Parabolic
10.99
12.08
2 3 4 5 6
2.582 3.306 6.555 7.381 11.40
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 11a. Glasgow: NAFEMS, Nov., 1987.
11.2 Thin Square Cantilevered Plate — Anti-symmetric Modes This test is a normal mode dynamic analysis of a thin, square, cantilevered plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 11b.
NX Nastran 8 Verification Manual
11-3
Chapter 11
Shell Element Test Cases
Attributes of this test are: •
Anti-symmetric modes
Test Case Data and Information Input Files •
nf011b.dat (linear (4-noded) quadrilateral)
•
nf011hb.dat (parabolic (8-noded) quadrilateral)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Two tests: •
32 linear quadrilateral thin shell (CQUAD4) elements — thickness = 0.05m
•
8 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.05m
Mesh only half the plate (10m × 5m).
Boundary Conditions •
X = Y = Rz = 0 at all grid points
•
Z = Ry = Rx = 0 along Y-axis
•
Rx = 0 along Y = 5m
11-4
NX Nastran 8 Verification Manual
Shell Element Test Cases
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = —1)
•
Using coupled mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass)(Hz)
NX Nastran Result (coupled mass(Hz)
1
1.029
Linear
1.019
1.000
1.020
Parabolic
1.018
1.005
1.022
Linear
3.839
3.570
3.767
Parabolic
3.710
3.597
3.725
Linear
8.313
7.091
8.113
Parabolic
7.768
7.026
7.786
Linear
9.424
8.047
9.025
Parabolic
8.483
8.133
8.690
11.73
9.940
11.69
11.19
10.15
11.19
17.82
14.22
17.44
15.76
14.21
16.78
2 3 4 5
3.753 7.730 8.561
not available Linear Parabolic
6
not available Linear Parabolic
NX Nastran 8 Verification Manual
11-5
Chapter 11
Shell Element Test Cases
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis Test No. 11b. Glasgow: NAFEMS, Nov., 1987.
11.3 Free Thin Square Plate This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 12.
Attributes of this test are: •
Rigid body modes (three modes)
•
Repeated eigenvalues
Test Case Data and Information Input Files •
nf012l_l.dat (linear (4-noded) quadrilateral, lumped mass)
•
nf012l_c.dat (linear (4-noded) quadrilateral, coupled mass)
•
nf012h_l.dat (parabolic (8-noded) quadrilateral, lumped mass)
•
nf012h_c.dat (parabolic (8-noded) quadrilateral, coupled mass)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
11-6
NX Nastran 8 Verification Manual
Shell Element Test Cases
•
n = 0.3
Finite Element Modeling Two tests: •
64 linear quadrilateral thin shell (CQUAD4) elements — thickness = 0.05m
•
16 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.05m
Boundary Conditions •
X = Y = Rz = 0 at all grid points
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method Results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
4
1.622
Linear
1.632
1.578
1.624
Parabolic
1.532
1.584
1.619
Linear
2.402
2.241
2.389
Parabolic
2.356
2.233
2.363
Linear
3.006
2.804
2.979
Parabolic
2.861
2.808
2.929
5 6
2.360 2.922
NX Nastran 8 Verification Manual
11-7
Chapter 11
Shell Element Test Cases
Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
7, 8
4.233
Linear
4.251
3.931
4.237
Parabolic
4.122
3.944
4.158
Linear
7.859
6.822
7.790
Parabolic
7.363
6.813
7.477
Linear
8.027
6.822
7.790
Parabolic
7.392
6.813
7.477
9
7.416
10
Not available
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 12. Glasgow: NAFEMS, Nov., 1987.
11.4 Simply Supported Thin Square Plate This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 13.
Attributes of this test are: •
Well established
•
Repeated eigenvalues
Test Case Data and Information Input Files •
11-8
nf013l_l.dat (linear quadrilateral, lumped mass)
NX Nastran 8 Verification Manual
Shell Element Test Cases
•
nf013l_c.dat (linear quadrilateral, coupled mass)
•
nf013h_l.dat (parabolic quadrilateral, lumped mass)
•
nf013h_c.dat (parabolic quadrilateral, coupled mass)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Two tests: •
64 linear quadrilateral thin shell (CQUAD4) elements — thickness = 0.05m
•
16 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.05m
Boundary Conditions •
X = Y = Rz = 0 at all grid points
•
Z = Rx = 0 along edges X = 0 and X = 10m
•
Z = Ry = 0 along edges Y = 0 and Y = 10m
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method NX Nastran results were obtained two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
NX Nastran 8 Verification Manual
11-9
Chapter 11
Shell Element Test Cases
Results Mode
Reference Value (Hz)
Mesh
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
2.377
Linear
2.332
2.392
Parabolic
2.376
2.382
Linear
5.797
6.181
Parabolic
5.938
6.026
Linear
8.963
9.933
Parabolic
9.747
10.22
Linear
11.67
13.27
Parabolic
11.87
12.39
Linear
14.45
17.07
Parabolic
16.56
18.17
2, 3
5.942
4
9.507
5, 6
11.88
7, 8
15.45
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 13. Glasgow: NAFEMS, Nov., 1987.
11.5 Simply Supported Thin Annular Plate This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 14.
11-10
NX Nastran 8 Verification Manual
Shell Element Test Cases
Attributes of this test are: •
Curved boundary (skewed coordinate system)
•
Repeated eigenvalues
Test Case Data and Information Input Files •
nf014l_l.dat (linear quadrilateral, lumped mass)
•
nf014l_c.dat (linear quadrilateral, coupled mass)
•
nf014h_l.dat (parabolic quadrilateral, lumped mass)
•
nf014h_c.dat (parabolic quadrilateral, coupled mass)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Two tests: •
160 linear quadrilateral thin shell (CQUAD4) elements — thickness = 0.06 m
•
48 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.06 m
NX Nastran 8 Verification Manual
11-11
Chapter 11
Shell Element Test Cases
Boundary Conditions •
X = Y = Rz = 0 at all grid points
•
Z¢ = Rx¢ = 0 around the circumference
Solution Type SOL 103 — Normal Mode Dynamics, Lanczos Method NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
Mesh
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
1.870
Linear
1.859
1.877
Parabolic
1.840
1.873
Linear
5.293
5.249
Parabolic
5.111
5.151
Linear
10.03
9.983
Parabolic
9.673
9.713
Linear
14.37
15.41
Parabolic
13.95
14.92
Linear
16.10
15.55
Parabolic
15.55
15.71
Linear
18.07
19.09
Parabolic
17.38
18.52
2, 3
5.137
4, 5
9.673
6
14.85
7, 8
15.57
9
18.38
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis,, Test No. 13. Glasgow: NAFEMS, Nov., 1987.
11.6 Clamped Thin Rhombic Plate This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 15.
11-12
NX Nastran 8 Verification Manual
Shell Element Test Cases
Attributes of this test are: •
Distorted elements
Test Case Data and Information Input Files •
nf015l.dat linear (lumped)
•
nf015ha.dat parabolic (lumped)
•
nf015hb.dat parabolic (consistent)
•
nf015hc.data linear (consistent)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Two tests: •
144 linear quadrilateral thin shell (CQUAD4) elements — thickness = 0.05 m
•
36 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.05 m
NX Nastran 8 Verification Manual
11-13
Chapter 11
Shell Element Test Cases
Boundary Conditions •
X = Y = Rz = 0 at all grid points
•
Z¢ = Rx¢ = Ry¢ = 0 along all four edges
Solution Type SOL103 — Normal Mode Dynamics NX Nastran results were obtained two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
7.938
Linear
8.142
7.818
7.955
Parabolic
7.873
7.902
7.929
Linear
13.89
12.83
13.39
Parabolic
12.48
12.85
13.01
Linear
20.04
17.81
19.07
Parabolic
17.31
17.95
18.47
Linear
20.17
18.55
19.24
Parabolic
18.74
18.96
19.17
2 3 4
11-14
12.84 17.94 19.13
NX Nastran 8 Verification Manual
Shell Element Test Cases
Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
5
24.01
Linear
27.70
23.67
26.19
Parabolic
27.95
23.88
25.23
Linear
32.05
27.70
29.82
Parabolic
25.88
27.91
28.81
6
27.92
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 15. Glasgow: NAFEMS, Nov., 1987.
11.7 Cantilevered Thin Square Plate with Distorted Mesh This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements. This document provides the input data and results for NAFEMSSelected Benchmarks for Natural Frequency Analysis, Test 16.
Attributes of this test are: •
Distorted meshes
Test Case Data and Information Input Files •
nf016a1.dat: (16 parabolic quad, lumped mass)
•
nf016a2.dat: (16 parabolic quad, coupled mass)
•
nf016b1.dat: (16 parabolic quad, lumped mass)
•
nf016b2.dat: (16 parabolic quad, coupled mass)
NX Nastran 8 Verification Manual
11-15
Chapter 11
Shell Element Test Cases
•
nf016c1.dat: (4 parabolic quad, lumped mass)
•
nf016c2.dat: (4 parabolic quad, coupled mass)
•
nf016d1.dat: (4 parabolic quad, lumped mass)
•
nf016d2.dat: (4 parabolic quad, coupled mass)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling All tests — parabolic quadrilateral thin shell elements — thickness = 0.05m Four tests: •
Test 1 — 16 elements
•
Test 2 — 16 elements with specified grid points at the following XY coordinates: Coordinates
11-16
Node
X
Y
1
4.000
4.000
2
2.250
2.250
3
4.750
2.500
4
7.250
2.750
5
7.500
7.250
6
5.250
7.250
7
5.250
7.250
8
2.250
7.250
9
2.500
4.750
NX Nastran 8 Verification Manual
Shell Element Test Cases
•
Test 3 — 4 elements
•
Test 4 — 4 elements with a specified grid point at the following XY coordinate: Coordinates Node
X
Y
1
4.000
4.000
Boundary Conditions •
X = Y = Z = Ry = 0 along Y-axis
NX Nastran 8 Verification Manual
11-17
Chapter 11
Shell Element Test Cases
Solution Type SOL103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
Test
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
0.4210
1
0.4174
0.4139
0.4181
2
0.4174
0.4135
0.4182
3
0.4144
0.4021
0.4189
4
0.4145
0.4000
0.4192
1
1.020
0.9985
1.024
2
1.020
0.9967
1.024
3
0.9990
0.9347
1.021
4
1.002
0.9202
1.025
1
2.564
2.444
2.569
2
2.571
2.445
2.566
3
2.554
2.132
2.708
4
2.565
2.112
2.698
2
3
11-18
1.029
2.582
NX Nastran 8 Verification Manual
Shell Element Test Cases
Mode
Reference Value (Hz)
Test
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
4
3.306
1
3.302
3.082
3.281
2
3.317
3.072
3.280
3
3.401
2.707
3.449
4
3.424
2.697
3.430
1
3.769
3.540
3.728
2
3.780
3.535
3.731
3
3.697
3.136
3.913
4
3.714
3.077
3.881
1
6.805
6.018
6.551
2
6.883
5.994
6.552
3
5.455
5.458
7.108
4
5.133
5.459
6.858
5
6
3.753
6.555
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 16. Glasgow: NAFEMS, Nov., 1987.
11.8 Simply Supported Thick Square Plate, Test A This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 21a.
Attributes of this test are:
NX Nastran 8 Verification Manual
11-19
Chapter 11
Shell Element Test Cases
•
Well established
•
Repeated eigenvalues
•
Effect of secondary restraints
Test Case Data and Information Input Files •
nf021a.dat: linear (lumped mass)
•
nf021ha.dat: parabolic (lumped mass)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Two tests: •
64 linear quadrilateral thin shell (CQUAD4) elements — thickness = 1.0 m
•
16 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 1.0 m
Boundary Conditions •
Z = 0 along all four edges
•
X = Y = Rz = 0 at all grid points
•
Rx = 0 along edges X = 0 and X = 10 m
11-20
NX Nastran 8 Verification Manual
Shell Element Test Cases
•
Ry = 0 along edges Y = 0 and Y = 10 m
Solution Type SOL103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
45.90
Linear
46.66
45.83
46.35
Parabolic
45.94
46.17
45.83
Linear
115.8
110.6
114.1
Parabolic
110.4
110.3
109.4
Linear
177.5
164.8
174.3
Parabolic
170.4
167.3
169.8
Linear
233.4
211.8
227.1
Parabolic
212.8
204.6
208.2
2, 3 4 5, 6
109.4 167.9 204.5
NX Nastran 8 Verification Manual
11-21
Chapter 11
Shell Element Test Cases
Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
7, 8
256.5
Linear
283.6
250.5
276.9
Parabolic
270.0
249.3
268.4
Linear
371.1
313.1
364.3
Parabolic
344.8
311.4
319.4
Linear
371.1
338.4
385.8
Parabolic
344.8
347.6
319.4
9
336.6
10
336.6
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 21a. Glasgow: NAFEMS, Nov., 1987.
11.9 Simply Supported Thick Square Plate, Test B This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 21b.
Attributes of this test are: •
Well established
•
Repeated eigenvalues
•
Effect of secondary restraints
11-22
NX Nastran 8 Verification Manual
Shell Element Test Cases
Test Case Data and Information Input Files •
nf021b_c.dat (quadrilateral thin shell elements — coupled mass)
•
nf021b_l.dat (quadrilateral thin shell elements — lumped mass)
•
nf021hb_c.dat (parabolic thin shell elements — coupled mass)
•
nf021hb_l.dat (parabolic thin shell elements — lumped mass)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Two tests: •
64 linear quadrilateral thin shell elements — thickness = 1.0 m
•
16 parabolic quadrilateral thin shell elements — thickness = 1.0 m
Boundary Conditions •
Z = 0 along all four edges; X = Y = Rz = 0 at all grid points
NX Nastran 8 Verification Manual
11-23
Shell Element Test Cases
Chapter 11
Solution Type SOL103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
45.90
Linear
44.75
44.65
44.96
Parabolic
44.13
44.82
44.49
Linear \
112.9
109.1
112.3
Parabolic
107.9
108.5
107.6
Linear
170.3
161.4
170.2
Parabolic
164.2
163.6
165.7
Linear
230.2
210.5
225.4
Parabolic
20.07
203.1
206.5
Linear
274.2
247.1
272.5
Parabolic
260.3
245.7
263.6
2, 3 4 5, 6 7, 8
11-24
109.4 167.9 204.5 256.5
NX Nastran 8 Verification Manual
Shell Element Test Cases
Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
9
336.6
Linear
356.0
308.8
358.4
Parabolic
342.8
307.2
318.6
Linear
356.0
337.6
384.8
Parabolic
342.8
346.9
318.6
10
336.6
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 21b. Glasgow: NAFEMS, Nov., 1987.
11.10 Clamped Thick Rhombic Plate This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 22.
Attributes of this test are: •
Distorted elements
Test Case Data and Information Input Files •
nf022l_l.dat
•
nf022l_c.dat
•
nf022h_l.dat
•
nf022h_c.dat
NX Nastran 8 Verification Manual
11-25
Chapter 11
Shell Element Test Cases
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Two tests: •
100 linear quadrilateral thin shell (CQUAD4) elements - thickness = 1.0 m
•
36 parabolic quadrilateral thin shell (CQUAD8) elements - thickness = 1.0 m
Boundary Conditions •
X = Y = Rz = 0 at all grid points
•
Z¢ = Rx¢ = Ry¢ = 0 along all four edges
Solution Type SOL 103 – Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (parm coupmass = –1)
•
Using coupled mass (param coupmass = 1)
11-26
NX Nastran 8 Verification Manual
Shell Element Test Cases
Results Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
134.0
Linear
137.8
131.2
134.3
Parabolic
133.9
134.9
135.2
Linear
218.5
200.4
211.9
Parabolic
203.3
204.4
206.3
Linear
295.4
262.0
286.6
Parabolic
271.4
270.3
276.4
Linear
296.8
273.6
287.0
Parabolic
283.7
286.9
289.1
Linear
383.6
327.0
373.3
Parabolic
346.4
337.5
353.8
Linear
426.6
372.2
410.6
Parabolic
386.6
384.7
394.0
2 3 4 5 6
201.4 265.8 282.7 334.5 Not available
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C.,Selected Benchmarks for Natural Frequency Analysis, Test No. 22. Glasgow: NAFEMS, Nov., 1987.
11.11 Simply Supported Thick Annular Plate This test is a normal mode dynamic analysis of a simply supported thick annular plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 23.
NX Nastran 8 Verification Manual
11-27
Chapter 11
Shell Element Test Cases
Attributes of this test are: •
Curved boundary (skewed coordinate system)
•
Repeated eigenvalues
Test Case Data and Information Input Files nf023l_l.dat nf023l_c.dat nf023h_l.dat nf023h_c.dat
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Two tests: •
160 linear quadrilateral thin shell (CQUAD4) elements — thickness = 0.6 m
•
48 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.6 m
11-28
NX Nastran 8 Verification Manual
Shell Element Test Cases
Boundary Conditions •
X = Y = Rz = 0 at all grid points
•
Z¢ = Rx¢ = 0 around the circumference
Solution Type SOL 103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmas = 1)
NX Nastran 8 Verification Manual
11-29
Chapter 11
Shell Element Test Cases
Results Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass(Hz)
1
18.58
Linear
18.82
18.40
18.64
Parabolic
18.59
18.53
18.65
Linear
49.82
50.00
50.81
Parabolic
49.02
49.22
49.41
Linear
96.06
93.09
96.00
Parabolic
92.90
93.41
93.73
Linear
148.3
134.6
147.0
Parabolic
140.9
140.2
143.1
Not available
Linear
153.7
144.0
152.1
Parabolic
146.6
147.0
148.2
166.4
Linear
174.5
162.2
177.1
Parabolic
167.3
166.9
170.4
2, 3
48.92
4, 5
92.59
6
140.2
7, 8 9
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 23. Glasgow: NAFEMS, Nov., 1987.
11.12 Cantilevered Square Membrane This test is a normal mode dynamic analysis of a cantilevered square membrane meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 31.
Attributes of this test are:
11-30
NX Nastran 8 Verification Manual
Shell Element Test Cases
•
Well established
Test Case Data and Information Input Files •
nf031l.dat (linear quadrilateral, lumped mass)
•
nf031a.dat (linear quadrilateral, coupled mass)
•
nf031h.dat (parabolic quadrilateral, lumped mass)
•
nf031j.dat (parabolic quadrilateral, coupled mass)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Two tests: •
64 linear quadrilateral thin shell (CQUAD4) elements - thickness = 0.05 m
•
16 parabolic quadrilateral thin shell (CQUAD8) elements - thickness = 0.05 m
NX Nastran 8 Verification Manual
11-31
Shell Element Test Cases
Chapter 11
Boundary Conditions •
X = Y = 0 along the Y axis
•
Z = 0 at all grid points
Solution Type SOL 103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
52.40
Linear
52.91
52.48
52.78
Parabolic
52.64
52.30
52.60
Linear
126.1
125.6
126.1
Parabolic
125.9
125.7
125.9
Linear
143.2
139.6
142.9
Parabolic
141.5
139.5
141.4
Linear
228.9
215.1
227.5
Parabolic
224.6
214.4
224.3
Linear
247.9
240.1
247.4
Parabolic
243.3
242.3
242.9
2 3 4 5
11-32
125.7 140.8 222.5 241.4
NX Nastran 8 Verification Manual
Shell Element Test Cases
Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
6
255.7
Linear
260.6
252.4
259.8
Parabolic
256.8
254.6
256.6
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 31. Glasgow: NAFEMS, Nov., 1987.
11.13 Cantilevered Tapered Membrane This test is a normal mode dynamic analysis of a cantilevered tapered membrane meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 32. Attributes of this test are:
•
Shear behavior
•
Irregular mesh
•
Symmetry
Test Case Data and Information Input Files •
nf032l.dat (linear quadrilateral, lumped mass)
•
nf032a.dat (linear quadrilateral, coupled mass)
•
nf032h.dat (parabolic quadrilateral, lumped mass)
NX Nastran 8 Verification Manual
11-33
Chapter 11
•
Shell Element Test Cases
nf032j.dat (parabolic quadrilateral, coupled mass)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Two tests: •
128 linear quadrilateral thin shell (CQUADR) elements — thickness = 0.1 m
•
32 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.1 m
Boundary Conditions •
X = Y = 0 along the Y axis
•
Z = 0 at all grid points
11-34
NX Nastran 8 Verification Manual
Shell Element Test Cases
Solution Type SOL 103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmas = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
44.62
Linear
44.91
44.66
44.78
Parabolic
44.64
44.54
44.63
Linear
132.1
130.3
131.8
Parabolic
130.1
129.7
130.1
Linear
162.8
162.6
162.8
Parabolic
162.7
162.7
162.7
Linear
253.0
246.1
252.3
Parabolic
246.6
245.1
246.4
Linear
393.3
377.9
393.2
Parabolic
382.0
377.9
381.4
Linear
396.3
389.7
395.0
Parabolic
391.6
390.9
391.5
2 3 4 5 6
130.0 162.7 246.1 379.9 391.4
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 32. Glasgow: NAFEMS, Nov., 1987.
11.14 Free Annular Membrane This test is a normal mode dynamic analysis of a free annular membrane meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 33.
NX Nastran 8 Verification Manual
11-35
Chapter 11
Shell Element Test Cases
Attributes of this test are: •
Repeated eigenvalues
•
Rigid body modes (three modes)
Test Case Data and Information Input Files •
nf033l.dat (linear quadrilateral, lumped mass)
•
nf033a.dat (linear quadrilateral, coupled mass)
•
nf033h.dat (parabolic quadrilateral, lumped mass)
•
nf033j.dat (parabolic quadrilateral, coupled mass)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
11-36
NX Nastran 8 Verification Manual
Shell Element Test Cases
Finite Element Modeling Two tests: •
160 linear quadrilateral thin shell (CQUAD4) elements — thickness = 0.06 m
•
48 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.06 m
Boundary Conditions •
Z = 0 at all grid points
Solution Type SOL 103 — Normal Mode Dynamics NX Nastran results were obtained two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
NX Nastran 8 Verification Manual
11-37
Chapter 11
Shell Element Test Cases
Results Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
4, 5
129.2
Linear
129.5
127.8
128.8
Parabolic
126.5
125.7
125.8
Linear
225.5
224.5
225.3
Parabolic
224.3
224.0
224.2
Linear
234.9
229.9
234.9
Parabolic
233.0
230.8
233.0
Linear
272.1
264.3
271.2
Parabolic
264.8
262.6
263.6
Linear
340.3
329.0
339.9
Parabolic
335.7
331.5
335.7
Linear
392.0
369.9
390.5
Parabolic
378.6
373.3
377.4
6
226.2
7, 8
234.7
9, 10
264.7
11, 12
336.6
13, 14
376.8
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 33. Glasgow: NAFEMS, Nov., 1987.
11.15 Cantilevered Thin Square Plate This test is a normal mode dynamic analysis of a cantilevered thin square plate meshed with shell elements. This document provides the input data and results for NAFEMSSelected Benchmarks for Natural Frequency Analysis, Test 73.
11-38
NX Nastran 8 Verification Manual
Shell Element Test Cases
Test Case Data and Information Input Files •
nf073a.dat (Test 1)
•
nf073b.dat (Test 2)
•
nf073c.dat (Test 3)
•
nf073d.dat (Test 4)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling 16 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.05 m
Boundary Conditions X = Y = Z = Ry = 0 along the Y axis
NX Nastran 8 Verification Manual
11-39
Shell Element Test Cases
Chapter 11
Solution Type SOL 103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
0.4210
Test 1
0.4174
0.4154
0.4183
Test 2
0.4174
0.4154
0.4183
Test 3
0.4175
0.4154
0.4184
Test 4
0.4184
0.4161
0.4192
Test 1
1.020
1.051
1.023
Test 2
1.020
1.006
1.023
Test 3
1.021
1.007
1.027
Test 4
1.032
1.015
1.024
Test 1
2.564
2.485
2.579
Test 2
2.597
2.509
2.605
Test 3
2.677
2.524
2.675
Test 4
2.850
2.563
2.672
Test 1
3.302
3.150
3.298
Test 2
3.345
3.180
3.332
Test 3
3.365
3.196
3.344
Test 4
3.571
3.373
3.535
Test 1
3.769
3.622
3.765
Test 2
3.888
3.713
3.862
Test 3
4.035
3.828
4.000
Test 4
5.466
4.935
5.360
Test 1
6.805
6.292
6.719
Test 2
7.517
6.901
7.399
Test 3
7.495
6.879
7.387
Test 4
——
——
——
2
3
4
5
6
11-40
1.029
2.582
3.306
3.753
376.8
NX Nastran 8 Verification Manual
Shell Element Test Cases
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 73. Glasgow: NAFEMS, Nov., 1987.
NX Nastran 8 Verification Manual
11-41
Chapter
12 Axisymmetric Solid and Solid Element Test Cases
12.1 Free Cylinder — Axisymmetric Vibration This test is a normal mode dynamic analysis of a free cylinder meshed with axisymmetric elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 41.
Attributes of this test are: •
Rigid body modes (one mode)
•
Coupling between axial, radial, and circumferential behavior
•
Close eigenvalues
Test Case Data and Information Input Files •
nf041.dat (linear axisymmetric, lumped mass)
•
nf041a.dat (linear axisymmetric, coupled mass)
•
nf041h.dat (parabolic axisymmetric, lumped mass)
•
nf041j.dat (parabolic axisymmetric, coupled mass)
Units SI
NX Nastran 8 Verification Manual
12-1
Chapter 12
Axisymmetric Solid and Solid Element Test Cases
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg / m3
•
n = 0.3
Finite Element Modeling Two tests: •
16 axisymmetric solid linear quadrilateral (CQUADX) elements
•
8 axisymmetric solid parabolic quadrilateral (CQUADX) elements
Boundary Conditions Unsupported
Solution Type SOL 103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
12-2
NX Nastran 8 Verification Manual
Axisymmetric Solid and Solid Element Test Cases
Results Mode #
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
2
243.5
Linear
244.0
243.1
243.9
Parabolic
243.5
243.4
243.5
Linear
379.4
372.1
378.4
Parabolic
377.5
376.4
377.4
Linear
395.4
385.8
394.4
Parabolic
394.3
392.4
394.2
Linear
401.4
386.9
398.5
Parabolic
397.9
392.8
397.9
Linear
421.9
391.7
415.4
Parabolic
406.4
397.2
406.0
3
377.4
4
394.1
5
397.7
6
405.3
Note The reference value refers to the accepted solution to the problem.
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 41. Glasgow: NAFEMS, Nov., 1987.
12.2 Thick Hollow Sphere — Uniform Radial Vibration This test is a normal mode dynamic analysis of a thick hollow sphere meshed using axisymmetric elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 42.
NX Nastran 8 Verification Manual
12-3
Chapter 12
Axisymmetric Solid and Solid Element Test Cases
Attributes of this test are: •
Curved boundary (skewed coordinate system)
•
Constraint equations
Test Case Data and Information Input Files •
nf042.dat (linear axisymmetric, lumped mass)
•
nf042a.dat (linear axisymmetric, coupled mass)
•
nf042h.dat (parabolic axisymmetric, lumped mass)
•
nf042j.dat (parabolic axisymmetric, coupled mass)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling •
12-4
10 axisymmetric solid linear quadrilateral (CQUADX) elements -a = 5°
NX Nastran 8 Verification Manual
Axisymmetric Solid and Solid Element Test Cases
Boundary Conditions •
Z¢ displacement = 0 at all grid points
•
Grid points at the same R¢ are constrained to have the same r¢ displacement
•
One constraint set
Solution Type SOL 103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode #
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
369.9
Linear
370.6
369.3
369.6
Parabolic
370.0
369.7
369.7
Linear
841.2
828.1
837.7
Parabolic
838.1
836.2
837.7
Linear
1473.
1416.
1468.
Parabolic
1453.
1445.
1451.
Linear
2192.
2023.
2186.
Parabolic
2132.
2100.
2117.
Linear
2976.
2595.
2967.
Parabolic
2853.
2764.
2799.
2 3 4 5
838.0 1451. 2117. 2796.
NX Nastran 8 Verification Manual
12-5
Chapter 12
Axisymmetric Solid and Solid Element Test Cases
Note The reference value refers to the accepted solution to the problem.
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis Test No. 42. Glasgow: NAFEMS, Nov., 1987.
12.3 Simply Supported Annular Plate — Axisymmetric Vibration This test is a normal mode dynamic analysis of a simply supported annular plate meshed with axisymmetric elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 43.
Attributes of this test are: •
Well established
Test Case Data and Information Input Files •
nf043a.dat (lumped mass)
•
nf043b.dat (coupled mass)
•
nf043c.dat (lumped mass)
•
nf043d.dat (coupled mass)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
12-6
NX Nastran 8 Verification Manual
Axisymmetric Solid and Solid Element Test Cases
Finite Element Modeling Two tests: •
60 axisymmetric solid linear quadrilateral (CQUADX) elements
•
5 axisymmetric solid parabolic quadrilateral (CQUADX) elements
Boundary Conditions •
Z = 0 at A
Solution Type SOL 103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode #
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
18.54
Linear
18.71
18.23
18.27
Parabolic
18.58
18.48
18.55
Linear
145.5
140.9
142.6
Parabolic
145.6
135.9
138.6
2
150.2
NX Nastran 8 Verification Manual
12-7
Chapter 12
Axisymmetric Solid and Solid Element Test Cases
Mode #
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
3
224.2
Linear
224.2
224.2
224.2
Parabolic
224.2
224.1
224.2
Linear
385.6
366.3
376.5
Parabolic
374.1
345.3
360.3
Linear
689.3
647.7
677.8
Parabolic
686.0
592.7
640.2
4
358.3
5
629.2
Note The reference value refers to the accepted solution to the problem.
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 43. Glasgow: NAFEMS, Nov., 1987.
12.4 Deep Simply Supported "Solid" Beam This test is a normal mode dynamic analysis of a deep, simply supported beam meshed with solid elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis , Test 51.
Attributes of this test are: •
Skewed coordinate system
•
Skewed restraints
12-8
NX Nastran 8 Verification Manual
Axisymmetric Solid and Solid Element Test Cases
Test Case Data and Information Input Files •
nf051a.dat (linear brick)
•
nf051b.dat (parabolic brick)
•
nf051c.dat (linear pyramid)
•
nf051d.dat (parabolic pyramid)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Four tests: •
30 solid linear brick (CHEXA) elements
•
5 solid parabolic brick (CHEXA) elements
•
180 solid linear pyramid (CPYRAM) elements (created by dividing each linear brick element into 6 pyramid elements)
•
30 solid parabolic pyramid (CPYRAM) elements (created by dividing each parabolic brick element into 6 pyramid elements)
NX Nastran 8 Verification Manual
12-9
Axisymmetric Solid and Solid Element Test Cases
Chapter 12
Boundary Conditions •
X¢ = Z¢ = 0 along AA¢
•
Z¢ = 0 along BB¢
•
Y¢ = 0 at all grid points on the plane Y¢ = 2.0 m
Solution Type SOL 103 — Normal Mode Dynamics NX Nastran results were obtained two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode #
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
1
38.20
linear brick
42.88
37.96
38.28
41.30
41.50
37.85
38.24
37.90
38.10
linear pyramid parabolic brick parabolic pyramid
12-10
NX Nastran 8 Verification Manual
38.82
Axisymmetric Solid and Solid Element Test Cases
Mode #
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
2
85.21
linear brick
93.82
83.38
83.95
89.30
89.60
87.12
87.52
86.30
86.50
152.7
157.6
163.0
166.0
151.8
157.0
152.0
155.0
251.6
264.9
269.0
276.0
248.5
258.2
250.0
255.0
288.0
298.3
303.0
309.0
289.6
305.6
291.0
300.0
linear pyramid parabolic brick
88.45
parabolic pyramid 3
152.2
linear brick
170.7
linear pyramid parabolic brick
159.4
parabolic pyramid 4
245.5
linear brick
286.1
linear pyramid parabolic brick
259.2
parabolic pyramid 5
297.1
linear brick
318.9
linear pyramid parabolic brick parabolic pyramid
307.9
Note The reference value refers to the accepted solution to the problem.
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis Test No. 51. Glasgow: NAFEMS, Nov., 1987.
12.5 Simply Supported "Solid" Square Plate This test is a normal mode dynamic analysis of a simply supported square plate meshed with solid elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 52.
NX Nastran 8 Verification Manual
12-11
Chapter 12
Axisymmetric Solid and Solid Element Test Cases
Attributes of this test are: •
Well established
•
Rigid body modes (three modes)
•
Kinematically incomplete suppressions
Test Case Data and Information Input Files •
nf052l.dat (linear brick)
•
nf052b.dat (parabolic brick)
•
nf052c.dat (linear pyramid)
•
nf052d.dat (parabolic pyramid)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
12-12
NX Nastran 8 Verification Manual
Axisymmetric Solid and Solid Element Test Cases
Finite Element Modeling Four tests: •
64 solid linear brick (CHEXA) elements
•
16 solid parabolic brick (CHEXA) elements
•
384 solid linear pyramid (CPYRAM) elements (created by dividing each linear brick element into 6 pyramid elements)
•
96 solid parabolic pyramid (CPYRAM) elements (created by dividing each parabolic brick element into 6 pyramid elements)
Boundary Conditions Z = 0 along the four edges on the plane Z = –0.5 m
NX Nastran 8 Verification Manual
12-13
Axisymmetric Solid and Solid Element Test Cases
Chapter 12
Solution Type SOL 103 normal modes NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
Results Mode #
Reference Mesh Value (Hz)
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
4
45.90
51.65
44.04
45.24
66.90
68.00
43.81
44.16
44.70
44.80
106.5
113.7
154.0
160.0
105.2
107.9
109.0
110.0
155.5
172.3
195.0
197.0
156.3
163.9
166.0
169.0
193.6
196.8
207.0
212.0
194.0
193.9
194.0
194.0
200.1
209.6
207.0
212.0
193.5
206.6
196.0
207.0
linear brick linear pyramid parabolic brick
44.76
parabolic pyramid 5, 6
109.4
linear brick
132.7
linear pyramid parabolic brick
110.5
parabolic pyramid 7
167.9
linear brick
194.4
linear pyramid parabolic brick
169.1
parabolic pyramid 8
193.6
linear brick
197.2
linear pyramid parabolic brick
193.9
parabolic pyramid 9
206.2
linear brick
210.6
linear pyramid parabolic brick parabolic pyramid
12-14
NX Nastran 8 Verification Manual
206.6
Axisymmetric Solid and Solid Element Test Cases
Mode #
Reference Mesh Value (Hz)
NAFEMS Target Value (Hz)
NX Nastran Result (lumped mass) (Hz)
NX Nastran Result (coupled mass) (Hz)
10
206.2
210.6
200.1
209.6
220.0
223.0
193.5
206.6
196.0
207.0
linear brick linear pyramid parabolic brick
206.6
parabolic pyramid Note
The reference value refers to the accepted solution to the problem.
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 52. Glasgow: NAFEMS, Nov., 1987.
12.6 Simply Supported "Solid" Annular Plate This test is a normal mode dynamic analysis of a simply supported annular plate meshed with solid elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 53.
Attributes of this test are: •
Curved boundary (skewed coordinate system)
•
Constraint equations
Test Case Data and Information Input Files •
nf053l.dat (linear brick)
NX Nastran 8 Verification Manual
12-15
Chapter 12
Axisymmetric Solid and Solid Element Test Cases
•
nf053h.dat (parabolic brick)
•
nf053c.dat (linear pyramid)
•
nf053d.dat (parabolic pyramid)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n = 0.3
Finite Element Modeling Four tests: •
60 solid linear brick (CHEXA) elements — a = 5°
•
5 solid parabolic brick (CHEXA) elements — a = 10°
•
360 solid linear pyramid (CPYRAM) elements (created by dividing each linear brick element into 6 pyramid elements)
•
30 solid parabolic pyramid (CPYRAM) elements (created by dividing each parabolic brick element into 6 pyramid elements)
12-16
NX Nastran 8 Verification Manual
Axisymmetric Solid and Solid Element Test Cases
Boundary Conditions •
q displacement = 0 at all grid points
•
Z displacement = 0 at all grid points along AA
•
Grid points at same R and Z are constrained to have same z displacement
•
One constraint set
Solution Type SOL 103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
NX Nastran 8 Verification Manual
12-17
Chapter 12
Axisymmetric Solid and Solid Element Test Cases
Results Mode #
Reference Value (Hz)
Mesh
NAFEMS Target Value (Hz)
NX Nastran NX Nastran Result Result (coupled mass) (lumped (Hz) mass) (Hz)
1
18.58
linear brick
19.66
18.57
18.61
19.90
19.90
18.45
18.58
21.30
21.50
138.8
140.5
147.0
148.0
135.9
140.3
140.0
143.0
224.2
224.4
224.0
224.0
223.7
224.2
224.0
225.0
361.8
372.1
383.0
390.0
351.2
371.9
359.0
376.0
643.8
674.7
684.0
690.0
624.7
679.6
640.0
683.0
linear pyramid parabolic brick
18.58
parabolic pyramid 2
140.2
linear brick
146.4
linear pyramid parabolic brick
140.4
parabolic pyramid 3
224.2
linear brick
224.3
linear pyramid parabolic brick
224.2
parabolic pyramid 4
358.3
linear brick
386.7
linear pyramid parabolic brick
374.0
parabolic pyramid 5
629.2
linear brick
689.5
linear pyramid parabolic brick parabolic pyramid
686.0
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 53. Glasgow: NAFEMS, Nov., 1987.
12-18
NX Nastran 8 Verification Manual
Axisymmetric Solid and Solid Element Test Cases
12.7 Cantilevered Solid Beam This test is a normal mode dynamic analysis of a cantilevered solid beam meshed using solid elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 72.
Attributes of this test are: •
Highly populated stiffness matrix
Test Case Data and Information Input Files •
nf072a.dat (parabolic bricks – conventional)
•
nf072b.dat (parabolic bricks – unconventional)
•
nf072c.dat (parabolic pyramids – conventional)
•
nf072d.dat (parabolic pyramids – unconventional)
Units SI
Material Properties •
E = 200E09 N/m2
•
r = 8000 kg/m3
•
n=3
NX Nastran 8 Verification Manual
12-19
Chapter 12
Axisymmetric Solid and Solid Element Test Cases
Finite Element Modeling Four tests: •
Test 1: solid parabolic brick (CHEXA) elements, conventional grid point numbering
•
Test 2: solid parabolic pyramid (CPYRAM) elements (created by dividing each brick element into 6 pyramid elements), conventional grid point numbering
•
Test 3: solid parabolic brick (CHEXA) elements, unconventional grid point numbering
•
Test 4: solid parabolic pyramid (CPYRAM) elements (created by dividing each brick element into 6 pyramid elements), unconventional grid point numbering
12-20
NX Nastran 8 Verification Manual
Axisymmetric Solid and Solid Element Test Cases
Boundary Conditions •
X = Y = Z = 0 at all grid points on X = 0 plane
•
Y = 0 at grid points on Y = 1 m plane
Solution Type SOL 103 — Normal Mode Dynamics NX Nastran results were obtained in two different ways: •
Using lumped mass (param coupmass = –1)
•
Using coupled mass (param coupmass = 1)
NX Nastran 8 Verification Manual
12-21
Chapter 12
Axisymmetric Solid and Solid Element Test Cases
Results Mode #
Mesh
NAFEMS Target Value (Hz)
NX Nastran NX Nastran Result (lumped Result (coupled mass) (Hz) mass) (Hz)
1
Test 1
16.01
15.82
15.99
15.90
16.00
15.82
15.99
15.90
16.00
83.18
87.09
84.30
87.00
83.18
87.09
84.30
87.00
125.5
126.0
126.0
126.0
125.5
126.0
126.0
126.0
193.5
209.1
198.0
209.0
193.5
209.1
198.0
209.0
310.1
349.9
323.0
350.0
310.1
349.9
323.0
350.0
364.2
375.8
367.0
375.0
364.2
375.8
367.0
375.0
Test 2 Test 3
16.01
Test 4 2
Test 1
87.23
Test 2 Test 3
87.23
Test 4 3
Test 1
126.0
Test 2 Test 3
126.0
Test 4 4
Test 1
209.6
Test 2 Test 3
209.6
Test 4 5
Test 1
351.1
Test 2 Test 3
351.1
Test 4 6
Test 1
375.8
Test 2 Test 3 Test 4
375.8
References NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 72. Glasgow: NAFEMS, Nov., 1987.
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NX Nastran 8 Verification Manual
Part
VI Verification Test Cases from the Societe Francaise des Mecaniciens
NX Nastran 8 Verification Manual
Chapter
13 Overview of Verification Test Cases Provided by the Societe Francaise des Mecaniciens
The purpose of these linear statics test cases is to verify the function of NX Nastran using standard benchmarks published by SFM (Societe Francaise des Mecaniciens. Paris, France) in Guide de validation des progiciels de calcul de structures. Included here are: •
Tests cases on mechanical structures using linear statics analysis, normal mode dynamics analysis, and model response.
•
Stationary thermal test cases using heat transfer analysis.
•
Thermo-mechanical test cases using linear statics analysis.
Results published in Guide de validation des progiciels de calcul de structures are compared with those computed using NX Nastran.
13.1 Understanding the Test Case Format Each test case is structured with the following information. •
Test case data and information: o
Input files
o
Units
o
Material properties
o
Finite element modeling information
o
Boundary conditions (loads and restraints)
o
Solution type
•
Results
•
Reference
NX Nastran 8 Verification Manual
13-1
Chapter 13
Overview of Verification Test Cases Provided by the Societe Francaise des Mecaniciens
13.2 Reference The following reference has been used in these test cases: Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990.
13-2
NX Nastran 8 Verification Manual
Chapter
14 Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
14.1 Short Beam on Two Articulated Supports This test is a linear statics analysis of a short, straight beam with plane bending and shear loading. It provides the input data and results for benchmark test SSLL02/89 from Guide de validation des progiciels de calcul de structures.
•
Area = 31E–04 m2
•
Inertia = 2810E–08 m4
•
Shear area ratio = 2.42
Test Case Data and Information Input Files ssll02.dat
Units SI
Material Properties •
E = 2E11 Pa
•
n = 0.3
NX Nastran 8 Verification Manual
14-1
Chapter 14
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Finite Element Modeling •
10 linear beam (CBAR) elements
•
11 grid points
The mesh is shown in the following figure:
Boundary Conditions •
Restrain both free ends of the beam in translation DOF. o
Edge load = 1E05 N/m in –Y direction
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Result
Bench Value
NX Nastran
Displacement at point B v (m) (Grid point 7)
–1.259E–3
–1.249E–3
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLL02/89.
14.2 Clamped Beams Linked by a Rigid Element This test is a linear statics analysis of a straight, cantilever beam with plane bending and a rigid element. It provides the input data and results for benchmark test SSLL05/89 from Guide de validation des progiciels de calcul de structures.
14-2
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Test Case Data and Information Input File ssll05.dat
Units SI
Material Properties •
E = 2E11 Pa
•
I = (4/3)E–08 m4
Finite Element Modeling •
20 linear beam (CBAR) elements
•
1 rigid element
•
26 grid points
The mesh is shown in the following figure:
Boundary Conditions •
Points A and C: Clamped
•
Point D: Set nodal force = 1000 N in –Y direction
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
NX Nastran 8 Verification Manual
14-3
Chapter 14
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Results Type
Grid point
Point
Bench Value
NX Nastran
v (m) Disp. Y
Grid point 6
B
–0.1250
–0.1250
v (m) Disp. Y
Grid point 3
D
–0.1250
–0.1250
V force (N) Y
Grid point 1
A
500.0
500.0
M moment (Nm) Rz
Grid point 1
A
500.0
500.0
V force (N) Y
Grid point 4
C
500.0
500.0
M moment (Nm) Rz
Grid point 4
C
500.0
500.0
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990 Test No. SSLL05/89.
14.3 Transverse Bending of a Curved Pipe This test is a linear statics analysis (three-dimensional problem) of a curved pipe with transverse bending and bending-torque loading. It provides the input data and results for benchmark test SSLL07/89 from Guide de validation des progiciels de calcul de structures.
•
R=1m
•
de = 0.02 m
•
di = 0.016 m
•
A = 1.131E-0–04 m2
•
Ix = 4.637E–09 m4
14-4
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Test Case Data and Information Input Files •
ssll07a.dat linear beam
•
ssll07b.dat curved beam
Units SI
Material Properties •
E = 2E11 Pa
•
n = 0.3
Finite Element Modeling Test 1 •
90 linear beam (CBAR) elements
•
91 grid points
Test 2 •
90 curved beam (CBEND) elements
•
91 grid points
To obtain the point where q = 15° with accuracy, use surface mapped meshing on 1/4 of a cylinder. Then mesh a curved edge with the Surface Coating command and undo the mesh on the surface. The mesh for Test 1 is shown in the following figure:
NX Nastran 8 Verification Manual
14-5
Chapter 14
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Boundary Conditions •
Clamp point A.
•
Grid point force F = 100 N in Z direction.
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Type
Grid point
Point
Bench Value
Test Number
NX Nastran
u (m) Disp. Z
Grid point 1
B
0.1346
1
0.1346
2
0.1346
1
76.67
2
77.51
1
–96.37
2
–95.70
Mt (Nm)*
Grid point 1
Mf (Nm)
Mf = bending moment Mt = torsional moment *See "Post Processing" below.
14-6
NX Nastran 8 Verification Manual
q = 15°
74.12 –96.59
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Post Processing Linear Beam (CBAR) Elements List beam forces on element 167, second end: •
Mf = torque
•
Mt = bending moment
Curved Beam (CBEND) Elements List beam forces on element 166, second end: •
Mf = torque
•
Mt = bending moment
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990.Test No. SSLL07/89..
14.4 Plane Bending Load on a Thin Arch This test is a linear statics analysis (plane problem) of a thin arc with plane bending. It provides the input data and results for benchmark test SSLL08/89 from Guide de validation des progiciels de calcul de structures.
•
R=1m
•
de = 0.02 m
•
di = 0.016 m
•
A = 1.131E–04 m2
•
Ix 4.637E–09 m4
NX Nastran 8 Verification Manual
14-7
Chapter 14
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Test Case Data and Information Input File ssll08.dat
Units SI
Material Properties •
E = 2E11 Pa
•
n = 0.3
Finite Element Modeling •
10 linear beam (CBAR) elements
•
11 grid points
14-8
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Boundary Conditions •
Point A: Articulated Z
•
Point B: Sets Y and Z displacement to 0
•
Force = 100N in –Y direction
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Type
Grid Point
Point
Bench Value
NX Nastran
Rz (rad)
2
A
–3.077E–2
–3.110E–2
Rz (rad)
1
B
3.077E–2
3.110E–2
Y (m)
7
C
-1.921E–2
–1.934E–2
X (m)
1
B
5.391E-2
5.374E–2
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLL08/89.
14.5 Grid Point Load on an Articulated CONROD Truss This test is a linear statics analysis of a plane truss with an articulated rod. It provides the input data and results for benchmark test SSLL11/89 from Guide de validation des progiciels de calcul de structures.
NX Nastran 8 Verification Manual
14-9
Chapter 14
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Test Case Data and Information Input File ssll11.dat
Units SI
Material Properties •
E = 1.962E11 Pa
14-10
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Finite Element Modeling •
4 rod (CONROD) elements
•
4 grid points
The mesh is shown in the following figure:
Element
Length (m)
Area (m2)
AC
2.000E–4
CB
2.000E–4
CD
1.000E–4
BD
1.000E–4
Boundary Conditions •
Point A and B: Articulated
•
Point D: Set Nodal force = 9.81 E3 N in –Y direction
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
NX Nastran 8 Verification Manual
14-11
Chapter 14
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Results Type
Grid Point
Point
Bench Value
NX Nastran
X (m)
18.00
C
0.2652E–3
0.2652E–3
Y (m)
18.00
C
0.08839E–3
0.08839E–3
X (m)
2.000
D
3.479E–3
3.479E–3
Y (m)
2.000
D
–5.601E–3
–5.600E–3
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. (Paris, Afnor Technique, 1990..) Test No. SSLL11/89.
14.6 Articulated Plane Truss This test is a linear statics analysis of a straight cantilever beam with plane bending and tension-compression. It provides the input data and results for benchmark test SSLL14/89 from Guide de validation des progiciels de calcul de structures.
•
I1 = 5E–04 m4
•
I2 = 2.5E–04 m4
14-12
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Test Case Data and Information Input Files •
ssll14a.dat (4 elements)
•
ssll14b.dat (10 elements)
Units SI
Material Properties •
E = 2.1E11 Pa
Finite Element Modeling Test 1 •
4 linear beam (CBAR) elements
•
5 grid points
Test 2 •
10 linear beam (CBAR) elements
•
11 grid points
The mesh for Test 2 is shown in the following figure:
NX Nastran 8 Verification Manual
14-13
Chapter 14
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Boundary Conditions •
Point A and B: Articulate
•
Set forces and moments to the following numeric values: o
p = –3,000 N/m
o
F1 = –20,000 N
o
F2 = –10,000 N
o
M = –100,000 Nm
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Type
Grid Point
Point
Bench Value
Test Number
NX Nastran
Vertical reaction (N)
1.000
A
3.150E4
1
3.150E4
2
3.320E4
Hortizontal reaction (N)
1.000
1
1.920E4
2
2.061E4
Vertical Displacement (m)
8.000
1
–0.02100
2
–0.03161
A C
2.024E4 0.03072
Note NX Nastran takes shear effect into account.
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NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLL14/89.
14.7 Beam on an Elastic Foundation This test is a linear statics analysis (plane problem) of a straight beam with plane bending and an elastic support. It provides the input data and results for benchmark test SSLL16/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input File ssll16.dat
Units SI
Material Properties •
E = 2.1E11 Pa
•
K = 8.4E05 N/m2
•
Each spring stiffness is set to: K * L/(number of spring elements).
NX Nastran 8 Verification Manual
14-15
Chapter 14
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Finite Element Modeling •
50 linear beam (CBAR) elements
•
49 spring (CBUSH) elements
•
51 grid points
The mesh is shown in the following figure:
14-16
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Boundary Conditions •
Point A and B: Articulated
•
Set forces and moments to the following numeric values: –F = –10000 N –p = –5000 N/m –M = 15000 Nm.
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Type
Point
Bench Value
NX Nastran
Rotation(rad) Rz
A
—0.003050
–0.003034
1.167E4
1.158E4
–0.4233E–2
–0.4216E–2
Vertical Reaction force (N) Vertical Disp. (m)
D
NX Nastran 8 Verification Manual
14-17
Chapter 14
Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements
Type
Point
M moment (Nm)*
Bench Value
NX Nastran
3.384E4
3.369E4
*List beam forces on element 26, first end, z bending moment.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLL16/89.
14-18
NX Nastran 8 Verification Manual
Chapter
15 Mechanical Structures — Linear Statics Analysis with Shell Elements
15.1 Plane Shear and Bending Load on a Plate This test is a linear statics analysis (plane problem) of a plate with plane bending. It provides the input data and results for benchmark test SSLP01/89 from Guide de validation des progiciels de calcul de structures.
•
Thickness = 1 mm
Test Case Data and Information Input File sslp01.dat
Units SI
Material Properties •
E = 3E10 Pa
•
n = 0.25
NX Nastran 8 Verification Manual
15-1
Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Finite Element Modeling •
100 linear quadrilateral thin shell (CQUAD4) elements
•
126 grid points
The mesh is shown in the following figure:
Boundary Conditions •
Clamped Plate
•
Set a shear force with parabolic distribution on width and constant distribution on thickness.
•
Resultant force: p = 40 N.
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Type
Grid point #
Location
Bench Value
NX Nastran
Y (mm)
Grid point 3
(L,y)
0.3413
0.3408
Displacement is shown in the following figure:
15-2
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990 Test No. SSLP01/89.
15.2 Infinite Plate with a Circular Hole This test is a linear statics analysis (plane problem) of a plate with tension-compression and a membrane effect. It provides the input data and results for benchmark test SSLP02/89 from Guide de validation des progiciels de calcul de structures.
NX Nastran 8 Verification Manual
15-3
Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Test Case Data and Information Input File sslp02.dat
Units SI
Material Properties •
E = 3E10 Pa
•
n = 0.25
15-4
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
Finite Element Modeling •
100 linear quadrilateral thin shell (CQUAD4) elements
•
121 grid points
The plate is meshed using the biasing option. The mesh is shown in the following figure:
Boundary Conditions •
u (0,y) = 0, Ry (y) = 0, Rz (y) = 0, (z = 0, all grid points)
•
n (x,0) = 0, Rx (x) = 0, Rz (x) = 0
•
Tension force P = 2.5 N/mm**2 (in plane force of 2500 N/m)
The boundary conditions are shown in the following figure:
NX Nastran 8 Verification Manual
15-5
Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Solution Type SOL 101 — Linear Statics
Results Type sqq
Point
Bench Value
NX Nastran
(a, 0)
7.500E7
7.528E7
sqq
(a, π/4)
2.500E7
2.511E7
sqq
(a, π/2)
–2.500E7
–2.452E7
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLP02/89.
15.3 Uniformly Distributed Load on a Circular Plate This test is a linear statics analysis (three-dimensional problem) of a circular plate fixed at the edge with transverse bending and a uniform load. It provides the input data and results for benchmark test SSLS03/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
ssls03a.dat linear quadrilateral
•
ssls03b.dat linear triangle
Units SI
15-6
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
Finite Element Modeling Test 1 •
38 linear quadrilateral thin shell (CQUAD4) elements
•
50 grid points
Test 2 •
53 linear triangular thin shell (CTRIA3) elements
•
38 grid points
Meshing is only done on 1/4 of the plate. The meshes are shown in the following figure:
NX Nastran 8 Verification Manual
15-7
Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Boundary Conditions •
Clamp free edges.
•
Uniform pressure p = –1000 Pa.
•
Symmetric conditions are applied to the sides.
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Result
Grid Point
Point
Bench Value
Test Number NX Nastran
Z
1.000
Center O
–0.006500
1
–0.006600
w (m)
1.000
2
–0.006500
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS03/89.
15.4 Torque Loading on a Square Tube This test is a linear statics analysis (three-dimensional problem) of a thin-walled tube loaded in torsion by pure shear at the free end. It provides the input data and results for benchmark test SSLS05/89 from Guide de validation des progiciels de calcul de structures.
15-8
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
Test Case Data and Information Input File ssls05.dat
Units SI
Material Properties • •
E = 2.1 x 1011 Pa = 0.3
Finite Element Modeling •
160 CQUAD4 elements
•
219 grid points
The mesh is shown in the following figure:
NX Nastran 8 Verification Manual
15-9
Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Boundary Conditions •
Plane X = 0
•
Clamped beam
•
Apply a torque equal to 10 Nm on the free end.
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Result
Grid Point
Bench Value
NX Nastran
Disp. Y (m)
193.0
–6.170E–7
.6.170E–7
Disp. Rx (rad)
1.230E–5
1.230E–5
Stress XY Shear (Pa)
–11.00E4
–11.00E4
–9.870E–7
–9.870E–7
Disp. Rx (rad)
1.970E–5
1.970E–5
Stress XY Shear (Pa)
–11.00E4
–11.00E4
Disp. Y (m)
208.0
Results are post-processed using the Shell surface: Bottom option.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS05/89.
15.5 Cylindrical Shell with Internal Pressure This test is a linear statics analysis of a thin cylinder loaded by internal pressure. It provides the input data and results for benchmark test SSLS06/89 from Guide de validation des progiciels de calcul de structures.
15-10
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
Test Case Data and Information Input Files •
ssls06a.dat
•
ssls06b.dat
Units SI
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
NX Nastran 8 Verification Manual
15-11
Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Finite Element Modeling The meshes are shown in the following figure:
Test 1 •
100 linear quadrilateral thin shell (CQUAD4) elements
•
121 grid points
Test 2 •
400 liinear quadrilateral thin shell (CQUAD4) elements
•
441 grid points
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NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
Boundary Conditions •
Free conditions: To set free boundary conditions, use symmetry about XZ, XY, and YZ planes.
•
Internal pressure = 10000 Pa.
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Type
Point
Bench Value
Test Number
NX Nastran
s11(Pa)
All
0
1
1.720
2
4.960
1
4.950E5
2
4.990E5
1
2.370E–6
2
2.380E–6
1
–1.420E–6
2
–1.430E–6
s22(Pa) ΔR(m) ΔL(m)
5.000E5 2.380E–6 –1.430E–6
All results are averages.
NX Nastran 8 Verification Manual
15-13
Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Post Processing •
s11 is the stress of z at grid point 11 (test 1) and grid point 21 (test 2)
•
s22 is the stress of x at grid point 111 (test 1) and grid point 421 (test 2)
•
ΔR(m) is the displacement of x at grid point 121 (test 1) and grid point 441 (test 2)
•
ΔL(m) is the displacement of z at grid point 121 (test 1) and grid point 441 (test 2)
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS06/89.
15.6 Uniform Axial Load on a Thin Wall Cylinder This test is a linear static analysis of a thin cylinder loaded axially. It provides the input data and results for benchmark test SSLS07/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
ssls07a.dat – parabolic quadrilateral, thin shell
•
ssls07b.dat – parabolic triangle, thin shell
Units SI
15-14
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
Finite Element Modeling Test 1 •
200 parabolic quadrilateral thin shell (CQUAD8) elements
•
661 grid points
Test 2 •
400 parabolic triangular thin shell (CTRIA6) elements
The meshes are shown in the following figure:
NX Nastran 8 Verification Manual
15-15
Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Boundary Conditions •
Axial displacement = 0 in. X = 0 section
•
Uniform axial load q = 10000 N/m
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Sstatics
Results Type
Point
Bench Value
Test Number
NX Nastran
s11(Pa)
Any
5.000E5
1
5.000E5
2
5.790E5
1
0
2
3.080E4
1
9.520E–6
2
9.560E–6
1
–7.140E-7
2
–7.330E–7
s22(Pa)
Any Any
ΔL(m) ΔR (m)
Any
0 9.520E–6 –7.140E–7
All results are averages.
Post Processing •
s11 is the stress of z at grid point 641 in coordinate system 2.
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NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
•
s22 is the stress of y at grid point 641 in coordinate system 2.
•
ΔR is the displacement of x at grid point 641 in coordinate system 2.
•
ΔL is the displacement of z at grid point 641 in coordinate system 2.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS07/89.
15.7 Hydrostatic Pressure on a Thin Wall Cylinder This test is a linear statics analysis of a thin cylinder loaded by hydrostatic pressure. It provides the input data and results for benchmark test SSLS08/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input File ssls08.dat
Units SI
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
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Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Finite Element Modeling •
200 parabolic quadrilateral thin shell (CQUAD8) elements
•
661 grid points
The mesh is shown in the following figure:
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NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
Boundary Conditions •
Restrain the grid points on side A (from grid point 21 to grid point 661) in the X translation and the Y and Z rotations.
•
Restrain the grid points on side B (from grid point 1 to grid point 641) in the Y translation and X and Z rotations.
•
Internal pressure p = p0 * Z/L with p0 = 20000 Pa.
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Type
Grid Point
Point
Bench Value
NX Nastran
s11(Pa)
321.0
Any
0
8.800E3
L/2s22 (Pa)
321.0
x = L/2
5.000E5
4.970E5
ΔR (m)
321.0
x = L/2
2.380E–6
2.380E–6
ΔL (m)
1.000
x=L
–2.860E–6
2.860E–6
Ψ (rad)
321.0
1.190E–6
1.190E–6
Ψ represents the rotation of a generator.
Post Processing •
s11is the stress of z at grid point 321 in coordinate system 2
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Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
•
s22 is the stress of y at grid point 321 in coordinate system 2
•
ΔR is the displacement of x at grid point 321 in coordinate system 2
•
ΔL is the displacement of z at grid point 1 in coordinate system 2
•
Ψ is the rotation of y at grid point 321 in coordinate system 2
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS08/89.
15.8 Gravity Loading on a Thin Wall Cylinder This test is a linear statics analysis of a thin cylinder loaded by its own weight. It provides the input data and results for benchmark test SSLS09/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
ssls09a.dat linear quadrilateral, thin shell
•
ssls09b.dat axisymmetric
Units SI
15-20
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
•
g = 7.85 x 104 N/m3
•
Mass = 8002 kg/m3
Finite Element Modeling Test 1 •
65 linear quadrilateral thin shell (CQUAD4) elements
•
84 grid points
Test 2 •
20 linear axisymmetric (CCONEAX) elements
•
21 grid points
The meshes are shown in the following figure:
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Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Boundary Conditions •
Axial displacement = 0 in. Z = 0 section.
•
Gravity loading; gravity acts in the Z direction.
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Type
Grid point
Point
Bench Value Test Number
NX Nastran
s22(Pa)
2.000
Any
0
1
–34.66
2
0
1
3.020E5
2
3.060E5
1
2.990E–6
2
2.990E–6
1
–4.390E–76
2
–4.480E–7
1
–1.120E–7
2
–1.120E–7
s11 (Pa)
2.000 1.000
Δz (m) ΔR (m) Ψ (rad)
2.000 10.00
x=0 x=L x=0 x–L
3.140E5 2.990E–6 –4.490E–7 1.120E–7
Post Processing Test 1 •
s11 is the stress of z at grid point 2 in coordinate system 2
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NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
•
s22is the stress of x at grid point 2 in coordinate system 2
•
Δz is the displacement of z at grid point 1 in coordinate system 2
•
ΔR is the displacement of x at grid point 2 in coordinate system 2
•
Ψ is the rotation of y at grid point 10 in coordinate system 2
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS09/89.
15.9 Pinched Cylindrical Shell This test is a linear statics analysis of a cylindrical shell with grid point forces, F, pinching as shown. It provides the input data and results for benchmark test SSLS20/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
ssls20a.dat linear triangle thin shells
•
ssls20b.dat linear quadrilateral thin shells
Units SI
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Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Material Properties •
E = 10.5 x 106 Pa
•
n = 0.3125
Finite Element Modeling Test 1 •
296 linear triangular thin shell (CTRIA3) elements
•
173 grid points
Test 2 •
140 linear quadrilateral thin shell (CQUAD4) elements
•
165 grid points
The meshes are shown in the following figure:
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Mechanical Structures — Linear Statics Analysis with Shell Elements
Boundary Conditions •
Free conditions To set free boundary conditions, use symmetry about XY, XZ, and YZ planes.
•
Grid point forces Fy = –25 N at point D
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Type
Point
Bench Value
Test Number NX Nastran
Disp. Y (Grid point 3) n(m)
D
–113.9E-3
1
–114.4E–3
2
–113.3E–3
Disp. Y (Grid point 3)
Post Processing •
n(m) is the displacement of y at grid point 3 (quadrilateral).
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS020/89.
15.10 Spherical Shell with a Hole This test is a linear statics analysis of a spherical shell with a hole with grid point forces. It provides the input data and results for benchmark test SSLS21/89 from Guide de validation des progiciels de calcul de structures.
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Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Test Case Data and Information Input Files •
ssls21a.dat – linear quadrilateral thing shells
•
ssls21b.dat – linear triangle thin shells
•
ssls21c – parabolic quadrilateral thin shells
Units SI
Material Properties •
E = 6.285 x 107 Pa
•
n = 0.3
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Mechanical Structures — Linear Statics Analysis with Shell Elements
Finite Element Modeling Test 1 •
100 linear quadrilateral thin shell (CQUAD4) elements
•
121 grid points
Test 2 •
200 linear triangular thin shell (CTRIA3) elements
•
121 grid points
Test 3 •
100 parabolic quadrilateral thin shell (CQUAD8) elements
•
441 grid points
The mesh is shown in the following figure:
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Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Boundary Conditions •
Free conditions To set free boundary conditions, use symmetry about XY and YZ planes.
•
Grid point forces F = 2 Newtons Due to the symmetric boundary conditions, only half of the load is applied.
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Result
Point
Bench Value
Test Number
NX Nastran
u (m) grid point 111
A(R,0,0)
9.400E–2
1
102.0E–3
Grid point 111
2
102.1E–3
Grid point 421
3
100.9E–3
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS021/89.
15.11 Bending Load on a Cylindrical Shell This test is a linear statics analysis of a cylindrical shell with bending and membrane effect. It provides the input data and results for benchmark test SSLS23/89 from Guide de validation des progiciels de calcul de structures.
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Mechanical Structures — Linear Statics Analysis with Shell Elements
Test Case Data and Information Input Files •
ssls23a.dat (Test 1, linear)
•
ssls23b.dat (Test 2, parabolic)
Units SI
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
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Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Finite Element Modeling Test 1 •
60 linear quadrilateral thin shell (CQUAD4) elements
•
78 grid points
Test 2 •
60 parabolic quadrilateral thin shell (CQUAD8) elements
•
215 grid points
The mesh is shown in the following figure:
Boundary Conditions •
AB side: Clamped in local system coordinates.
•
AD and BC sides: Restrain Z translation, qx and qy.
•
DC side: Set bending moment CZ to 1000 Nm/m. Set in plane force to 0.6E6 N/m.
•
ABCD surface: Set internal pressure to 0.6E06 N/m**2.
•
AD and DC sides are restrained in the global coordinate system.
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
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Mechanical Structures — Linear Statics Analysis with Shell Elements
Results Use coordinate system 3 (the cylindrical coordinate system) to display the results. Results are post-processed using the Shell surface middle option. Result
Point
Bench Value Test Number
Grid point 35
E
60.00 MPa
Grid point 93
NX Nastran
1
60.70
2
59.60
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS023/89.
15.12 Uniformly Distributed Load on a Simply-Supported Rectangular Plate This test is a linear statics analysis of a plate with pressure loading and simple supports. It provides the input data and results for benchmark test SSLS24/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
ssls24a.dat (Test 1, coarse mesh)
•
ssls24b.dat (Test 2, fine mesh)
•
ssls24c.dat (Test 3, very fine mesh)
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Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Units SI
Material Properties •
E = 1.0 x 107 Pa
•
n = 0.3
Finite Element Modeling Test 1 — a/b = 1 •
100 linear quadrilateral thin shell (CQUAD4) elements
•
121 grid points
Test 2 — a/b = 2 •
200 linear quadrilateral thin shell (CQUAD4) elements
•
231 grid points
Test 3 — a/b = 5 •
500 linear quadrilateral thin shell (CQUAD4) elements
•
561 grid points
The mesh is shown in the following figure:
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Mechanical Structures — Linear Statics Analysis with Shell Elements
Boundary Conditions Restraints •
All edges: w = 0
•
One corner fixed
Loads •
Set pressure = 1 N/m**2 in the –Z direction
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Result
a/b
Parameters
Bench Value
Test Number
NX Nastran
61z direction
1.000
1.000a
0.004440
1
0.004500
116z direction
2.000
2.000a
0.01110
2
0.01110
281z direction
5.000
5.000a
0.01417
3
0.01406
61x component top surface
1.000
1.000b
2874.
1
2867.
116x component top surface
2.000
2.000b
6102.
2
6034.
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Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Result
a/b
Parameters
Bench Value
Test Number
NX Nastran
281x component top surface
5.000
5.000b
7476.
3
7331.
Where: q = distributed load b = dimension t = thickness E = elastic modules b values of reference from the Guide de Validation are incorrect. The correct values are extracted from Formulas for Stress and Strain (Roark/Young). Note Note that the shell top surface corresponds to the side of the plate with negative global Z coordinates.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS024/89.
15.13 Uniformly Distributed Load on a Simply-Supported Rhomboid Plate This test is a linear statics analysis (three-dimensional problem) of a plate with pressure and transverse bending. It provides the input data and results for benchmark test SSLS25/89 from Guide de validation des progiciels de calcul de structures.
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Mechanical Structures — Linear Statics Analysis with Shell Elements
•
Thickness = 0.01 m
•
b = 1.0 m
•
a = 2.0 m
Test Case Data and Information Input Files •
ssls25a.dat (Test 1)
•
ssls25b.dat (Test 2)
Units SI
Material Properties •
E = 36.0 x 106 Pa
•
n = 0.3
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Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Finite Element Modeling •
a/b = 2
•
Linear quadratic thin shell (CQUAD4) elements
Test 1 •
q = 30°
Test 2 •
q = 45°
The mesh is shown in the following figure:
Boundary Conditions •
All edges: w = 0, one corner fixed
•
Pressure = 1 N/m2 in the –Z direction
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
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NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Shell Elements
Results Parameter a
Test Case
Bench Value
NX Nastran
Test 1
z displacement
116z displacement
ssls25a
–3.277E–3 m
–2.963E–3 m
Y stress
116y stress
–5.700E3 N/m2
–5.831E3 N/m2
Test 2
z displacement
116z displacement
ssls25b
–3.000E-3 m
–2.720E–3 m
Y stress
116Y stress
–5.390E3 N/m2
–5.441E3 N/m2
b a
b
Where: q = distributed load b = dimension t = thickness E = elastic modulus Values of reference from the Guide de validation are incorrect. The correct values are extracted from Formulas for Stress and Strain (Roark/Young), table 26, case number 14a.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS025/89.
15.14 Shear Loading on a Plate This test is a linear statics analysis of a thin plate with torque and shear loading. It provides the input data and results for benchmark test SSLS27/89 from Guide de validation des progiciels de calcul de structures.
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Chapter 15
Mechanical Structures — Linear Statics Analysis with Shell Elements
Test Case Data and Information Input Files •
ssls27a.dat (Test 1, Mindlin)
•
ssls27b.dat (Test 2, Kirchoff)
•
ssls27c.dat (Test 3, Mindlin)
Units SI
Material Properties •
E = 1.0 x 107 Pa
•
n = 0.25
Finite Element Modeling Test 1 — Mindlin •
6 linear quadrilateral thin shell (CQUAD4) elements
•
14 grid points
Test 2 — Kirchhoff •
6 linear quadrilateral thin shell (CQUAD4) elements
•
14 grid points
Test 3 — Mindlin •
48 linear quadrilateral thin shell (CQUAD4) elements
•
75 grid points
The meshes are shown in the following figure:
All tests are executed with mapped meshing
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Mechanical Structures — Linear Statics Analysis with Shell Elements
Boundary Conditions •
Clamp AD side
•
Point B: grid point force Fz = –1N
•
Point C: grid point force –Fz = 1N
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results at Location C Displacement at Grid point
Bench Value
Test Number
NX Nastran
14.00
3.537E–2
1
3.585E–2
14.00
3.537E–2
2
3.573E–2
75.00
3.537E–2
3
3.603E–2
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLS027/89.
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Chapter
16 Mechanical Structures — Linear Statics Analysis with Solid Elements
16.1 Solid Cylinder in Pure Tension This test is a linear statics analysis of a solid cylinder with tension-compression. It provides the input data and results for benchmark test SSLV01/89 from Guide de validation des progiciels de calcul de structures.
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Chapter 16
Mechanical Structures — Linear Statics Analysis with Solid Elements
Test Case Data and Information Input Files •
sslv01a.dat (Test 1)
•
sslv01b.dat (Test 2)
•
sslv01c.dat (Test 3)
•
sslv01d.dat (Test 4)
•
sslv01e.dat (Test 5)
•
sslv01f.dat (Test 6)
Units SI
Material Properties •
E = 2.0 x 1011 Pa
•
n = 0.30
16-2
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Solid Elements
Finite Element Modeling Test 1 •
155 parabolic tetrahedron (CTETRA) elements
•
342 grid points
Test 2 •
144 linear brick (CHEXA) elements & 48 linear solid wedge (CPENTA) elements
•
307 grid points
Test 3 (Results for this test will be provided in the NX Nastran 7 Verification Manual) •
48 linear quadrilateral axisymmetric solid elements
•
65 grid points
Test 4 (Results for this test will be provided in the NX Nastran 7 Verification Manual) •
96 linear triangular axisymmetric solid elements
•
65 grid points
Test 5 (Results for this test will be provided in the NX Nastran 7 Verification Manual) •
18 parabolic quadrilateral axisymmetric solid elements
•
95 grid points
Test 6 •
864 linear pyramid (CPYRAM) elements created by dividing each brick element in test 2 into 6 pyramid elements. 48 linear wedge (CPENTA) elements remain.
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Chapter 16
Mechanical Structures — Linear Statics Analysis with Solid Elements
The meshes are shown in the following figure:
16-4
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Solid Elements
Boundary Conditions •
Uniaxial deformation of the cylinder section
•
Set uniformly distributed force –F/A on the free end in the Z direction
•
F/A = 100 MPa
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results linear statics * axisymmetric data will be provided in version 7 Test Number
NX Nastran
1
1.500E–3
A & C 279
2
1.500E–3
A&C 1
3
*
A&C 4
4
*
A&C 1
5
*
Point Grid Point
Displacement Bench Value
A&C 6
u (m)
1.500E–3
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Chapter 16
Point Grid Point
Mechanical Structures — Linear Statics Analysis with Solid Elements
Displacement Bench Value
A & C 279
Test Number
NX Nastran
6
1.500E–3
1
1.500E–3
B
4
B
307
2
1.500E–3
B
53
3
*
B
3
4
*
B
39
5
*
B
307
6
1.500E–3
D
37
1
1.000E–3
D
189
2
1.000E–3
D
5
3
*
D
25
4
*
D
7
5
*
D
189
6
1.000E–3
E
41
1
0.500E–3
E
99
2
0.500E–3
E
9
3
*
E
29
4
*
E
13
5
*
E
99
6
0.500E–3
1
–0.150E–3
A & C 279
2
–0.150E–3
A&C 1
3
*
A&C 4
4
*
A&C 1
5
*
A & C 279
6
–0.1500E–3
1
–0.1500E–3
A&C 6
u (m)
u (m)
u (m)
w (m)
1.500E–3
1.000E-3
0.5000E-3
–0.1500E–3
D
37
D
189
2
–0.1500E–3
D
5
3
*
D
25
4
*
D
7
5
*
D
189
6
–0.1500E–3
E
41
1
–0.1500E–3
E
99
2
–0.1500E–3
E
9
3
*
E
29
4
*
16-6
w (m)
w (m)
NX Nastran 8 Verification Manual
–0.1500E-3
–0.1500E–3
Mechanical Structures — Linear Statics Analysis with Solid Elements
Point Grid Point
Displacement Bench Value
Test Number
NX Nastran
E
13
5
*
E
99
6
–0.1500E–3
Post Processing To view the results for Test 1 and Test 2, use coordinate system 2 (cylindrical). u is the radial displacement and w is the axial displacement.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLV01/89.
16.2 Internal Pressure on a Thick-Walled Spherical Container This test is a linear statics analysis of a thick sphere with internal pressure. It provides the input data and results for benchmark test SSLV03/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
sslv03a.dat (Test 1)
•
sslv03b.dat (Test 2)
•
sslv03c.dat (Test 3)
•
sslv03d.dat (Test 4)
•
sslv03e.dat (Test 5)
•
sslv03f.dat (Test 6)
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Chapter 16
Mechanical Structures — Linear Statics Analysis with Solid Elements
Units SI
Material Properties •
E = 2 x 105 Pa
•
n = 0.3
Finite Element Modeling Test 1 •
1600 linear brick (CHEXA) elements & linear solid wedge (CPENTA) elements
•
1898 grid points
Test 2 •
200 parabolic brick (CHEXA) elements & 50 solid wedge (CPENTA) elements
•
1256 grid points
Test 3 (Results for this test will be provided in the NX Nastran 7 Verification Manual) •
400 linear quadrilateral axisymmetric solid elements
•
451 grid points
Test 4 (Results for this test will be provided in the NX Nastran 7 Verification Manual) •
400 parabolic quadrilateral axisymmetric solid elements
•
1301 grid points
Test 5 •
Linear pyramid (CPYRAM) elements created by dividing each brick element in test 1 into 6 pyramid elements. Wedge (CPENTA) elements remain.
Test 6 •
16-8
Parabolic pyramid (CPYRAM) elements created by dividing each brick element in test 2 into 6 pyramid elements. Wedge (CPENTA) elements remain.
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Solid Elements
The meshes from these tests are shown in the following figure:
NX Nastran 8 Verification Manual
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Chapter 16
Mechanical Structures — Linear Statics Analysis with Solid Elements
Boundary Conditions •
The equivalent of the center of the sphere being fixed is modeled via symmetric boundary conditions.
•
Uniform radial pressure = 100 MPa.
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results * axisymmetric data will be provided in version 7 Point
Grid Displacement Point Stress
Bench Value
Test Number
NX Nastran
r=1 m
1
–100.0
1
–90.15
1
2
–97.29
451
3
*
451
4
*
1
5
–90.84
1
6
-103.8
1
72.09
1
16-10
srr (MPa)
sq (MPa)
NX Nastran 8 Verification Manual
71.43
Mechanical Structures — Linear Statics Analysis with Solid Elements
Point
Test Number
NX Nastran
1
2
77.23
451
3
*
451
4
*
1
5
72.06
1
6
73.30
1
0.4000E–3
1
2
0.4000E–3
451
3
*
451
4
*
1
5
0.3991E–3
1
6
0.4006E–3
Grid Displacement Point Stress
1
u (m)
Bench Value
0.4000E–3
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Chapter 16
Mechanical Structures — Linear Statics Analysis with Solid Elements
Point
Grid Displacement Point Stress
Bench Value
Test Number
NX Nastran
r=2 m
1826 srr (MPa)
0
1
–0.0280
2221
2
0.2240
411
3
*
411
4
*
1826
5
–0.2530
2221
6
–0.5259
1
21.18
2221
2
21.18
411
3
*
411
4
*
1826
5
21.40
2221
6
21.74
1
1.500E–4
2221
2
1.500E–4
411
3
*
411
4
*
1826
5
1.506E–4
2221
6
1.499E–4
1826 sq (MPa)
1826 u (m)
21.43
1.500E–4
All stress results are averaged. Use the spherical coordinate system for the stress results.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLV03/89.
16.3 Internal Pressure on a Thick-Walled Infinite Cylinder This test is a linear statics analysis of a thick cylinder with internal pressure. It provides the input data and results for benchmark test SSLV04/89 from Guide de validation des progiciels de calcul de structures.
16-12
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Solid Elements
Test Case Data and Information Input Files •
sslv04a.dat (Test 1)
•
sslv04b.dat (Test 2)
•
sslv04c.dat (Test 3)
•
sslv04d.dat (Test 4)
•
sslv04e.dat (Test 5)
•
sslv04f.dat (Test 6)
Units SI
Material Properties •
E = 2 x 105 mPa
•
n = 0.3
Finite Element Modeling Test 1 •
400 linear brick (CHEXA) elements
•
902 grid points
Test 2 •
240 parabolic brick (CHEXA) elements
•
1873 grid points
NX Nastran 8 Verification Manual
16-13
Chapter 16
Mechanical Structures — Linear Statics Analysis with Solid Elements
Test 3 •
600 linear quadrilateral axisymmetric solid elements
•
656 grid points
Test 4 •
600 parabolic quadrilateral axisymmetric solid elements
•
1911 grid points
Test 5 •
Linear pyramid (CPYRAM) elements created by dividing each brick element in test 1 into 6 pyramid elements.
Test 6 •
Parabolic pyramid (CPYRAM) elements created by dividing each brick element in test 2 into 6 pyramid elements.
The brick meshes are shown in the following figure:
16-14
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Solid Elements
Boundary Conditions •
Unlimited cylinder
•
Internal pressure p = 60 MPa
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results All results are averaged. Test Case Grid Point
Displacement / Stress sr
Bench Value NX Nastran
sslv04a
411
sslv04b
977
–60.00
sslv04c
616
*
sslv04d
1831
*
sslv04e
411
–57.30
sslv04f
977
–60.74
sslv04a
411
sslv04b
977
102.0
sslv04c
616
*
sslv04d
1831
*
sslv04e
411
99.68
sslv04f
977
100.9
sslv04a
411
sslv04b
977
81.00
sslv04c
616
*
sslv04d
1831
*
sq
tmax
–60.00 (MPa)
100.0 (MPa)
80.00 (MPa)
–57.00
99.70
79.34
NX Nastran 8 Verification Manual
16-15
Mechanical Structures — Linear Statics Analysis with Solid Elements
Chapter 16
Test Case Grid Point
Displacement / Stress
Bench Value NX Nastran
sslv04e
411
80.82
sslv04f
977
80.82
sslv04a
411
sslv04b
977
59.00E–6
sslv04c
616
*
sslv04d
1831
*
sslv04e
411
58.85E–6
sslv04f
977
59.00E–6
sslv04a
451
ur
sr
59.00E–6 (m)
0 (MPa)
59.00E–6
–0.006500
sslv04b
–0.04480
sslv04c
*
sslv04d
*
sslv04e
–0.1563
sslv04f
–0.1900
sslv04a
sq
40.00 (MPa)
39.66
sslv04b
40.39
sslv04c
*
sslv04d
*
sslv04e
39.84
sslv04f
40.16
sslv04a
tmax
20.00 (MPa)
20.08
sslv04b
20.17
sslv04c
20.07
sslv04d
19.99
sslv04e
20.10
sslv04f
20.17
sslv04a
ur
40.00E–6 (m)
40.00E–6
sslv04b
40.00E–6
sslv04c
*
sslv04d
*
sslv04e
39.93E–6
sslv04f
40.00E–6
16-16
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Solid Elements
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLV04/89.
16.4 Prismatic Rod in Pure Bending This test is a linear statics analysis of a solid rod with bending. It provides the input data and results for benchmark test SSLV08/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
sslv08a.dat (Test 1)
•
sslv08b.dat (Test 2)
•
sslv08c.dat (Test 3)
•
sslv08d.dat (Test 4)
•
sslv08e.dat (Test 5)
•
sslv08f.dat (Test 6)
Units SI
NX Nastran 8 Verification Manual
16-17
Chapter 16
Mechanical Structures — Linear Statics Analysis with Solid Elements
Material Properties •
E = 2 x 105 MPa
•
n = 0.3
16-18
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Solid Elements
Finite Element Modeling Test 1 •
198 linear solid tetrahedral (CTETRA) elements
•
76 grid points
Test 2 •
198 parabolic solid tetrahedral (CTETRA) elements
•
409 grid points
Test 3 •
48 linear brick (CHEXA) elements
•
117 grid points
Test 4 — Mapped meshing •
48 parabolic brick (CHEXA) elements
•
381 grid points
Test 5 •
288 linear pyramid (CPYRAM) elements created by dividing each brick element in test 3 into 6 pyramid elements.
Test 6 •
288 parabolic pyramid (CPYRAM) elements created by dividing each brick element in test 4 into 6 pyramid elements.
The meshes from these tests are shown in the following figure:
NX Nastran 8 Verification Manual
16-19
Chapter 16
Mechanical Structures — Linear Statics Analysis with Solid Elements
Boundary Conditions •
Clamp Point B.
•
Other points of B section: Set Z-displacement to 0. NOTE: In these tests some grid points of section B are also restrained in the x direction about the x-axis at the free end of the rod.
•
Set moment Mx equal to (4/3)E+7 N.m
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Test #
Point
Grid Point
1
F or G
5
Displacement Stress szz
Bench Value
NX Nastran
–10.00E6 (Pa)
–4.268E6
2
5
–10.03E6
3
75
–10.00E6
4
245
–9.995E6
5
75
–7.929E6
6
245
–9.992E6
1
A
26
uA
4.000E–4 (m)
2.964E–4
2
90
4.000E–4
3
77
4.000E–4
4
251
4.000E–4
16-20
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Solid Elements
Test #
Point
Grid Point
Displacement Stress
Bench Value
NX Nastran
5
77
3.443E–4
6
251
4.000E–4
1
H
19
wB
2.000E–4 (m)
2.000E–4
2
40
2.000E–4
3
76
2.000E–4
4
249
2.000E–4
5
76
1.721E–4
6
249
2.000E–4
1
F or G
5
vF = -vG
0.1500E-4 (m)
0.07450E–4
2
5
0.1508E–4
3
75
0.1500E–4
4
245
0.1503E–4
5
75
0.1005E–4
6
245
0.1503E–4
1
D or E
8
vD = -vE
-0.1500E-4 (m)
–6.262E–4
2
8
–0.1505E–4
3
73
–0.1500E–4
4
241
–0.1503E–4
5
73
–0.1005E–4
6
241
–0.1503E–4
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLV08/89.
16.5 Thick Plate Clamped at Edges This test is a linear statics analysis of a thick plate with pressure and transverse bending. It provides the input data and results for benchmark test SSLV09/89 from Guide de validation des progiciels de calcul de structures.
NX Nastran 8 Verification Manual
16-21
Chapter 16
Mechanical Structures — Linear Statics Analysis with Solid Elements
Test Case Data and Information Input Files •
sslv09a.dat (Test 1)
•
sslv09b.dat (Test 2)
•
sslv09c.dat (Test 3)
Units SI
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
16-22
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Solid Elements
Finite Element Modeling Test 1 •
25 parabolic linear brick (CHEXA) elements
•
228 grid points
•
l =10, 20, 50, 75, 100
Test 2 •
25 linear quadrilateral thin shell (CQUAD4) elements
•
36 grid points
•
l =10, 20, 50, 75, 100
Test 3 •
150 linear pyramid solid (CPYRAM) elements created by dividing each brick element in test 1 into 6 pyramid elements
Test 2 is done using CQUAD4 elements with the thicknesses specified in the physical property table. The meshes from these tests are shown in the following figure:
NX Nastran 8 Verification Manual
16-23
Chapter 16
Mechanical Structures — Linear Statics Analysis with Solid Elements
Boundary Conditions •
AB and AD sides: clamped
•
BC and DC sides: symmetry
•
Load case 1: Pressure p = 1E06 Pascals in –Z direction
•
Load case 2: Point C Grid Point force F = 1E06 N in –Z direction
The boundary conditions are shown in the following figure:
Solution Type SOL 101 Linear statics
16-24
NX Nastran 8 Verification Manual
Mechanical Structures — Linear Statics Analysis with Solid Elements
Results Test Case 1 (z displacement at location C) Part Name
Load Case
Grid Point
Analytical
Reference FEM
NX Nastran
10
Pressure
242
–0.6552E-4
–0.7620E–4
–0.7379E–4
Force
242
–0.2915E-3
–0.4300E–3
–0.3684E–3
Pressure
1242
–0.5242E-3
–0.5383E–3
–0.5266E–3
Force
1242
–0.2332E–2
–0.2535E–2
–0.2456E–2
Pressure
2242
–0.8190E–2
–0.8029E–2
–0.7935E–2
Force
2242
–0.3643E–1
–0.3574E–1
–0.3602E–1
Pressure
3242
–0.2764E–1
–0.2690E–1
–0.2666E-1
Force
3242
–0.1230
–0.1184
–0.1206
Pressure
4242
–0.6552E–1
–0.6339E–1
–0.6305E–1
Force
4242
–0.2915
–0.2779
–0.2849
20
50
75
100
Test Case 2 (z displacement at location C) Part Name
Load Case
Grid Point
Analytical
Reference FEM
NX Nastran
10
Pressure
1
–0.6552E–4
–0.7866E–4
–0.8131E–4
Force
1
–0.2915E–3
–0.4109E–3
–0.4050E–3
20
Pressure
36
–0.5242E–3
–0.5557E–3
–0.5775E–3
Force
36
–0.2332E–2
–0.2595E–2
–0.2668E–2
50
Pressure
36
–0.8190E–2
–0.8348E–2
–0.8669E–2
Force
36
–0.3643E–1
–0.3745E–1
–0.3878E–1
75
100
Pressure
36
–0.2764E–1
–0.2805E–1
–0.2906E–1
Force
36
–0.1230
–0.1253
–0.1292
Pressure
36
–0.6552E–1
–0.6639E–1
–0.6864E–1
Force
36
–0.2915
-0.2958
–0.3042
Test Case 3 (z displacement at location C) Part Name
Load Case
Grid Point
Analytical
Reference FEM
NX Nastran
10
Pressure
242
–0.6552E-4
–0.7620E–4
–0.7491E–4
Force
242
–0.2915E-3
–0.4300E–3
–0.3736E–3
Pressure
1242
–0.5242E-3
–0.5383E–3
–0.5342E–3
Force
1242
–0.2332E–2
–0.2535E–2
–0.2458E–2
Pressure
2242
–0.8190E–2
–0.8029E–2
–0.7875E–2
Force
2242
–0.3643E–1
–0.3574E–1
–0.3470E–1
Pressure
3242
–0.2764E–1
–0.2690E–1
–0.2605E-1
Force
3242
–0.1230
–0.1184
–0.1135
20
50
75
NX Nastran 8 Verification Manual
16-25
Chapter 16
Part Name 100
Mechanical Structures — Linear Statics Analysis with Solid Elements
Load Case
Grid Point
Analytical
Reference FEM
NX Nastran
Pressure
4242
–0.6552E–1
–0.6339E–1
–0.6068E–1
Force
4242
–0.2915
–0.2779
–0.2627
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SSLV09/89.
16-26
NX Nastran 8 Verification Manual
Chapter
17 Mechanical Structures — Normal Mode Dynamics Analysis
17.1 Lumped Mass-Spring System This test is a normal mode dynamics analysis of an elastic link with lumped mass. It provides the input data and results for benchmark test SDLD02/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input File sdld02.dat
Units SI
Material Properties Spring constant
NX Nastran 8 Verification Manual
17-1
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Finite Element Modeling •
8 lumped mass (CONM2) elements
•
9 spring (CBUSH) elements
•
8 grid points
The mesh is shown in the following figure:
Boundary Conditions •
Clamp points A and B
•
Other points: n=0;q=0
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Modes
17-2
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Results Frequency Results (Hz) Normal Mode
Bench Value
NX Nastran
1
5.527
5.527
2
10.89
10.89
3
15.92
15.92
4
20.46
20.46
5
24.38
24.38
6
27.57
27.57
7
29.91
29.91
8
31.35
31.35
Mode Shapes Results The mode shapes results are exact. The multiplication coefficient is 3.162. Normal Mode
Point
Bench Value
NX Nastran
1
P1
0.1612
0.05100
P2
0.3030
0.09580
P3
0.4082
0.1291
P4
0.4642
0.1468
P5
0.4642
0.1468
P6
0.4082
0.1291
P7
0.3030
0.09580
P8
0.1612
0.05100
P1
0.1612
0.05100
P2
–0.3030
–0.09580
P3
0.4082
0.1291
P4
–0.4642
–0.1468
P5
0.4642
0.1468
P6
–0.4082
–0.1291
P7
0.3030
0.09580
P8
–0.1612
–0.05100
8
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLD02/89, p. 178.
NX Nastran 8 Verification Manual
17-3
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
17.2 Short Beam on Simple Supports This test is a modal analysis of a straight short beam with simple supports both inline and offset. It provides the input data and results for benchmark test SDLL01/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
sdll01a.dat (Test 1)
•
sdll01b.dat (Test 2)
Units SI
Material Properties •
E = 2 x 101111 Pa
•
n = 0.3
•
r = 7800 kg/m3
17-4
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Finite Element Modeling •
10 linear beam (CBAR) elements
•
11 grid points
The meshes are shown in the following figure:
NX Nastran 8 Verification Manual
17-5
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Boundary Conditions Problem 1 •
Point A (grid point 1): Constrain in all directions, except the Z rotation.
•
Point B (grid point 2): Constrain in the Y and Z translations and X and Y rotations.
•
All other grid points (3-11): Constrain in the Z translation and X and Y rotations.
•
No load case.
Problem 2 •
Point C (grid point 1): Constrain in all directions, except the Z rotation.
•
Point D (grid point 2): Constrain in the Y and Z translations and X and Y rotations.
•
All other grid points (3-11): Constrain in the Z translation and X and Y rotations.
•
No load case.
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Modes
17-6
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Results Problem 1: Frequency results (Hz) Normal Mode
Bench Value
NX Nastran
Bending 1
431.6
437.2
Tension 1
1266.
1265.
Bending 2
1498.
1539.
Bending 3
2871.
2925.
Tension 2
3798.
3763.
Bending 4
4378.
4328.
Problem 2: Frequency results (Hz) Mode Number
Bench Value
NX Nastran
1
392.8
398.5
2
902.2
927.3
3
1592.
1666.
4
2629.
2815.
5
3126.
3266.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLL01/89.
17.3 Axial Loading on a Rod This test is a modal analysis of a simply-supported beam with stress stiffening. It provides the input data and results for benchmark test SDLL05/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
sdll05a.dat
•
sdll05b.dat
NX Nastran 8 Verification Manual
17-7
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Units SI
Material Properties •
E = 2 x 1011 Pa
•
r = 7800 kg/m3
Finite Element Modeling •
10 linear beam (CBAR) elements
•
11 grid points
The mesh is shown in the following figure:
17-8
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Boundary Conditions •
Points A: u = v = 0
•
Points B: v = 0
•
Load case 2 (grid point 2): Fx = 1E05N in –X direction
•
Stress stiffening on
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Modes
Results Frequency results (Hz) Load Case
Normal Mode
Bench Value
NX Nastran
1
Bending 1
28.70
28.68
Bending 2
114.8
114.4
Bending 1
22.43
22.40
Bending 2
109.1
108.7
2
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLL05/89.
NX Nastran 8 Verification Manual
17-9
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
17.4 Cantilever Beam with a Variable Rectangular Section This test is a modal analysis of a straight cantilever beam with a variable section. It provides the input data and results for benchmark test SDLL09/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
sdll09a.dat
•
sdll09b.dat
Units SI
Material Properties •
E = 2 x 1011 Pa
•
r = 7800 kg/m3
17-10
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Finite Element Modeling •
10 tapered beam (CBEAM) elements
•
11 grid points
The mesh is shown in the following figure:
Boundary Conditions •
Clamp point A
•
No load case
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Modes
Results Frequency results (Hz) b
Normal Mode
Bench Value
NX Nastran
4
1
54.18
54.24
2
171.9
172.4
NX Nastran 8 Verification Manual
17-11
Chapter 17
b
5
Mechanical Structures — Normal Mode Dynamics Analysis
Normal Mode
Bench Value
NX Nastran
3
384.4
384.9
4
697.2
695.4
5
1112.
1104.
1
56.55
56.59
2
175.8
176.3
3
389.0
389.5
4
702.4
700.6
5
1118.
1109.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLL09/89.
17.5 Thin Circular Ring This test is a modal analysis of a thin curved beam. It provides the input data and results for benchmark test SDLL11/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input File sdll11.dat
Units SI
17-12
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Material Properties •
E = 7.2 x 1010 Pa
•
n = 0.3
•
r = 2700 kg/m3
Finite Element Modeling •
36 linear beam (CBAR) elements
•
36 grid points
The mesh is shown in the following figure:
NX Nastran 8 Verification Manual
17-13
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Boundary Conditions •
Free conditions
•
Create one constraint set (kinematic DOF) to fully constrain the three grid points shown below (grid points 7, 21, 30).
•
No load case
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Modes
Results Frequency results (Hz) Normal Mode
Bench Value
NX Nastran
ADS #
Plane mode 1,2,3
0
0
1.000, 2.000, 3.000
Plane mode 4,5
318.4
319.0
7.000, 8.000
Plane mode 6,7
900.5
900.9
11.00, 12.00
Plane mode 8,9
1727.
1724.
15.00, 16.00
Plane mode 10,11
2792.
2781.
17.00, 18.00
Transverse Mode 1,2,3
0
0
4.000, 5.000, 6.000
Transverse Mode 4,5
511.0
511.0
9.000, 10.00
Transverse Mode 6,7
1590.
1585.
13.00, 14.00
Transverse Mode 8,9
3184.
3159.
19.00, 20.00
17-14
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLL11/89.
17.6 Thin Circular Ring Clamped at Two Points This test is a modal analysis of a thin curved beam. It provides the input data and results for benchmark test SDLL12/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input File sdll12.dat
Units SI
Material Properties •
E = 7.2 x 1010 Pa
•
n = 0.3
•
r = 2700 kg/m3
NX Nastran 8 Verification Manual
17-15
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Finite Element Modeling •
29 linear beam (CBAR) elements
•
29 grid points
The mesh is shown in the following figure:
17-16
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Boundary Conditions •
Points A and B: Clamped in local coordinate system
•
No load case
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Modes
Results Frequency results (Hz) Normal Mode
Bench Value
NX Nastran
1
235.3
235.9
2
575.3
575.2
3
1106.
1103.
4
1406.
1399.
5
1751.
1743.
6
2557.
2536.
7
2802.
2723.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLL12/89.
NX Nastran 8 Verification Manual
17-17
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
17.7 Vibration Modes of a Thin Pipe Elbow This test is a modal analysis of a straight cantilever beam, and a thin curved beam. It provides the input data and results for benchmark test SDLL14/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
sdll14a.dat (test 1, L=0)
•
sdll14b.dat (test 2, L=0.6)
•
sdll14c.dat (test 3, L=2.0)
Units SI
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
•
r = 7800 kg/m3
17-18
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Finite Element Modeling •
L = 0 or L = 0.6: 18 linear beam (CBAR) elements 19 grid points
•
L = 2: 28 linear beam (CBAR) elements 29 grid points
Two of the meshes are shown in the following figure:
NX Nastran 8 Verification Manual
17-19
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Boundary Conditions •
Clamp points C and D
•
Point A: v = 0; w = 0
•
Point B: u = 0; w = 0
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Modes
Results Frequency results (Hz) L
Normal Mode
Bench Value
NX Nastran
ADS#
0
Transverse 1
44.23
44.07
1.000
Plane 1
119.0
119.2
2.000
Transverse 2
125.0
125.4
3.000
Plane 2
227.0
225.0
4.000
Transverse 1
33.40
33.15
1.000
Plane 1
94.00
94.42
2.000
Transverse 2
100.0
98.50
3.000
Plane 2
180.0
183.7
4.000
Transverse 1
17.90
17.65
1.000
Plane 1
24.80
24.40
3.000
0.6000
2.000
17-20
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
L
Normal Mode
Bench Value
NX Nastran
ADS#
Transverse 2
25.30
24.94
2.000
Plane 2
27.00
26.67
4.000
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLL14/89.
17.8 Cantilever Beam with Eccentric Lumped Mass This test is a modal analysis of a straight cantilever beam and a lumped mass. It provides the input data and results for benchmark test SDLL15/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
sdll15a.dat
•
sdll15b.dat
Units SI
NX Nastran 8 Verification Manual
17-21
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Material Properties •
E = 2.1 x 1011 Pa
•
r = 7800 kg/m3
Finite Element Modeling Test 1: •
10 linear beam (CBEAM) elements
•
1 rigid (RBAR) element from point B to point C
•
1 lumped mass (CONM2) element at point C
•
11 grid points
Test 2: •
10 linear beam (CBAR) elements
•
1 rigid (RBAR) element from point B to point C
•
1 lumped mass (CONM2) element at point C
•
11 grid points
The mesh both tests is is shown in the following figure:
Boundary Conditions •
Clamp point A
The boundary conditions are shown in the following figure:
17-22
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Solution Type SOL 103 normal mode dynamics — SVI
Results Frequency results (Hz) yc
Normal Mode
Bench Value
NX Nastran
0
Transverse 1,2
1.650
1.650
Transverse 3,4
16.07
15.88
Transverse 5,6
50.02
48.64
Tension 1
76.47
76.42
Torsion 1
80.47
80.68
Transverse 7,8
103.2
97.89
1
1.636
1.633
2
1.642
1.638
3
13.46
13.36
4
13.59
13.59
5
28.90
29.20
6
31.96
31.57
7
61.61
59.85
8
63.93
61.72
1
Mode shapes results yc
Normal Mode
Modal Displacement
Bench Value
NX Nastran
1
1
wc/wb
1.030
1.030
2
uc/vb
0.1480
–0.1480
3
uc/vb
2.882
–2.904
4
wc/wb
–0.9220
–0.9800
•
wc = z displacement at point C
•
wb = z displacement at point B
•
uc = x displacement at point C
•
vb = y displacement at point B
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLL15/89.
NX Nastran 8 Verification Manual
17-23
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
17.9 Thin Square Plate (Clamped or Free) This test is a normal mode dynamics analysis (three-dimensional problem) of a thin plate. It provides the input data and results for benchmark test SDLS01/89 from Guide de validation des progiciels de calcul de structures.
Test Case Data and Information Input Files •
sdls01a.dat
•
sdls01b.dat
Units SI
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
•
r = 7800 kg/m3
17-24
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Finite Element Modeling •
100 linear quadrilateral thin shell (CQUAD4) elements
•
121 grid points
The mesh is shown in the following figure:
Boundary Conditions •
Problem 1: AB side clamped
•
Problem 2: Free plate; 1 kinematic DOF set (grid points 1, 11, 111)
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Modes
NX Nastran 8 Verification Manual
17-25
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Results Problem 1: Frequency results (Hz) Normal Mode
Bench Value
NX Nastran
1
8.727
8.638
2
21.30
20.89
3
53.55
52.42
4
68.30
65.77
5
77.74
75.14
6
136.0
127.8
Problem 2: Frequency results (Hz) Normal Mode
Bench Value
NX Nastran
7
33.71
32.91
8
49.46
47.42
9
61.05
59.19
10,11
87.52
83.08
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLS01/89..
17.10 Simply-Supported Rectangular Plate This test is a normal mode dynamics analysis (three-dimensional problem) of a thin plate. It provides the input data and results for benchmark test SDLS03/89 from Guide de validation des progiciels de calcul de structures.
17-26
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Test Case Data and Information Input Files sdls03.dat
Units SI
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
•
r = 7800 kg/m3
Finite Element Modeling •
150 linear quadrilateral thin shell (CQUAD4) elements
•
176 grid points
The mesh is shown in the following figure:
NX Nastran 8 Verification Manual
17-27
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Boundary Conditions •
Z-displacement = 0 on all sides of the plate
•
One DOF set
•
No load case
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Mode Dynamics
Results Frequency results (Hz) Normal Mode
Bench Value
NX Nastran
1
35.63
35.27
2
68.51
67.29
3
109.6
108.5
4
123.3
120.8
5
142.5
138.2
6
197.3
188.2
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLS03/89.
17.11 Thin Ring Plate Clamped on a Hub This test is a normal mode dynamics analysis (three-dimensional problem) of a thin plate. It provides the input data and results for benchmark test SDLS04/89 from Guide de validation des progiciels de calcul de structures.
17-28
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
•
Re = 0.1 m
•
Ri = 0.2 m
•
Thickness = .001 m
Test Case Data and Information Input Files sdls04.dat
Units SI
Material Properties •
E = 2 x 1011 Pa
•
n = 0.3
•
r = 7800 kg/m3
NX Nastran 8 Verification Manual
17-29
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Finite Element Modeling •
400 linear quadrilateral thin shell (CQUAD4) elements
•
440 grid points
The mesh is shown in the following figure:
Boundary Conditions •
If r = Ri: Clamp in local coordinate system.
•
No load case.
The boundary conditions are shown in the following figure:
17-30
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Solution Type SOL 103 — Normal Modes
Results Frequency results (Hz) Normal Mode
Bench Value
NX Nastran
1
79.26
79.22
2,3
81.09
80.72
4,5
89.63
88.83
6,7
112.8
111.3
8,9
Not available
152.7
10,11
Not available
212.9
12,13
Not available
290.1
14,15
Not available
382.9
16,17
Not available
490.3
18
518.9
510.9
19,20
528.6
519.7
21,22
559.1
546.2
23
609.7
590.3
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLS04/89.
17.12 Vane of a Compressor - Clamped-free Thin Shell This test is a normal mode dynamics analysis (three-dimensional problem) of a cylindrical thin shell. It provides the input data and results for benchmark test SDLS05/89 from Guide de validation des progiciels de calcul de structures.
NX Nastran 8 Verification Manual
17-31
Chapter 17
•
Mechanical Structures — Normal Mode Dynamics Analysis
a = 0.5 rad
•
AD = L = 0.3048m
•
r = 2L = 0.6096m
•
thickness = 3.048 x 10–3 m
Test Case Data and Information Input Files •
sdls05a.dat (coarse mesh)
•
sdls05b.dat (fine mesh)
Units SI
Material Properties •
E = 2.0685 x 1011 Pa
•
n = 0.3
•
r = 7857.2 kg/m3
17-32
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Finite Element Modeling — Coarse Mesh •
100 linear quadrilateral thin shell (CQUAD4) elements
•
121 grid points
The coarse mesh is shown in the following figure:
Finite Element Modeling — Fine Mesh •
225 linear quadrilateral thin shell (CQUAD4) elements
•
256 grid points
The fine mesh is shown in the following figure:
NX Nastran 8 Verification Manual
17-33
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Boundary Conditions •
AD side: Clamped in local coordinate system.
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Modes
Results Frequency results (Hz) Normal Mode
Bench Value
NX Nastran coarse mesh
NX Nastran fine mesh
1
85.60
84.60
85.30
2
134.5
137.1
137.8
3
259.0
240.7
243.9
4
351.0
333.3
338.1
5
395.0
370.0
378.3
6
531.0
503.7
515.4
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLS05/89.
17.13 Bending of a Symmetric Truss This test is a normal mode dynamics analysis (plane problem) of a straight cantilever beam structure. It provides the input data and results for benchmark test SDLX01/89 from Guide de validation des progiciels de calcul de structures.
17-34
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
•
h = 0.0048 m
•
b = 0.029 m
•
A = 1.392 x 10–4 m2
•
Iz = 2.673 x 10–10 m4
Test Case Data and Information Input File sdlx01.dat
Units SI
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
•
r = 7800 kg/m3
NX Nastran 8 Verification Manual
17-35
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Finite Element Modeling •
24 linear beam (CBAR) elements
•
24 grid points
The mesh is shown in the following figure:
Boundary Conditions •
Clamp points A and B
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Modes
17-36
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Results Frequency results (Hz) Normal Mode
Bench Value
NX Nastran
1
8.800
8.769
2
29.40
29.34
3
43.80
43.82
4
56.30
56.25
5
96.20
95.43
6
102.6
102.5
7
147.1
146.2
8
174.8
173.1
9
178.8
177.4
10
206.0
202.9
11
266.4
262.4
12
320.0
309.7
13
335.0
321.9
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLX01/89.
17.14 Hovgaard’s Problem — Pipes with Flexible Elbows This test is a normal mode dynamics analysis (three-dimensional problem) of a straight cantilever beam structure. It provides the input data and results for benchmark test SDLX02/89 from Guide de validation des progiciels de calcul de structures.
NX Nastran 8 Verification Manual
17-37
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
•
A = 0.3439 x 10E–2 m2
•
R = 0.922 m
•
e = 0.00612 m
•
Re = 0.0925 m
•
Ri = 0.08638 m
•
Iy = Iz = 0.1377x10–4 m4 (straight elements)
•
Iy = Iz = 0.5887x10–5 m4 (curved elements)
Test Case Data and Information Input Files sdlx02.dat
Units SI
Material Properties •
E = 1.658 x 1011 Pa
•
n = 0.3
•
r = 13404.106 kg/m3
17-38
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Finite Element Modeling •
25 linear beam (CBAR) elements
•
26 grid points
The mesh is shown in the following figure:
Boundary Conditions •
Clamp points A and B
The boundary conditions are shown in the following figure:
NX Nastran 8 Verification Manual
17-39
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Solution Type SOL 103 — Normal Modes
Results Frequency results (Hz) Normal Mode
Bench Value
NX Nastran
1
10.18
10.39
2
19.54
19.85
3
25.47
25.32
4
48.09
47.74
5
52.86
51.78
6
75.94
83.00
7
80.11
85.12
8
122.3
125.8
9
123.2
127.7
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLX02/89.
17.15 Rectangular Plates This test is a normal mode dynamics analysis (three dimensional problem) of a thin plate with rigid body modes. It provides the input data and results for benchmark test SDLX03/89 from Guide de validation des progiciels de calcul de structures.
17-40
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis
Test Case Data and Information Input Files sdlx03.dat
Units SI
Material Properties •
E = 2.1 x 1011 Pa
•
n = 0.3
•
r = 7800 kg / m3
Finite Element Modeling •
300 linear quadrilateral thin shell (CQUAD4) elements
•
320 grid points
The mesh is shown in the following figure:
NX Nastran 8 Verification Manual
17-41
Chapter 17
Mechanical Structures — Normal Mode Dynamics Analysis
Boundary Conditions •
Free plate
•
One DOF set
The boundary conditions are shown in the following figure:
Solution Type SOL 103 — Normal Mode Dynamics
Results Frequency results (Hz) Normal Mode
Bench Value
NX Nastran
1
584.0
577.0
2
826.0
813.0
3
855.0
844.0
4
911.0
895.0
5
1113.
1062.
6
1136.
1118.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLX03/89.
17-42
NX Nastran 8 Verification Manual
Chapter
18 Mechanical Structures — Normal Mode Dynamics Analysis and Model Response
18.1 Transient Response of a Spring-Mass System with Acceleration Loading This test is an undamped transient response by modal superposition. It provides the input data and results for benchmark test SDLD04/89 from Guide de validation des progiciels de calcul de structures.
Where: •
m = 1 kg
•
k = 1000 N/m
Test Case Data and Information Input Files sdld04.dat
Units SI
NX Nastran 8 Verification Manual
18-1
Chapter 18
Mechanical Structures — Normal Mode Dynamics Analysis and Model Response
Material Properties Spring constant.
Finite Element Modeling •
3 lumped mass (CONM) elements
•
3 translational spring (CELAS) elements
The mesh is shown in the following figure:
Boundary Conditions •
Points A: Clamped (u = v = 0 : q - 0)
•
Points B, C and D: v = 0 ; = 0
•
Point A: Set acceleration: u(t) ˝ = 2E5 * (t2) ; (0 < t < 0.1 s)
•
Initial condition: u(0) = 0 ; u(0) = 0 at every point
The mesh and the boundary conditions are shown in the following figure:
Solution Type SOL 112 — Modal Transient Response
Results The mode shapes results are exact. Frequency results (Hz) Normal Mode
Bench Value
NX Nastran
1
2.239
2.239
18-2
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis and Model Response
Normal Mode
Bench Value
NX Nastran
2
6.275
6.275
3
9.069
9.069
Mode shapes results Normal Mode
Point
Bench Value
NX Nastran
1
B
0.4450
0.4450
C
0.8019
0.8019
D
1.000
1.000
B
1.000
1.000
C
0.4450
0.4450
D
–0.8019
–0.8019
B
–0.8019
–0.8019
C
1.000
1.000
D
–0.4450
–0.4450
2
Transient response (Point D: X-displacement in meters) Time (sec)
Bench Value
NX Nastran
0.02000
–0.002700
–0.002670
0.04000
–0.04260
–0.04270
0.05000
–0.1041
–0.1041
0.06000
–0.2158
–0.2160
0.08000
–0.6813
–0.6818
0.1000
–1.658
–1.659
NX Nastran 8 Verification Manual
18-3
Chapter 18
Mechanical Structures — Normal Mode Dynamics Analysis and Model Response
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLD04/89.
18.2 Transient Response of a Clamped-free Post This test is a transient response of a straight cantilever beam with acceleration and force loadings, and modal damping. It provides the input data and results for benchmark test SDLL06/89 from "Guide de validation des progiciels de calcul de structures."
18-4
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis and Model Response
Test Case Data and Information Input Files sdll06.dat
Units SI
Material Properties •
E = 4 x 1010 Pa
•
Iz = 3.285 x 10–1 m4
•
r=0
Finite Element Modeling •
8 linear beam (CBAR) elements
•
9 grid points
The mesh is shown in the following figure:
NX Nastran 8 Verification Manual
18-5
Chapter 18
Mechanical Structures — Normal Mode Dynamics Analysis and Model Response
Boundary Conditions To apply an acceleration üA(t) at point A, we can do the following: •
Points A: Clamped (u = v = 0 : q - 0)
•
Point B: Set nodal force Fx(t) equal to mB * üA(t) in the -X direction Fx(t) = –m * üA(t)
•
Initial conditions: u(0) = 0 ; u (0) = 0 at every point
The mesh and the boundary conditions are shown in the following figure:
18-6
NX Nastran 8 Verification Manual
Mechanical Structures — Normal Mode Dynamics Analysis and Model Response
Solution Type SOL 109 — Direct Transient Response
Results uB displacement (mm) Time (s)
Bench Value
NX Nastran
0.01000
–0.06500
–0.06570
0.02000
–0.5130
–0.5152
0.03000
–1.679
–1.682
0.04000
–3.457
–3.464
0.05000
–5.316
–5.333
0.06000
–6.764
–6.804
0.07000
–7.609
–7.682
0.08000
–7.774
–7.891
0.09000
–7.244
–7.413
0.1000
–6.068
–6.289
0.1200
–2.242
–2.542
0.1400
2.367
2.070
0.1600
6.149
5.977
0.1800
7.783
7.847
0.2000
6.698
7.042
The problem with damping is not computed.
NX Nastran 8 Verification Manual
18-7
Chapter 18
Mechanical Structures — Normal Mode Dynamics Analysis and Model Response
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. SDLL06/89.
18-8
NX Nastran 8 Verification Manual
Chapter
19 Stationary Thermal Tests — Heat Transfer Analysis
19.1 Hollow Cylinder - Fixed Temperatures This test is a steady-state heat transfer analysis of a 2D axisymmetric cylinder with fixed temperatures. It provides the input data and results for benchmark test TPLA01/89 from "Guide de validation des progiciels de calcul de structures."
•
Re = 0.30 m
•
Ri = 0.35 m
Test Case Data and Information Input Files htpla01.dat
Units SI
NX Nastran 8 Verification Manual
19-1
Chapter 19
Stationary Thermal Tests — Heat Transfer Analysis
Material Properties •
l = 1 W/m °C
Finite Element Modeling •
10 linear axisymmetric solid (CTRIAX6) elements
The mesh is shown in the following figure:
Boundary Conditions •
One temperature set: – Internal temperature Ti = 100 °C – External temperature Te = 20 °C
Solution Type SOL 153 — Steady State Heat Transfer
Results Temperature results Radius (m)
Bench Value (°C)
NX Nastran (°C)
0.3000
100.0
100.0
0.3100
82.98
82.98
0.3200
66.51
66.51
0.3300
50.54
50.54
0.3400
35.04
35.04
0.3500
20.00
20.00
Radius (m)
Bench Value (W/m2)
NX Nastran (W/m2)
0.3000
1730.
1702.
0.3100
1674.
1666.
0.3200
1622.
1614.
Flux results
19-2
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
Radius (m)
Bench Value (W/m2)
NX Nastran (W/m2)
0.3300
1573.
1565.
0.3400
1526.
1519.
0.3500
1483.
1505.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. TPLA01/89.
19.2 Hollow Cylinder - Convection This test is a steady-state heat transfer analysis of a 2D axisymmetric cylinder with convection. It provides the input data and results for benchmark test TPLA03/89 from "Guide de validation des progiciels de calcul de structures."
•
Re = 0.300 m
•
Ri = 0.391 m
Test Case Data and Information Input Files htpla03.dat
Units SI
Material Properties •
l = 40.0 W/m °C
NX Nastran 8 Verification Manual
19-3
Chapter 19
Stationary Thermal Tests — Heat Transfer Analysis
Finite Element Modeling •
20 linear axisymmetric solid (CTRIAX6) elements
The mesh is shown in the following figure:
Boundary Conditions •
Convection on internal surface: hi = 150.0 W/m2 / °C Ti = 500 °C
•
Convection on external surface: he = 142.0 W/m2 / °C Ti = 20 °C
Solution Type SOL 153 — Steady State Heat Transfer
Results Temperature / Flux
Bench Value
NX Nastran
Ti (°C)
272.3
272.5
Te (°C)
205.1
204.6
i (W/m2)
3.416E4
3.378E4
e (W/m2)
2.628E4
2.642E4
f/l=f*2*π*R So: f / l= 34173.82 * 2 * π * 0.300 = 64416.13 W/m
19-4
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. TPLA03/89.
19.3 Cylindrical Rod - Flux Density This test is a steady-state heat transfer analysis of a 2D axisymmetric rod with fixed temperatures and flux density. It provides the input data and results for benchmark test TPLA05/89 from "Guide de validation des progiciels de calcul de structures."
Test Case Data and Information Input Files htpla05.dat
Units SI
Material Properties •
l = 33.33 W/m °C
Finite Element Modeling •
20 linear axisymmetric solid (CTRIAX6) elements
•
42 grid points
NX Nastran 8 Verification Manual
19-5
Chapter 19
Stationary Thermal Tests — Heat Transfer Analysis
The meshes are shown in the following figure:
Boundary Conditions •
z=0 Set temperature to 0 °C
•
z=1 Set temperature to 500 °C
•
Cylindrical surface Set flux
to –200 W/m2
The boundary conditions are shown in the following figure:
19-6
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
Solution Type SOL 153 — Steady State Heat transfer
Results Temperature results (°C) Grid Point #
z (m)
Bench value
NX Nastran
Grid point 3
0
0
0
Grid point 41
0.1000
-4.000
-4.020
Grid point 39
0.2000
4.000
3.980
Grid point 37
0.3000
24.00
23.97
Grid point 35
0.4000
56.00
55.97
Grid point 33
0.5000
100.0
99.97
Grid point 31
0.6000
156.0
156.0
Grid point 29
0.7000
224.0
224.0
Grid point 27
0.8000
304.0
304.0
Grid point 25
0.9000
396.0
396.0
Grid point 4
1.000
500
500.0
Results are post-processed on the internal surface. NX Nastran does not make the approximation, T = cte when r is fixed.
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. TPLA05/89.
19.4 Hollow Cylinder with Two Materials - Convection This test is a steady-state heat transfer analysis of a 2D axisymmetric cylinder with two materials and convection. It provides the input data and results for benchmark test TPLA08/89 from "Guide de validation des progiciels de calcul de structures."
NX Nastran 8 Verification Manual
19-7
Chapter 19
•
Ri = 0.30 m
•
Rm = 0.35 m
•
Re = 0.37 m
Stationary Thermal Tests — Heat Transfer Analysis
Test Case Data and Information Input Files htpla08.dat
Units SI
Material Properties •
Material 1: l1 = 40.0 W/m °C
•
Material 2: l2 = 20.0 W/m °C
Finite Element Modeling •
14 linear axisymmetric solid (CTRIAX6) elements
•
16 grid points
19-8
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
The mesh is shown in the following figure:
Boundary Conditions •
Convection on internal surface hi = 150.0 W/m2 °C Ti = 70 °C
•
Convection on external surface he = 200.0 W/m2 °C Te = –15 °C
Solution Type SOL 153 — Steady State Heat Transfer
Results Grid point #
Temperature Flux
Bench Value
NX Nastran
Grid point 9
Ti (°C)
25.42
25.45
Grid point 14
Tm (°C)
17.69
17.68
Grid point 16
Te (°C)
12.11
12.09
Grid point 9
Grid point 9 (W/m2)
6687.
6609.
Grid point 14
Grid point 14 (W/m**2)
5732.
5768.
Grid point 16
Grid point 16 e (W/m2)
5422.
5497.
i
m
f/l = f * 2 * π * R So: f/l= 5733.33 * 2 * π * 0.35 = 12608.25 W/m
NX Nastran 8 Verification Manual
19-9
Chapter 19
Stationary Thermal Tests — Heat Transfer Analysis
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. TPLA08/89.
19.5 Wall-Convection This test is a steady-state heat transfer analysis of a 1D wall with fixed convection. It provides the input data and results for benchmark test TPLL03/89 from "Guide de validation des progiciels de calcul de structures."
Test Case Data and Information Input Files htpl03.dat
Units SI
Material Properties •
l = 1.0 W/m °C
Finite Element Modeling •
1 linear quadrilateral thin shell (CQUAD4) element
•
4 grid points
The thin shell element thickness is set to 1 m. The mesh is shown in the following figure:
19-10
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
Boundary Conditions •
Convection on internal surface hA = 20.0 W/m2 °C TA = –20.0 °C
•
Convection on external surface hB = 10.0 W/m2 °C TB = 500.0 °C
•
Convection coefficient is defined as energy / (length * time * temperature) in the current system of units. The boundary conditions are shown in the following figure:
Solution Type SOL 153 — Steady State Heat Transfer
NX Nastran 8 Verification Manual
19-11
Chapter 19
Stationary Thermal Tests — Heat Transfer Analysis
Results Temperature results (°C) NX Nastran
Grid point #
Temperature/Flux Bench Value
Grid point 2
TA (°C)
21.71
21.71
Grid point 4
TB (°C)
416.6
416.6
Grid point 1
(W/m2)
834.2
834.3
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. TPLL03/89.
19.6 Wall-Fixed Temperatures This test is a steady-state heat transfer analysis of a 1D wall with fixed temperatures. It provides the input data and results for benchmark test TPLL01/89 from "Guide de validation des progiciels de calcul de structures."
Test Case Data and Information The mesh is shown in the following figure:
19-12
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
Input Files htpl01.dat
Units SI
Material Properties •
l = 0.75 W/m °C
Finite Element Modeling •
5 linear beam (CBAR) elements
•
6 grid points
Boundary Conditions •
Internal temperature Ti = 100 °C
•
External temperature Te = 20 °C
Solution Type SOL 153 — Steady State Heat Transfer
Results Temperature results (°C) Grid point #
Length: x (m)
Bench Value
NX Nastran
Grid point 1
0
100.0
100.0
Grid point 3
0.01000
84.00
84.00
Grid point 4
0.02000
68.00
68.00
Grid point 5
0.03000
52.00
52.00
Grid point 6
0.04000
36.00
36.00
Grid point 2
0.05000
20.00
20.00
The flux
calculated with NX Nastran is exact:
= 1200 Ω / µ2
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No. TPLL01/89.
NX Nastran 8 Verification Manual
19-13
Chapter 19
Stationary Thermal Tests — Heat Transfer Analysis
19.7 L-Plate This test is a steady-state heat transfer analysis of a 2D L-plate with fixed temperatures. It provides the input data and results for benchmark test TPLP01/89 from "Guide de validation des progiciels de calcul de structures."
Test Case Data and Information Input Files htpp01a.dat - linear quadrilateral thin shell elements htpp01b.dat - parabolic quadrilateral thin shell elements
Units SI
Material Properties •
l = 1.0 W/m °C
Finite Element Modeling •
Test 1 – 12 linear quadrilateral thin shell (CQUAD4) elements
•
Test 2 – 12 parabolic quadrilateral thin shell (CQUAD8) elements
The mesh is shown in the following figure:
19-14
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
Boundary Conditions •
AF side Set temperature to 10 °C
•
DE side Set temperature to 0 °C
Solution Type SOL153 — Steady State Heat Transfer
Results Temperature Results (°C) Node
Bench Value
NX Nastran CQUAD4
NX Nastran CQUAD8
8
7.869
7.924
7.882
NX Nastran 8 Verification Manual
19-15
Chapter 19
Stationary Thermal Tests — Heat Transfer Analysis
Node
Bench Value
NX Nastran CQUAD4
NX Nastran CQUAD8
9
5.495
5.613
5.519
10
2.816
2.885
2.834
19
8.018
8.043
8.015
18
5.680
5.821
5.665
20
2.881
2.963
2.877
17
8.514
8.425
8.518
6
6.667
6.667
6.667
16
2.972
3.148
2.962
21
9.001
8.992
9.107
15
8.640
8.356
8.668
14
9.316
9.189
9.282
5
9.009
8.773
8.961
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No.TPLP01/89.
19.8 Orthotropic Square This test is a steady-state heat transfer analysis of a square plate with orthotropic conduction and convection. It provides the input data and results for benchmark test TPLP02/89 from "Guide de validation des progiciels de calcul de structures."
Test Case Data and Information Input Files htpp02.dat
Units SI
19-16
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
Material Properties •
lx = 1.00 W/m °C
•
lx =.75 W/m °C
Finite Element Modeling •
100 linear quadrilateral thin shell (CQUAD4) elements
•
121 grid points
The thin shell element thickness is set to 1 m. The mesh is shown in the following figure:
Boundary Conditions •
Flux density
y
= 60 W/m2 for face y = –0.1. (Entry)
•
Flux density
y
= –60 W/m2 for face y = 0.1. (Exit)
•
Convection on the faces X = –0.1 and x = 0.1: – h = 15.0 W/m2 °C
•
Linear variation of the external temperatures: – Te = 30 – 80y on the face x = –0.1 – Te = 15 – 80y on the face x = 0.1
•
Convection coefficient is defined as: – Energy / (length * time * temperature)
•
Flux density is defined as: – Energy / (length * time) in the current system of units
The boundary conditions are shown in the following figure:
NX Nastran 8 Verification Manual
19-17
Chapter 19
Stationary Thermal Tests — Heat Transfer Analysis
Solution Type SOL 153 — Steady State Heat Transfer
Results Temperature Results Point
Bench Value (°C)
NX Nastran (°C)
0
22.50
22.50
A
35.00
34.80
B
26.00
25.80
C
10.00
10.20
D
19.00
19.20
E
30.50
30.50
F
18.00
18.00
G
14.50
14.50
H
27.00
27.00
Grid Point
Bench Value
NX Nastran
61 X
45.00
45.00
61 Y
60.00
59.55
Flux Results (W/m2)
19-18
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No.TPLP02/89.
19.9 Hollow Sphere - Fixed Temperatures, Convection This test is a steady-state heat transfer analysis of a 3D sphere with fixed temperatures and convection. It provides the input data and results for benchmark test TPLV02/89 from "Guide de validation des progiciels de calcul de structures."
•
Ri = 0.30 m
•
Re = 0.35 m
Test Case Data and Information Input Files htpv02.dat (CHEXA and CPENTA) htpv02p.dat (CPYRAM and CPENTA)
Units SI
Material Properties •
l = 1 W/m °C
Finite Element Modeling Test 1: Brick and wedge element test •
500 linear brick (CHEXA) and linear wedge (CPENTA) elements
•
766 grid points
NX Nastran 8 Verification Manual
19-19
Chapter 19
Stationary Thermal Tests — Heat Transfer Analysis
The test is executed on 1/8 mapped meshed sphere. The mesh is shown in the following figure:
Test 2: Pyramid and wedge element test •
Linear pyramid (CPYRAM) elements created by dividing each brick element in test 1 into 6 pyramid elements. Linear wedge (CPENTA) elements remain.
Boundary Conditions •
Convection on internal surface hi = 30 W/m2 °C Ti = 100 °C
•
Set external surface temperature Te to 20 °C
The load sets are shown in the following figure:
19-20
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
Solution Type SOL 153 — Steady State Heat Transfer
Results Temperature results (°C) Test
Radius r (m)
Bench Value
NX Nastran
Test 1
0.3000
65.00
64.88
Test 2
0.3000
65.00
64.86
Test 1
0.3100
54.84
54.75
Test 2
0.3100
54.84
54.72
Test 1
0.3200
45.31
45.25
Test 2
0.3200
45.31
45.23
Test 1
0.3300
36.36
36.33
Test 2
0.3300
36.36
36.30
Test 1
0.3400
27.94
27.92
Test 2
0.3400
27.94
27.91
Test 1
0.3500
20.00
20.00
Test 2
0.3500
20.00
20.00
Flux results (W/m 2): (X-direction) Test
Radius r (m)
Bench Value
NX Nastran
Test 1
0.3000
1050.
1013.
Test 2
0.3000
1050.
1013.
Test 1
0.3100
983.4
981.4
Test 2
0.3100
983.4
981.6
Test 1
0.3200
922.9
921.2
Test 2
0.3200
922.9
921.3
Test 1
0.3300
867.5
866.3
NX Nastran 8 Verification Manual
19-21
Chapter 19
Stationary Thermal Tests — Heat Transfer Analysis
Test
Radius r (m)
Bench Value
NX Nastran
Test 2
0.3300
867.5
866.3
Test 1
0.3400
817.5
816.3
Test 2
0.3400
817.5
816.1
Test 1
0.3500
771.4
792.4
Test 2
0.3500
771.4
792.1
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No.TPLV02/89.
19.10 Hollow Sphere with Two Materials - Convection This test is a steady-state heat transfer analysis of a 3D sphere with two materials and convection. It provides the input data and results for benchmark test TPLV04/89 from "Guide de validation des progiciels de calcul de structures."
•
Ri = 0.30 m
•
Rm = 0.35 m
•
Re = 0.37 m
Test Case Data and Information Input Files htpv04a.dat (CHEXA & CPENTA) elements htpv04b.dat (CTETRA) elements htpv04c.dat (CTRIAX6) elements htpv04p.dat (CPYRAM & CPENTA) elements
19-22
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
Units SI
Material Properties •
Material 1: l1 = 40.0 W/m °C
•
Material 2: l2 = 20.0 W/m °C
Finite Element Modeling •
Test 1 - 700 solid linear brick (CHEXA) & solid linear wedge (CPENTA) elements
•
Test 2 - 2192 solid parabolic tetrahedron (CTETRA) elements
•
Test 3 - 8 axisymmetric parabolic elements (Results for this test will be provided in the NX Nastran 7 Verification Manual)
•
Test 4- Linear pyramid (CPYRAM) elements created by dividing each brick element in test 1 into 6 pyramid elements. Linear wedge (CPENTA) elements remain.
The test is executed on a 1/8 meshed sphere
NX Nastran 8 Verification Manual
19-23
Chapter 19
Stationary Thermal Tests — Heat Transfer Analysis
The meshes are shown in the following figure:
Boundary Conditions •
Convection on internal surface: hi = 150.0 W/m2 °C Ti = 70 °C
•
Convection on external surface: he = 200.0 W/m2 °C Te = –9 °C
19-24
NX Nastran 8 Verification Manual
Stationary Thermal Tests — Heat Transfer Analysis
The boundary conditions are shown in the following figure:
Solution Type SOL 153 — Steady State Heat Transfer
Results Temperature Results * axisymmetric data will be provided in version 7 TemperatureBench Flux (°C) Value
CHEXA & CPENTA
CTETRA
Axisymmetric
CPYRAM & CPENTA
Ti
25.06
N1 25.02
N19 25.06
*
N1 23.66
Tm
17.84
N556 17.84
N9 17.84
*
N556 16.26
Te
13.16
N778 13.18
N5 13.15
*
N778 13.85
6741.
N1 6487.
N19 5865.
*
N1 6683.
(W/m2) 4952.
N556 4931.
N9 4765.
*
N556 5080.
4431.
N778 4531.
N5 4551.
*
N778 4669.
i
(W/m2)
m e
(W/m2)
f = f * 4 * π * R2 So: f = 4931.20 * 4 * π * 0.352 = 7590.00 W Flux is in the x direction
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No.TPLV04/89.
NX Nastran 8 Verification Manual
19-25
Chapter
20 Thermo-mechanical Tests — Linear Statics Analysis
20.1 Orthotropic Cube This test is a steady-state heat transfer analysis of a 3D cube with convection and flux density. It provides the input data and results for benchmark test TPLV07/89 from "Guide de validation des progiciels de calcul de structures."
Test Case Data and Information Input Files htpv07.dat (CHEXA) htpv07p.dat (CPYRAM)
Units SI
NX Nastran 8 Verification Manual
20-1
Chapter 20
Thermo-mechanical Tests — Linear Statics Analysis
Material Properties •
lx = 1.00 W/m °C
•
ly = 0.75 W/m °C
•
lz = 0.50 W/m °C
Finite Element Modeling Test 1: Brick element test •
512 linear brick (CHEXA) elements
•
729 grid points
The mesh is shown in the following figure:
Test 2: Pyramid element test •
3072 linear pyramid (CPYRAM) elements created by dividing each brick element in test 1 into 6 pyramid elements.
Boundary Conditions •
Flux density
y = 60 W/m2 for face y = –0.1 (Entry)
•
Flux density
y = –60 W/m2 for face y = 0.1 (Exit)
•
Flux density
z = 30 W/m2 for face z = –0.1 (Entry)
•
Flux density
z = –30 W/m2 for face z = 0.1 (Exit)
•
Convection on the faces X = –0.1 and x = 0.1: –h = 15.0 W/m2 °C
•
Linear variation of the external temperatures: –Te = 30 – 80y – 60z on the face x = –0.1 –Te = 15 – 80y – 60z on the face x = 0.1
20-2
NX Nastran 8 Verification Manual
Thermo-mechanical Tests — Linear Statics Analysis
The boundary conditions are shown in the following figure:
Solution Type SOL 153 — Steady State Heat Transfer
Results Temperature results (°C) Test
Point
Bench Value NX Nastran
Test1
A
35.00
34.70
Test2
A
35.00
34.70
Test1
B
26.00
25.70
Test2
B
26.00
25.70
Test1
C
10.00
10.30
Test2
C
10.00
10.30
Test1
D
19.00
19.30
Test2
D
19.00
19.30
Test1
S
30.50
30.40
Test2
S
30.50
30.40
Test1
F
18.00
18.00
Test2
F
18.00
18.00
Test1
M
14.50
14.60
Test2
M
14.50
17.70
Test1
H
27.00
27.00
Test2
H
27.00
27.00
NX Nastran 8 Verification Manual
20-3
Chapter 20
Thermo-mechanical Tests — Linear Statics Analysis
Test
Point
Bench Value NX Nastran
Test1
N
29.00
29.00
Test2
N
29.00
29.00
Test1
P
20.00
20.00
Test2
P
20.00
20.00
Test1
J
4.000
4.600
Test2
J
4.000
4.590
Test1
I
13.00
13.60
Test2
I
13.00
13.60
Test1
E
16.50
16.60
Test2
E
16.50
16.60
Test1
R
41.00
40.40
Test2
R
41.00
40.40
Test1
Q
32.00
31.40
Test2
Q
32.00
31.40
Test1
K
16.00
16.00
Test2
K
16.00
16.00
Test1
L
25.00
25.00
Test2
L
25.00
25.00
Test1
G
28.50
28.40
Test2
G
28.50
28.40
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No.TPLV07/89.
20.2 Thermal Gradient on a Thin Pipe This test is a thermo-mechanical linear statics analysis of a thin pipe with thermal gradient and plane strain. It provides the input data and results for benchmark test HSLA01/89 from "Guide de validation des progiciels de calcul de structures."
20-4
NX Nastran 8 Verification Manual
Thermo-mechanical Tests — Linear Statics Analysis
•
Ri = 0.020 m
•
Re = 0.025 m
Test Case Data and Information Input Files hsla01.dat
Units SI
Material Properties • • •
E = 1.0 x 1011 Pa = 0.3 Coefficient of expansion: a = 1.0 x 10–5/C°
Finite Element Modeling •
1000 linear axisymmetric solid (CTRIAX6) elements
•
561 grid points
NX Nastran 8 Verification Manual
20-5
Chapter 20
Thermo-mechanical Tests — Linear Statics Analysis
The mesh is shown in the following figure:
Boundary Conditions •
Articulate AB side
•
Radial temperature
with Ti = 100 °C, and Te = 0 °C.
The boundary conditions are shown in the following figure:
20-6
NX Nastran 8 Verification Manual
Thermo-mechanical Tests — Linear Statics Analysis
Solution Type SOL 101 Linear statics
Results Point
Stress
Bench Value
NX Nastran
r=Ri
sr (Pa) –265x
0
–14.03 E6
sq (Pa) –265y
–74.07 E6
–79.84 E6
sr (Pa) –270x
–3.950 E6
–3.908 E6
sq (Pa) –270y
1.306 E6
1.469 E6
sr (Pa) –275x
0
–11.31 E6
sq (Pa) –275y
68.78 E6
73.69 E6
r = (Re + Ri) / 2 r = Re
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No.HSLA01/89.
20.3 Simply-Supported Arch This test is a thermo-mechanical linear statics analysis of a thin curved beam with thermal gradient and articulation. It provides the input data and results for benchmark test HSLL01/89 from "Guide de validation des progiciels de calcul de structures."
•
R = 10 m
•
A = 144 x 10–4 m2
•
I = 1.728 x 10–5 m4
Beam cross section:
NX Nastran 8 Verification Manual
20-7
Chapter 20
Thermo-mechanical Tests — Linear Statics Analysis
Test Case Data and Information Input Files hsll01.dat
Units SI
Material Properties • • •
E = 0.2 x 1011 Pa = 0.3 Coefficient of expansion: a = 11.0 x 10–6/C°
Finite Element Modeling •
50 linear beam (CBAR) elements
•
51 grid points
The mesh is shown in the following figure:
Boundary Conditions •
20-8
Articulate point A and B
NX Nastran 8 Verification Manual
Thermo-mechanical Tests — Linear Statics Analysis
•
Top temperature Ts = 160 °C
•
Middle temperature Tm = 100 °C
•
Bottom temperature Ti = 40 °C
The boundary conditions are shown in the following figure:
Solution Type SOL 101 — Linear Statics
Results Point
Force Moment
Bench Value
NX Nastran
q = π/2
M
0
4.040 e–5
N
0
15.10
T
–479.2
–527.6
M
3388.
3729.
N
–338.8
–373.2
T
–338.8
–373.2
M
4792.
5277.
N
–479.2
527.5
T
0
15.00
q = π/4
q=0
Post Processing List the beam forces •
M - Z bending moment
•
N - axial force
•
T - Y shear force
NX Nastran 8 Verification Manual
20-9
Chapter 20
Thermo-mechanical Tests — Linear Statics Analysis
References Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris, Afnor Technique, 1990. Test No.HSLL01/89.
20-10
NX Nastran 8 Verification Manual
Part
VII Material Nonlinear (Plasticity) Verification Using Standard NAFEMS Benchmarks
NX Nastran 8 Verification Manual
Chapter
21 Overview of the Material Nonlinear (Plasticity) Verification Using NAFEMS Test Cases
The purpose of this section is to verify the accuracy and robustness of NX Nastran. The plasticity verification uses test cases published by the National Agency for Finite Element Methods and Standards (NAFEMS) in Fundamental Tests for Two and Three Dimensional, Small Strain, Elastoplastic Finite Element Analysis. (See Reference.) To perform the tests, input data is applied to single elements including plane strain elements, plane stress elements, axisymmetric solid elements, and solid elements. Results are tabulated and compared to results published by NAFEMS. The plasticity verification includes perfect plasticity and isotropic hardening tests. Within these categories, results for uniaxial, biaxial, and triaxial displacement tests are provided.
21.1 Understanding the Verification Format The format for the nonlinear section of the Solver Verification document looks somewhat different from the linear section. Each test case in this section provides a brief description of the test including input data. The results are then displayed in the form of a graph comparing NX Nastran Nonlinear results published by NAFEMS for the same test case.
21.2
Reference
The following reference has been used in the NX Nastran Plasticity verification problems: Hinton, E., and Ezatt, M.H. Fundamental Tests for Two and Three Dimensional, Small Strain, Elastoplastic Finite Element Analysis. East Kilbride, Glasgow, UK: National Agency for Finite Element Methods and Standards, April, 1987.
NX Nastran 8 Verification Manual
21-1
Chapter
22
Test Cases
22.1 Plane Strain Elements - Perfect Plasticity Tests This article provides input data and results for perfect plasticity tests including prescribed uniaxial and prescribed biaxial displacement tests. The tests were run on these plane stress elements: •
Linear triangle (CTRIA3) elements
•
Linear quadrilateral (CQUAD4) elements
The material description and initial boundary conditions are the same for the uniaxial and biaxial displacement tests.
Test Case Data and Information Input Files nlspls89.dat (uniaxial) nlspls90.dat (biaxial)
Units Inch
Attributes Load Control
NX Nastran 8 Verification Manual
22-1
Chapter 22
Test Cases
Material Properties • •
E = 250000.0 = 0.25
•
sy = 5.0
•
H = 0.0
•
o = 0.000025 (strain at first yield)
Boundary Conditions The following figure shows the plane strain elements and the boundary conditions applied to each. The strain state is completely defined as a function of time since all degrees of freedom are suppressed or prescribed. These boundary conditions represent initial conditions only and do not illustrate the time history of the applied conditions.
22-2
NX Nastran 8 Verification Manual
Test Cases
Results Uniaxial Displacement Test — Applied Strain History The following graph shows results of the uniaxial displacement test for the plane strain elements. Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear test results compared with NAFEMS test results for plane strain with perfect plasticity.
History
Strain XX
Strain YY
Strain ZZ
1
0.2500D–4
0D+00
0D+00
2
0.5000D–4
0D+00
0D+00
3
0.2500D–4
0D+00
0D+00
4
0D+00
0D+00
0D+00
10 increments per strain history step
NX Nastran 8 Verification Manual
22-3
Chapter 22
Test Cases
Biaxial Displacement Test — Applied Strain History The following graph shows results of the biaxial displacement test for the plane strain elements. Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results for plane strain with perfect plasticity.
History Stage
Strain XX
Strain YY
Strain ZZ
1
0.2500D–4
0D+00
0D–00
2
0.5000D–4
0D+00
0D–00
3
0.5000D–4
0.2500D–4
0D–00
4
0.5000D–4
0.5000D–4
0D–00
5
0.2500D–4
0.5000D–4
0D–00
6
0D+00
0.5000D–4
0D+00
7
0D+00
0.2500D–4
0D+00
8
0D+00
0D+00
0D+00
10 increments per strain history step
22-4
NX Nastran 8 Verification Manual
Test Cases
References Hinton, E., and Ezatt, M.H. Fundamental Tests for Two and Three Dimensional, Small Strain, Elastoplastic Finite Element Analysis. East Kilbride, Glasgow, UK: National Agency for Finite Element Methods and Standards, April, 1987 pp. 2.3-2.25.
22.2 Plane Strain Elements - Isotropic Hardening Tests This article provides input data and results for isotropic hardening tests including prescribed uniaxial and prescribed biaxial displacement tests. The tests were run on these plane strain elements: •
Linear triangle (CTRIA3) elements
•
Linear quadrilateral (CQUAD4) elements
The material description and initial boundary conditions are the same for the uniaxial and biaxial displacement tests.
Test Case Data and Information Input Files nlspls91.dat (uniaxial) nlspls92.dat (biaxial)
Units Inch
Attributes Load Control
Material Properties • • •
E = 250000.0 = 0.25 sy = 5.0
NX Nastran 8 Verification Manual
22-5
Chapter 22
Test Cases
•
H = 62500.0
•
o = 0.000025 (strain at first yield)
Boundary Conditions The following figure shows the plane strain elements and the boundary conditions applied to each. The strain state is completely defined as a function of time since all degrees of freedom are suppressed or prescribed. These boundary conditions represent initial conditions only and do not illustrate the time history of the applied conditions.
22-6
NX Nastran 8 Verification Manual
Test Cases
Results Uniaxial Displacement Test — Applied Strain History The following graph shows results of the biaxial displacement test for the plane strain elements. Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results for plane strain with isotropic hardening.
History
Strain XX
Strain YY
Strain ZZ
1
0.2500D–4
0D+00
0D+00
2
0.5000D–4
0D+00
0D+00
3
0.2500D–4
0D+00
0D+00
4
0D–00
0D+00
0D+00
10 increments per strain history step
NX Nastran 8 Verification Manual
22-7
Chapter 22
Test Cases
Biaxial Displacement Test — Applied Strain History The following graph shows results of the uniaxial displacement test for the plane strain elements. Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test result for plane strain with isotropic hardening.
History Stage
Strain XX
Strain YY
Strain ZZ
1
0.2500D–4
0D+00
0D+00
2
0.5000D–4
0D+00
0D+00
3
0.5000D–4
0.2500D–4
0D+00
4
0.5000D–4
0.5000D–4
0D+00
5
0.2500D–4
0.5000D–4
0D+00
6
0D–00
0.5000D–4
0D+00
7
0D–00
0.2500D–4
0D+00
8
0D–00
0D–00
0D+00
10 increments per strain history step
22-8
NX Nastran 8 Verification Manual
Test Cases
References Hinton, E., and Ezatt, M.H. Fundamental Tests for Two and Three Dimensional, Small Strain, Elastoplastic Finite Element Analysis. East Kilbride, Glasgow, UK: National Agency for Finite Element Methods and Standards, April, 1987 pp. 2.26 - 2.35.
22.3 Plane Stress Elements - Perfect Plasticity Tests This article provides input data and results for perfect plasticity tests including prescribed uniaxial and prescribed biaxial displacement tests. The tests were run on these plane strain elements: •
Linear triangle (CTRIA3) elements
•
Linear quadrilateral (CQUAD4) elements
The material description and initial boundary conditions are the same for the uniaxial and biaxial displacement tests. The following figure shows the geometry:
Test Case Data and Information Input Files nlspls61.dat (uniaxial test), linear quadrilateral (CQUAD4) elements nlspls62.dat (uniaxial test), linear triangle (CTRIA3) elements nlspls65.dat (biaxial test), linear quadrilateral (CQUAD4) elements nlspls66.dat (biaxial test), linear triangle (CTRIA3) elements
Units Inch
Material Properties • • •
E = 250000.0 = 0.25 sy = 5.0
NX Nastran 8 Verification Manual
22-9
Chapter 22
•
H = 0.0
•
o
Test Cases
= 0.2080126 x 10–4 (strain at first yield)
Boundary Conditions The following figure shows the plane strain elements and the boundary conditions applied to each. The strain state is completely defined as a function of time since all degrees of freedom are suppressed or prescribed. These boundary conditions represent initial conditions only and do not illustrate the time history of the applied conditions.
22-10
NX Nastran 8 Verification Manual
Test Cases
Results Uniaxial Displacement Test — Applied Strain History The following graph shows results of the uniaxial displacement test for the plane strain elements. Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results for plane stress with perfect plasticity.
History
Strain XX
Strain YY
Strain ZZ
1
0.2080D–4
0D+00
-0.6934D–5
2
0.4160D–4
0D+00
-0.2538D–4
3
0.2080D–4
0D+00
-0.1835D–4
4
0.4235D–21
0D+00
-0.1128D–4
10 increments per strain history step Biaxial Displacement Test — Applied Strain History The following graph shows results of the biaxial displacement test for the plane strain elements.
NX Nastran 8 Verification Manual
22-11
Chapter 22
Test Cases
Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.
History Stage
Strain XX
Strain YY
Strain ZZ
1
0.2080D–4
0D+00
-0.6934D–5
2
0.4160D–4
0D+00
-0.2528D–4
3
0.4160D–4
0.2080D–4
-0.4284D–4
4
0.4160D–4
0.4160D–4
-0.6513D–4
5
0D–00
0.4160D–4
-0.5035D–4
6
0D–00
0.1872D–4
-0.3871D–4
7
0D–00
0D–00
-0.1867D–4
10 increments per strain history step
22-12
NX Nastran 8 Verification Manual
Test Cases
References Hinton, E., and Ezatt, M.H. Fundamental Tests for Two and Three Dimensional, Small Strain, Elastoplastic Finite Element Analysis. East Kilbride, Glasgow, UK: National Agency for Finite Element Methods and Standards, April, 1987 pp. 2.36 - 2.47.
22.4 Plane Stress Elements - Isotropic Hardening Tests This article provides input data and results for isotropic hardening tests including prescribed uniaxial and prescribed biaxial displacement tests. The tests were run on the these plane stress elements: •
Linear triangle (CTRIA3) elements
•
Linear quadrilateral (CQUAD4) elements
The material description and initial boundary conditions are the same for the uniaxial and biaxial displacement tests. The following figure shows the geometry:
Test Case Data and Information Input Files nlspls71.dat (uniaxial test), linear quadrilateral (CQUAD4) elements nlspls72.dat (uniaxial test), linear triangle (CTRIA3) elements nlspls75.dat (biaxial test), linear quadrilateral (CQUAD4) elements nlspls76.dat (biaxial test), linear triangle (CTRIA3) elements
Units Inch
Material Properties • • •
E = 250000.0 = 0.25 sy = 5.0
NX Nastran 8 Verification Manual
22-13
Chapter 22
•
Test Cases
H = 62500.0
•
o
= 0.2080126 x 10–4 (strain at first yield)
Boundary Conditions The following figure shows the plane strain elements and the boundary conditions applied to each. The strain state is completely defined as a function of time since all degrees of freedom are suppressed or prescribed. These boundary conditions represent initial conditions only and do not show the time history of the applied conditions.
22-14
NX Nastran 8 Verification Manual
Test Cases
Results Uniaxial Displacement Test — Applied Strain History The following graph shows results of the uniaxial displacement test for the plane strain elements. Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.
History
Strain XX
Strain YY
Strain ZZ
1
0.2080D–4
0D+00
-0.6934D–5
2
0.4160D–4
0D+00
-0.2249D–4
3
0.2080D–4
0D+00
-0.1555D–4
4
0.4235D–21
0D+00
-0.8619D–5
10 increments per strain history step
NX Nastran 8 Verification Manual
22-15
Chapter 22
Test Cases
Biaxial Displacement Test — Applied Strain History The following graph shows results of the biaxial displacement test for the plane strain elements. Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.
History Stage
Strain XX
Strain YY
Strain ZZ
1
0.2080D–4
0D+00
-0.6934D–5
2
0.4160D–4
0D+00
-0.2249D–4
3
0.4160D–4
0.2080D–4
-0.3569D–4
4
0.4160D–4
0.4160D–4
-0.5406D–4
5
0.2080D–4
0.4160D–4
-0.4712D–4
6
0D–00
0.4160D–4
-0.4102D–4
7
0D–00
0.2080D–4
-0.3408D–4
8
0D–00
0D–00
-0.2715D–4
10 increments per strain history step
22-16
NX Nastran 8 Verification Manual
Test Cases
References Hinton, E., and Ezatt, M.H. Fundamental Tests for Two and Three Dimensional, Small Strain, Elastoplastic Finite Element Analysis. East Kilbride, Glasgow, UK: National Agency for Finite Element Methods and Standards, April, 1987 pp. 2.47 - 2.58.
22.5 Solid Element - Perfect Plasticity Tests This article provides input data and results for perfect plasticity tests including prescribed uniaxial, biaxial, and triaxial displacement tests. The tests were run on the solid parabolic brick element.
Test Case Data and Information Input Files nlspls08.dat
Units Inch
Material Properties •
E = 250000.0 = 0.25
• • • •
y
= 5.0
H = 0.0 o
= 0.000025 (strain at first yield)
Boundary Conditions The following figure shows the parabolic brick (CHEXA) element and the boundary conditions applied to it. The strain state is completely defined as a function of time since all degrees of freedom are suppressed or prescribed. These boundary conditions represent initial conditions only and do not show the time history of the applied conditions.
NX Nastran 8 Verification Manual
22-17
Chapter 22
Test Cases
Results Uniaxial Displacement Test — Applied Strain History History
Strain XX
Strain YY
Strain ZZ
1
2.500E–5
0E+00
0E+00
2
5.000E–5
0E+00
0E+00
3
2.500E–5
0E+00
0E+00
4
0E+00
0E+00
0E+00
10 increments per strain history step
22-18
NX Nastran 8 Verification Manual
Test Cases
The following graph shows results of the uniaxial displacement test for the solid brick element. It shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.
NX Nastran 8 Verification Manual
22-19
Chapter 22
Test Cases
Biaxial Displacement Test — Applied Strain History The following graph shows results of the biaxial displacement test for the solid brick element. The graph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.
History
Strain XX
Strain YY
Strain ZZ
1
2.500E–5
0E+00
0E+00
2
5.000E–5
0E+00
0E+00
3
5.000E–5
2.500E–5
0E+00
4
5.000E–5
5.000E–5
0E+00
5
2.500E–5
5.000E–5
0E+00
6
0E+00
5.000E–5
0E+00
7
0E+00
2.500E–5
0E+00
8
0E+00
0E+00
0E+00
- 10 increments per strain history step
22-20
NX Nastran 8 Verification Manual
Test Cases
Triaxial Displacement Test — Applied Strain History The following graph shows results of the triaxial displacement test for the solid brick element. The graph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.
History
Strain XX
Strain YY
Strain ZZ
1
2.500E–5
0E+00
0E+00
2
5.000E–5
0E+00
0E+00
3
5.000E–5
2.500E–5
0E+00
4
5.000E–5
5.000E–5
0E+00
5
5.000E–5
5.000E–5
2.500E–5
6
5.000E–5
5.000E–5
5.000E–5
7
2.500E–5
5.000E–5
5.000E–5
8
0E+00
5.000E–5
5.000E–5
9
0E+00
2.500E–5
5.000E–5
10
0E+00
0E+00
5.000E–5
11
0E+00
0E+00
2.500E– 5
NX Nastran 8 Verification Manual
22-21
Test Cases
Chapter 22
History
Strain XX
Strain YY
Strain ZZ
12
0E+00
0E+00
0E+00
- 10 increments per strain history step
References Hinton, E., and Ezatt, M.H. Fundamental Tests for Two and Three Dimensional, Small Strain, Elastoplastic Finite Element Analysis. East Kilbride, Glasgow, UK: National Agency for Finite Element Methods and Standards, April, 1987 pp. 2.59-2.79.
22.6 Solid Element - Isotropic Hardening Tests This article provides input data and results for isotropic hardening tests including prescribed uniaxial, biaxial, and triaxial displacement tests. The tests were run on the solid parabolic brick element (CHEXA), which has 20 grid points.
Test Case Data and Information Input Files nlspls09.dat
Units Inch
Material Properties •
E = 250000.0
•
= 0.25
• •
y
= 5.0
H = 62500.0
•
o
= 0.000025 (strain at first yield)
Boundary Conditions The following figure shows the parabolic brick element and the boundary conditions applied to it. The strain state is completely defined as a function of time since all degrees of freedom are suppressed or prescribed. These boundary conditions represent initial conditions only and do not show the time history of the applied conditions.
22-22
NX Nastran 8 Verification Manual
Test Cases
NX Nastran 8 Verification Manual
22-23
Chapter 22
Test Cases
Results Uniaxial Displacement Test — Applied Strain History The following graph shows results of the uniaxial displacement test for the solid brick element. It shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.
History
Strain XX
Strain YY
Strain ZZ
1
2.500E–5
0E+00
0E+00
2
5.000E–5
0E+00
0E+00
3
2.500E–5
0E+00
0E+00
4
0E+00
0E+00
0E+00
- 10 increments per strain history step
22-24
NX Nastran 8 Verification Manual
Test Cases
Biaxial Displacement Test — Applied Strain History The following graph shows results of the biaxial displacement test for the solid brick element. The graph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.
History
Strain XX
Strain YY
Strain ZZ
1
2.500E–5
0E+00
0E+00
2
5.000E–5
0E+00
0E+00
3
5.000E–5
2.500E–5
0E+00
4
5.000E–5
5.000E–5
0E+00
5
2.500E–5
5.000E–5
0E+00
6
0E+00
5.000E–5
0E+00
7
0E+00
2.500E–5
0E+00
8
0E+00
0E+00
0E+00
- 10 increments per strain history step
NX Nastran 8 Verification Manual
22-25
Chapter 22
Test Cases
Triaxial Displacement Test — Applied Strain History The following graph shows results of the triaxial displacement test for the solid brick element. The graph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.
History
Strain XX
Strain YY
Strain ZZ
1
2.500E–5
0E+00
0E+00
2
5.000E–5
0E+00
0E+00
3
5.000E–5
2.500E–5
0E+00
4
5.000E–5
5.000E–5
0E+00
5
5.000E–5
5.000E–5
2.500E–5
6
5.000E–5
5.000E–5
5.000E–5
7
2.500E–5
5.000E–5
5.000E–5
8
0E+00
5.000E–5
5.000E–5
9
0E+00
2.500E–5
5.000E–5
10
0E+00
0E+00
5.000E–5
11
0E+00
0E+00
2.500E–5
22-26
NX Nastran 8 Verification Manual
Test Cases
History
Strain XX
Strain YY
Strain ZZ
12
0E+00
0E+00
0E+00
- 10 increments per strain history step
References Hinton, E., and Ezatt, M.H. Fundamental Tests for Two and Three Dimensional, Small Strain, Elastoplastic Finite Element Analysis. East Kilbride, Glasgow, UK: National Agency for Finite Element Methods and Standards, April, 1987 pp. 2.80-2.92.
NX Nastran 8 Verification Manual
22-27
Part
VIII Geometric Nonlinear Verification Using Standard NAFEMS Benchmarks
NX Nastran 8 Verification Manual
Chapter
23 Overview of the Geometric Nonlinear Verification Using NAFEMS Test Cases
This section verifies the accuracy and robustness of the arc-length method of NX Nastran. The geometric nonlinear verification uses test cases published by the National Agency for Finite Element Methods and Standards (NAFEMS) in NAFEMS Non-Linear Benchmarks and A Review of Benchmark Problems for Geometric Non-linear Behaviour of 3-D Beams and Shells. (See References.)
23.1 Understanding the Verification Format Each test case includes the following information. •
Test case data and information: - Units - Material properties - Finite element modeling information - Boundary conditions (loads and restraints) - Solution type
•
Results — time history versus Load Factor plots are presented. (Note that in NX Nastran, the load factor is displayed as "eigenvalue".)
•
Reference
23.2 Reference The following references have been used for these verification problems: •
NAFEMS Non-Linear Benchmarks. Glasgow: NAFEMS, Oct., 1989., Rev. 1. Test No. NL6.
•
NAFEMS, A Review of Benchmark Problems for Geometric Non-Linear Behaviour of 3-D Beams and Shells (Summary) (Glasgow: NAFEMS, Ref. R0024.)
NX Nastran 8 Verification Manual
23-1
Chapter
24
Test Cases
24.1 Straight Cantilever with End Moment This test is a nonlinear analysis of a single row of equal-sized elements. This document provides the input data and results for NAFEMS Non-linear Benchmarks NL5.
Test attributes: •
Bending action only
•
Initially straight elements
•
Load control
Test Case Data and Information Input Files nfnl05a.dat (load control) nfnl05b.dat (arc-length control)
Units SI
NX Nastran 8 Verification Manual
24-1
Test Cases
Chapter 24
Material Properties • •
E = 210 x 109 N / m2 = 0.0
SI
Finite Element Modeling 32 linear beam (CBEAM) elements
Boundary Conditions •
U=V=
•
Concentrated load at Point A applied in equal increments up to a maximum value of M L / 2 π E I = 1.0
= 0 at point B
Solution Type SOL 106 — Geometric Nonlinear •
Loading method — arc-length control.
•
Adaptive search control:
24-2
NX Nastran 8 Verification Manual
Test Cases
– Initial increment factor = 0.05 – Target number of iterations = 6 – Maximum number of splits = 3 – Max increment factor = 1 – Number of reporting steps = 18 Geometric nonlinear 2 •
Loading method — load control.
•
6 equal steps.
Results Normalizing Constants E I / L = 3436.12 x 103 Nm
•
2
•
L = 3.2 m
•
2 = 6.28319
NX Nastran 8 Verification Manual
24-3
Chapter 24
Test Cases
Graphs of Results •
24-4
Free end axial displacement vs. Load Factor
NX Nastran 8 Verification Manual
Test Cases
•
Vertical displacement at grid point 33 vs. Load Factor
NX Nastran 8 Verification Manual
24-5
Chapter 24
•
Test Cases
Rotational displacement at grid point 33 vs. Load Factor
References National Agency for Finite Element Methods and Standards, NAFEMS Non-Linear Benchmarks (Glasgow: NAFEMS, Oct., 1989., Rev. 1). Test No. NL5.
24.2 Straight Cantilever with Axial End Point Load - Brick Elements This test is a nonlinear analysis of a straight cantilever with an axial end point load, made up of a single row of straight elements. This document provides the input data and results for NAFEMS Non-linear Benchmarks NL6.
24-6
NX Nastran 8 Verification Manual
Test Cases
Attributes of this test are: •
Combined bending and membrane action.
•
Presence of bifurcation.
•
Initially straight elements.
•
Load control.
Test Case Data and Information Input Files nlsarg07.dat
Units SI
Material Properties • •
E = 210 x 109 N/m2 = 0.0
NX Nastran 8 Verification Manual
24-7
Chapter 24
Test Cases
Finite Element Modeling 256 solid parabolic brick (CHEXA) elements.
Boundary Conditions •
U = V = q = 0 at point B.
•
Concentrated load at Point A applied in increments up to a value of PL2 / EI = 22.493.
Solution Type SOL 106 — Geometric Nonlinear
Results Normalizing Constants: •
EI / L2 = 170898 N
•
L + 3.2 m
•
= 3.14159
24-8
NX Nastran 8 Verification Manual
Test Cases
Graphs of results: •
X-displacement at cantilever end point vs. Load Factor.
NX Nastran 8 Verification Manual
24-9
Chapter 24
•
Test Cases
Y-displacement at cantilever end point vs. Load Factor
Reference National Agency for Finite Element Methods and Standards. NAFEMS Non-Linear Benchmarks. Glasgow: NAFEMS, Oct., 1989., Rev. 1. Test No. NL6.
24-10
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Test Cases
24.3 Straight Cantilever with Axial End Point Load - BEAM Elements This test is a nonlinear analysis of a single row of straight elements. This document provides the input data and results for NAFEMS Non-linear Benchmarks NF6.
Test Case Data and Information Input Files nlsarp01.dat
Units SI
Material Properties • •
E = 210 x 109 N/m2 = 0.0
Finite Element Modeling 32 linear (CBEAM) elements
NX Nastran 8 Verification Manual
24-11
Test Cases
Chapter 24
Boundary Conditions • •
U = V = q = 0 at point B. Concentrated load at Point A applied in increments up to a value of PL2 / EI = 22.493 or P = –3.85 x 106 N
Solution Type SOL 106 — Geometric Nonlinear
Results Normalizing Constants: • •
EI / L
2
= 170898 N
π = 3.14159
24-12
NX Nastran 8 Verification Manual
Test Cases
Graphs of results: •
X-displacement at grid point 33 vs. Load Factor
NX Nastran 8 Verification Manual
24-13
Chapter 24
•
24-14
Test Cases
Y-displacement at grid point 33 vs. Load Factor
NX Nastran 8 Verification Manual
Test Cases
•
Rz-displacement at grid point 33 vs. Load Factor
Reference National Agency for Finite Element Methods and Standards, NAFEMS Non-Linear Benchmarks. Glasgow: NAFEMS, Oct., 1989., Rev. 1. Test No. NL6.
24.4 Lee’s Frame Buckling Problem This test is a nonlinear analysis of a single row of straight elements. This document provides the input data and results for NAFEMS Non-linear Benchmarks NF7. Attributes of this test are:
NX Nastran 8 Verification Manual
24-15
Chapter 24
Test Cases
Test Case Data and Information Input Files nlsarg01.dat
Units SI
Material Properties • •
24-16
E = 71.74 x 109 N/m2 = 0.0
NX Nastran 8 Verification Manual
Test Cases
Finite Element Modeling 20 linear beam (CBEAM) elements
Boundary Conditions • •
U = V = 0; q ≠ 0 at points B and C Concentrated load at Point A applied incrementally using arc-length constraint with automatic adjustment of arc length (P = –20000 N)
Solution Type SOL 106 — Geometric Nonlinear
NX Nastran 8 Verification Manual
24-17
Chapter 24
Test Cases
Results Normalizing Constants EI / L2 = 996.389 N, L = 1.2 m Graphs of results: Y-displacement at grid point 13 vs. Load Factor
Reference National Agency for Finite Element Methods and Standards. NAFEMS Non-Linear Benchmarks. Glasgow: NAFEMS, Oct., 1989., Rev. 1. Test No. NL7.
24.5 Large Displacement Elastic Response of a Hinged Spherical Shell Under Uniform Pressure Loading This test is a nonlinear analysis of a hinged spherical shell element under uniform pressure loading. This document provides the input data and results for A Review of Benchmark Problems for Geometric Non-Linear Behaviour of 3-D Beams and Shells (Summary) 3DNLG-7.
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Test Cases
Test Case Data and Information Input Files nlsarg05.dat
Units SI
Material Properties • •
E = 69 = 0.3
Finite Element Modeling •
The shell midsurface is defined in terms of the global Cartesian coordinate system where Z = 2.0285 x 10 –4 [X (1570 – X) + Y (1570 – Y)].
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Chapter 24
Test Cases
Boundary Conditions •
Evenly distributed follower pressure load normal to shell surface. Maximum pressure = 0.1. Pressure follows the deformation of the shell surface.
Solution Type SOL 106 — Geometric Nonlinear •
Loading method: o
•
Arc-length control
Adaptive search control: o
Initial increment factor = 0.3
o
Target number of iterations = 6
o
Maximum number of splits = 3
o
Maximum increment factor = 1
o
Number of reporting steps = 18
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Test Cases
24.6 Results Magnitude displacement at grid point 145 vs. Load Factor
24.7 Reference •
National Agency for Finite Element Methods and Standards. A Review of Benchmark Problems for Geometric Non-Linear Behaviour of 3-D Beams and Shells (Summary) Glasgow: NAFEMS, Ref. R0024. Test No. 3DNLG-7
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