The COSMOS Companion, Understanding COSMOS Accuracy - Meshing and Convergence

The COSMOS Companion Understanding Understandin g COSMOS COSMOS Accuracy Accuracy – Meshi Meshing ng and Convergence Volume 103

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What is the COSMOS Companion? • The COSMOS Companion is a series of short subjects to help design engineers build better products with SolidWorks Analysis • Video presentations and accompanying accompanying exercises • A tool for Continuous Learning on your schedule • Pre-recorded videos are accompanied by a more detailed webcast with Q & A  –  Download videos and review webcast schedule at: http://www.cosmosm.com/pages/news/COSMOS_Companion.html

• It is not an alternative to instructor-led introductory training  –  We highly recommend you take a course with your local reseller to build a solid knowledge base

What is the COSMOS Companion? • The COSMOS Companion is a series of short subjects to help design engineers build better products with SolidWorks Analysis • Video presentations and accompanying accompanying exercises • A tool for Continuous Learning on your schedule • Pre-recorded videos are accompanied by a more detailed webcast with Q & A  –  Download videos and review webcast schedule at: http://www.cosmosm.com/pages/news/COSMOS_Companion.html

• It is not an alternative to instructor-led introductory training  –  We highly recommend you take a course with your local reseller to build a solid knowledge base

Mesh Me sh Ba Basi sics cs - So Soli lids ds • Solid models are filled (Meshed) with Solid Elements with a Tetrahedron shape • A basic (draft) tetrahedron has four (4) corner Nodes

Mesh Basics - Surfaces

• Shell elements model thin structures more efficiently • Shell elements are Triangles • A basic (draft) triangle has three (3) corner nodes

Mesh Basics – Nodes & Elements • A Finite Element solution calculates the displacement of the nodes first and the resulting strain in the attached elements second • Calculating the deformed mesh when a structure is in equilibrium is the key to an accurate FEA solution • Mesh quality in a nutshell – The initial mesh must represent the initial shape of the model and be ‘flexible’ enough to capture the deformed shape at equilibrium • The deformed shape at small features where stresses can be expected to change greatly must be captured even more accurately to calculate these stresses.

Mesh Basics – Nodes & Elements Draft vs. High Quality Elements

Draft Quality Linear Edges 3 Nodes

Draft Quality Linear Edges 4 Nodes

High Quality Parabolic Edges 6 Nodes

High Quality Parabolic Edges 10 Nodes

Mesh Basics – Nodes & Elements • The calculated shape of an element edge is limited by it’s order  –  Draft = Linear = 1st Order  –  High = Parabolic = 2 nd Order

• Therefore, curvature, either initial or calculated, must be approximated with straight facets in a draft mesh and 2 nd order segments in a high quality mesh • The difference between the ideal curvature and the modeled curvature is called Discretization Error

F l1 l0

F

Does Size Matter? • Generally speaking, with more elements in a mesh, the solution is more precise:  –  There are more nodes that are available for calculating response and thus the solution is more precise  –  More elements means smaller elements so discretization error is minimized

• The practical limit where further mesh size reductions add no benefit to the solution can be found in the Convergence process • A converged mesh for a given geometry is dependent upon the applied loads and restraints

Does Size Matter? • Same Part and Load Magnitude • Different Converged Mesh

Load magnitude is not a factor in convergence for a linear study

Convergence in COSMOSWorks • COSMOSWorks provides 3 techniques for converging a model  –  Automatic h-adaptive  –  Automatic p-adaptive  –  Manual h-adaptive (None)

• These can accessed in the Study Properties under the Adaptive tab

Convergence in COSMOSWorks Automatic h-Adaptive  –  Only available for single part static studies  –  Reduces mesh size in areas where calculated strain energy error (More on this later) is high  –  Can coarsen (increase mesh size) in regions where strain energy error is low  –  Target Accuracy defines the error threshold that causes a refinement loop – Default of 98% is still fast  –  Accuracy Bias • Set to Local if your response is dominated by localized stress hot spots • Set to Global if you are more interested in overall part stiffness, not stress • If you aren’t sure, leave at Default

 –  Works with Draft or High Quality meshes… • Does it matter if you are assured an accurate solution? • Who said you are assured an accurate solution?

Convergence in COSMOSWorks H-adaptive convergence using Draft Quality elements:

13.6mm

3.4mm

75.6 MPa 44.0 MPa Δ

= 42%

Convergence in COSMOSWorks H-adaptive convergence using High Quality elements:

13.6mm

3.4mm

82.1 MPa 79.3 MPa Δ

= 3%

Convergence in COSMOSWorks Automatic p-Adaptive  –  Only available for static studies but does work with bonded assemblies – No contact  –  Default convergence criteria tracks changes in Total Strain Energy – RMS Displacement and Von Mises Stress criterion don’t typically improve solution  –  Default settings usually sufficient and Max P-Order and # of Loops rarely needed  –  Must use High Quality starting mesh  –  Mostly insensitive to starting mesh size  –  Jacobian (Distortion) errors frequent –  No feedback on location

Convergence in COSMOSWorks P-adaptive convergence using High Quality elements:

13.6mm

83.8 MPa

3.4mm

102 MPa

Local 1.0mm Global 5.0 mm

80.0 MPa

Convergence in COSMOSWorks What is a P-element? P-Elements: Y = A + BX +CX2 + DX3 + … + ZXn H-Elements: Yn = AnX + Bn

Draft Quality Elements – 1st Order (Linear) Edges High Quality Elements – 2nd Order Edges P-Elements – Up to 5th Order Edges Can capture more deformation with larger elements but are more computationally intensive than h-elements

Convergence in COSMOSWorks • Recommendations:  –  For single parts: • Use h-adaptivity, high quality elements and the default mesh size

 –  For bonded assemblies: • Use p-adaptivity, high quality elements and default mesh size. • If a Jacobian error occurs, a second run with a different initial mesh size is warranted to avoid erroneous high stresses

 –  For assemblies with connectors and/or contact: • Use traditional Manual h-element convergence • Mesh with default element size – high quality • Apply initial mesh control to ensure conformity to undeformed geometry • Use local mesh control to achieve convergence where required

Manual Convergence Checking • Relative Convergence  –  How much does stress change with successive studies having incrementally refined meshes  –  Use refinements of 2:1 with each pass so change is meaningful  –  Watch for distortion if local mesh size > 1 or Negative

b

Aspect Ratio = a/b

Impact of Geometry on Accuracy • Sliver Surfaces & Short Edges are most common cause of meshing problems • Mesher must respect all edges so surface dimensions much smaller than nominal element size may cause distorted elements

Impact of Geometry on Accuracy Problems… InOther assembly modeling, the placement of parts with respect to each other may cause element distortion

Where possible, use the “Incompatible Mesh” option in Contact Options

Shell Meshing vs. Solids • Shell Elements are a more efficient way to model thin walled structures • How thin is thin?  –  “Thin” is not an absolute description  –  If the wall thickness