The COSMOS CompanionUnderstanding COSMOS Accuracy – Meshing and Convergence

Volume 103Sponsored by:

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 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 Basics - Solids

• 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

High QualityParabolic Edges

6 NodesDraft QualityLinear Edges

3 Nodes

Draft QualityLinear Edges

4 Nodes

High QualityParabolic 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 = 2nd Order

• Therefore, curvature, either initial or calculated, must be approximated with straight facets in a draft mesh and 2nd

order segments in a high quality mesh

• The difference between the ideal curvature and the modeled curvature is called Discretization Error

F F

l0l1

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

13.6mm 3.4mm

75.6 MPa

44.0 MPa

H-adaptive convergence using Draft Quality elements:

Δ = 42%

Convergence in COSMOSWorks

13.6mm 3.4mm

82.1 MPa79.3 MPa

H-adaptive convergence using High Quality elements:

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

13.6mm 3.4mm

P-adaptive convergence using High Quality elements:

83.8 MPa102 MPa

80.0 MPa

Local 1.0mmGlobal 5.0 mm

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) EdgesHigh Quality Elements – 2nd Order EdgesP-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 << global mesh size

10 mm66 MPa

5 mm68 MPa

5 / 2 mm71 MPa

3 / 1 mm80 MPa

80

70

60

3 / .5 mm80 MPa

Von

Mis

es S

tress

(MP

a)

10 5 5 / 2 3 / 1 3 / 0.5

Δ=3% Δ=4% Δ=12% Δ=0%

Δ=21%

Manual Convergence Checking

• Contour Quality– Stress contours in continuous geometry should be continuous– Use Discrete Fringe Option (Plot Settings) to better see discontinuity or

“jaggies”– Not an absolute test of convergence but can show areas to check– Plotting element edges with results can show how they impact

results…they shouldn’t.

Manual Convergence Checking

• Error Estimates– Energy Error Norm plots indicate the difference in stress between adjacent

elements. Ideally…no difference– Not an absolute test of convergence but high error in areas of concern

should be investigated– Excellent way to compare the convergence level between design

iterations. If the error estimate in a region being optimized is kept consistent, results comparison should be valid

Edit Definition10 mm Global Mesh 3 / 0.5 mm Global / Local Mesh

Manual Convergence Checking

• Nodal vs. Elemental Results– Nodal results show the averaged result at each node based on the stress

from the adjacent elements– Elemental results show the nominal stress calculated for each element– Ideally, there should be very little difference.

Elemental Results Nodal Results

COSMOSWorks Options - Mesh

• Mesh Quality– Use Draft on large models only when doing Trend Studies.

Otherwise, use High Quality when stress magnitudes are important

• Mesher Type– Only use Alternate Mesher if Standard fails and other

techniques for correction fail – No impact on accuracy

• Jacobian Check– More points = more stringent quality checks– No good data to support tightening this

• Mesh Control– Automatic Transition – mesher automatically applies mesh

controls to small features, holes, fillets, and other fine details of your model

• Can create larger models but a good option if you aren’t diligent about convergence checking

– Smooth Surface – mesher slightly relocates the boundary nodes to improve the initial mesh

• Automatic Looping– Meant to aid meshing problems – If this kicks in, mesh is

probably doomed and requires manual interaction– No impact on quality

COSMOSWorks Options - Mesh

Automatic Transition Off Automatic Transition On

Added Elements

Mesh Creation – Global Parameters

• Mesh Property Manager– Default size selected by program, based on the

model volume and surface area– Global Size – average element size– Tolerance – defaults to 5% of the global element

size

• Global mesh size needs to be small enough to provide a good overall stiffness solution– If the global stiffness is incorrect, local results

have no chance

Mesh Creation – Mesh Control

Mesh Control– Control vertices, edges, faces, and components– Parameters

1. Element Size for the selected components• Important when stress on one part is critical

2. Local Mesh Size on selected entities3. Element Growth Ratio – value multiplied by control

element size each subsequent layer4. Number of Layers of Elements – number of

element layers suggested for growth of element size from control size to global size, if the mesher needs more layers for a smooth transition to grow the element size to the global size it will automatically use more

1.

2.

3.

4.

Mesh Creation – Mesh Control

0.2 Global

Mesh Creation – Mesh Control

Recommendations:

• Use Mesh Control to place a refined mesh strategically in your model to improve accuracy without making your mesh overly large

• Choose a local mesh size 1/3 to 1/2 the global mesh size (or that of the surrounding surfaces)

• Use the defaults for Ratio and Layers unless there is a compelling reason to change them

Impact of Geometry on Accuracy

• Element shape can impact the accuracy of the element and resultant stresses– Recall the Jacobian error in an earlier example

• The more an element deviates from the ideal shape, the more error is introduced – the element calculates more stiff than it should

• Element distortion results from placing too large an element into tight curvature or a rapid transition from one size to another

• The features on your SolidWorks model can affect this

Jacobian = 1Jacobian >> 1

or Negative

Aspect Ratio = a/b

b

a

Ideal Triangle or Tri FaceEquilateral Triangle

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

Other Problems…In 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 << smallest feature size, shells

might be an option– Put another way, the area smallest face should be

much larger that the area of the feature edge– Rule of thumb: If you can model your part with a mid-

surface and it looks the same as the solid, shells are probably valid

• Accuracy local to joints is lost using shells

Shell Meshing vs. Solids

Half Wall Thickness Gap Must be Corrected for Mesh Continuity

T/2

Shell Meshing vs. Solids

This part is a good candidate for a shell model.Would shells be more accurate than solids?

106”

0.12”

Shell Meshing vs. Solids

6.596.5765.105.1354.344.3442.022.0231.721.6421.331.061ShellSolidModeFrequency & Static Study Results:

SolidsMode 5

ShellsMode 5

• Both Models used 1.0 Global Mesh Size• Frequency Studies are good for comparing model

stiffness• A static bending study shows that the stress

response can vary greatly.

Presentation Summary

• In this COSMOS Companion unit, we explored the impact of the meshing decisions you make on the accuracy of the solution. In this context, we discussed:– Basic meshing concepts– Controlling mesh sizing with local and global controls– Convergence and automatic adaptivity options– Means to evaluate mesh quality– The impact geometry has on mesh quality– The choice between shell and solid elements

• Examples were presented that showed how important mesh quality and convergence is to making correct interpretations of the results

• Some recommendations on mesh control and other mesh settings were made.

• Finally, we emphasized the importance of user involvement in ensuring reliable results. The wrong answers can look a lot like the right answers so your diligence is always required.

Conclusion

• For more information…– Contact your local reseller for more in-depth training or

support on mesh and solution accuracy.– Review the on-line help for a more detailed description

of the features discussed– Attend, or better yet, present at a local COSMOS or

SolidWorks user group. • See http://www.swugn.org/ for a user group near you