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# Divergence and Convergence for Simulation Results

Divergence in a model  leads to a stress quantity that continually increases as the user refines the mesh globally or in areas of localized high stress.  Divergence is typically encountered when the load transfer concentrates in the geometry at a sharp corner. The stress will continue to rise based on its own definition;

Stress=Force/Area

With a sharp corner the area becomes, zero.  This drives the stress value upwards with each new, tighter mesh. In manufacturing a perfect edge does not exist. All modern manufacturing methods will create small fillets.  The fillet helps transfer the load over a larger area hence eliminating the stress concentration.

Lets Discuss Convergence In a Simulation Model:

In Finite Element Analysis (FEA) the results are an approximation.  The way a user becomes comfortable with the stress, strain, and deflection calculated by an analysis depends on convergence.  A recommended variation of 5% stress between runs usually indicates good stress convergence.

To reach convergence a user can apply multiple methods, over the course of their analysis studies.

Global Mesh Refinement

The Global mesh refinement method indicates that a user over the course of three or four studies tightens the global mesh size incrementally until the calculated results are within the users specified convergence range.

Plus: Easy to adjust the setting of global mesh size.

Minus: Larger run times due to areas of low stress having the mesh refined as well.  The more elements in the Finite Element Model the longer the computing time.

Mesh Control

Mesh control allows a user to specify mesh refinement in localized areas of high stress leaving the global mesh density larger.  This is the recommended method.

Plus: Allows user more control over the mesh in areas of high stress. Keeps computation time shorter as only areas of interest are being refined.

Minus: This takes more time to setup and identify areas to add mesh control.Adaptive Meshing (H Method)

Adaptive meshing allows the users to apply “mesh cruise control”.  Simulation looks for convergence based on parameters the user specifies, usually a target accuracy for the Strain Energy Norm.  Simulation automatically adds mesh control in areas of calculated high stress. It is important that the original mesh starts at default settings, and it is recommended this method be used with standard meshing. Five iterations is usually a good starting point.  Note that H Adaptive is only run once, as the software completes the mesh refinement and runs for you.  Remember that if the target accuracy is not achieved, you can re-run the H-adaptive study again and it will continue from the last iteration.

Plus: Simulation automates the process.

Minus: Additional analysis setup time is required.When adding mesh control or mesh refinement always take small steps.  Mesh density should be adjusted in small increments. For example if a mesh control starts at 0.25″ the next change would be 0.2″.  We generally recommend a 20% reduction in mesh size with each successive analysis for applied mesh controls.

Let’s discuss Standard versus Curvature based mesh:

The Standard Mesh has been used from the beginning of SOLIDWORKS Simulation.  The Standard mesher uses the Voronoi-Delaunay meshing scheme for subsequent meshing operations. The Standard mesher incorporates a global size that reads the thinnest area of the component and dictates at minimum cross section at least two elements define the thickness in the mesh.  This may lead to mesh refinement  in areas that may not be required.  Manual mesh control can then be applied to refine specified areas.

The Curvature based mesh creates more elements in higher-curvature areas automatically (without the need to apply mesh controls).  Typically curvature based meshes do not need additional user applied mesh controls, and take less steps to achieve convergence.

Mesh Quality

The output from any simulation is mesh dependent.  An analysis of a model with a  good quality mesh will have different answers than the same model with a poor quality mesh. It is always important to look at the mesh plot and investigate the aspect ratio of the mesh.  Aspect ratio is a measure of the skew of an element, defined as the ratio of the longest edge/ shortest edge.  For a high Quality element, the Aspect Ratio should be less than 3.  Overall 85% to 90% of the elements in a mesh should have an Aspect Ratio of less than 3. A high Aspect Ratio will cause higher stress to be calculated in that element than surrounding cells.