In any numerical analysis it’s important to achieve convergence, which is the state where analysis has reached a solution that is (nearly) independent of the step size used. Let me illustrate.

In the figure above, there is a solid curve representing something we are trying to calculate. In reality, we have no idea what the form of this curve looks like, that’s the point of the analysis. For illustration purposes, I’ve shown it. Calculating values at two points, the start and the end, and connecting them with a straight line, gives a bad representation. This is shown in the image above by the line with triangular markers on it. To determine a value in the middle by using this line would give an invalid solution.

Calculating values at many points and connecting them with straight lines, we get a more accurate representation. With more and more points used, the representation of the solution comes closer to the actual solution. That is convergence. Values that don’t lie directly on these points can be calculated by interpolation, which is acceptable because once convergence is reached, the difference between the interpolated values and true values is small.

**If we don’t know the true values, how do we know we are close?**

I’m going to show how to use the plots from design studies in SolidWorks Simulation in order to perform a convergence analysis.. If the mesh is not fine enough, the problem is poorly represented. To ensure that the calculated values are independent of the mesh size, start with a coarse mesh and refine it. Look for changes in values along the way.

Take stress for consideration. Stress is a force/unit area. As mesh refines, elements become smaller. Since their area is shrinking, stress should increase. If maximum stress values drop, the mesh was too coarse making the problem mesh dependent. As the mesh starts to reach an adequate level of refinement, the stress should start a trend of increasing. Once these increases taper off the analysis is considered converged.

The figures above show an assembly of a clamp. Fixed on the bottom, with a load on the top. The concern is the maximum von Mises stress in the curved portion at the back. A design study linking the size of the mesh control on those curved faces and tracking the Maximum von Mises stress was used to create the plot shown above.

A couple conclusions can be drawn from this plot. The first is that at a size of 30mm on the mesh control was too coarse to be accurate. This is known because the stress decreases with the next refinement. Like I said previously, stress = force/area, as area shrinks, stress should increase. If it doesn’t then the force distribution is changing as a result of the mesh being too coarse. It can also be seen that around 18mm the mesh size starts to be appropriate for the problem and convergence starts its process. Looking at the curve from the 18mm size to the 0.75 mm size, it settles in on a value becoming horizontally asymptotic.

The second conclusion that can be drawn is that the maximum von Mises stress value is 101.2 MPa. This is the value of the asymptote and is the “true” value of the stress. The reason true is in quotes is because while it is the actual solution of the analysis, the analysis may have an idealized setup that leaves out some real world conditions like scratches, manufacturing tolerances, damages, fluctuations in material properties, idealized fixtures, etc.

In part 2, which will be published on Thursday, I will give you a step-by-step setup of how to do this in SolidWorks Simulation.

*By: Brandon Donnelly, Simulation Applications Engineer**Tune in to the SolidNotes blog on Thursday, May 1 for Part 2! For more SolidWorks Simulation Tips and Tricks, read Handling Difficult Shell Alignments.*