When presented with FEA results, stress results are often the focus. But how do you interpret those FEA results? And how do you build confidence that the results presented are accurate? We often scrutinise model geometry, boundary conditions and inputs, but commonly overlook mesh convergence. Mesh convergence is often not included in analysis reports, despite it being a key step in interpreting and validating FEA.
Why should I pay attention to the mesh?
Appropriate mesh sizing is a balancing act. A very fine mesh will tend to give more accurate results, but may take a long time to compute. A coarse mesh may run quickly, but at the expense of accuracy. The best mesh is one that gives an acceptably accurate result in the fastest time possible.
Analysts use a combination of experience and an understanding of the physical behaviour of materials to select suitable mesh sizes. Most people don’t even see this happening, they simply receive the results at the end.
So how can we gauge whether the analyst made the right choice? The answer is a convergence check.
Do high stresses actually represent failure?
It may be tempting to see a result that exceeds the yield stress and interpret it as a failure. But this may not be the case. Think about what physically happens in this scenario. Will the part bend, break, or simply see some small deformation in an isolated area? To make things more complicated, the maximum stress may not even be real at all—in some cases it can even grow as the mesh size is reduced, eventually stretching out to infinity.
What if your mesh isn’t converging?
Sometimes, reducing mesh size has the opposite of the intended result. The observed stress can begin to grow at an increasing rate! This is referred to as a singularity. Singularities may have a number of causes, including:
- Point loads (loads applied over an infinitesimally small surface area)
- Discontinuities in the model geometry (sharp edges)
- Inappropriate constraints (boundary conditions)
- Numerical errors in the solution of the FEA equations
One approach to dealing with singularities is to simply ignore them. Saint-Venant’s Principle states that the effects of a singularity will decay quickly—and if we consider the stress a short distance away the result will be accurate.
But what if we want more accurate results in the region in question? The sharp edge problem may be solved by adding a small fillet, however this needs to be physically representative and have an appropriately sized mesh applied!
In some cases, it may be necessary to consider a non-linear model that more accurately represents the behaviour of the material after yield stress is reached.
Whatever the application, understanding mesh sizing and convergence is crucial to interpreting, and building confidence in, your FEA results.