# What is a stress singularity in SOLIDWORKS Simulation?

With SOLIDWORKS Simulation it is possible to test your design during the engineering phase of your project. It’s a powerful tool to provide you direct answers to difficult engineering questions. And to get the right answers, it is important that you interpret the results of your Simulation study in the correct way. But sometimes a high stress value at a certain location is difficult to clarify. For instance a very high stress value at a point or a line. Can it be trusted? In this tech blog I want to help you with an issue like this.

# The basic principle of convergence

Let’s assume the following model, with a fixed geometry fixture in the two holes and a force pushing in the counterbore hole.

I created 5 static studies, and in each study I changed the mesh element size at the location where the highest stress exist. I used a mesh control to decrease the element size at this location. Below you can see the result of the 5 different meshes.

Figure 1: Mesh control element size of the different studies.

After running the studies, the following maximum stresses are obtained.

Figure 2: Maximum Von Mises stress of the different studies.

As expected, the stress value becomes more reliable with smaller element sizes. This can be noticed by the way the colours are displayed. With a 4mm element size, the maximum stress spot is quite small, like it is concentrated at an element node. After refining the mesh a couple of times, the maximum stress does not change also. Let’s review this in the graph below.

Figure 3: Convergence graph of the different studies.

The graph above is a convergence graph. It shows us the convergence of the stress at a certain location, based on the element size. Under normal conditions you will notice that from a certain element size, the stress will not change anymore. Now we obtained a converged value for the maximum stress, which can be used for the conclusion of the analysis. Further refinement of the mesh is not necessary, because it will not influence the solution of the study.

# My solution does not converge!

This can happen quite often in a Simulation study. This behaviour is called a stress singularity. A stress singularity is a point of the mesh where the stress does not converge towards a specific value. As we keep refining the mesh, the stress at this point keeps increasing. Theoretically, the stress at the singularity is infinite!

Typical situations where stress singularities occur are the appliance of a point load, sharp corners, corners of bodies in contact and point fixtures.

Let’s review this with the same model as before, but this time I suppressed the fillet feature at the location of the maximum stress. This introduces a sharp corner. Again, I created 5 studies, with the same mesh controls at the sharp edges. After running the studies, the following maximum stresses are obtained.

Figure 4: Maximum Von Mises stress of the different studies with sharp corner.

This time the maximum stress at the sharp corner keeps increasing. In the images above, it can be seen that the maximum stress is also concentrating at the sharp corner (the red area is very small). This is the typical behaviour of a stress singularity. Let’s review this in the graph below.

Figure 5: Convergence graph of the different studies with sharp corner.

# Conclusion

A sharp corner introduces a stress singularity in SOLIDWORKS Simulation. This can easily be solved by adding a fillet radius at that corner. This means that the stresses at that location can converge, and the singularity will disappear. Instead, a stress concentration takes over.

A stress concentration should not be confused with a stress singularity. A stress concentration will converge towards a finite value, when the mesh is refined. A stress singularity does not mean that your study is completely wrong. It introduces a deviation at or close to the singularity. But at some distance from the singularity the stress results can be trusted. Also the displacement results are correct, even at the singularity point.

If you have doubts about a stress in your study, then SOLIDWORKS Simulation can also help you. Right click at the Results folder of your study and select Stress Hot Spot Diagnostics. In the PropertyManager, select Run Stress Hot Spot Diagnosis. This tool identifies elements with high stress gradients. And can indicate the presence of stress singularities or stress concentrations. After the first run, the tool even gives you the possibility to run a check for stress singularities. Select Run Stress Singularity Diagnosis, to do so.

To conclude, I hope you have learned everything about stress singularities or stress concentrations. And it’s good to know that SOLIDWORKS can even help you with the Stress Hot Spot Diagnostics.

Written by Martijn Visser, Elite Application Engineer, CAD2M