# Stress Singularity in SOLIDWORKS Simulation

In the midst to produce the best quality products, designers and engineers often use simulation to simulate the circumstances that a product will experience when subjected to different forces and stress. One thing that always bothers designers and engineers is that the accuracy of the simulation sometimes might not seem to be reliable. Hence, in this session, I am going to discuss about the stress singularity in SOLIDWORK Simulation. Of course, all the contents are referred to SOLIDWORKS Tech Blog CAD2M.

Before the manufacturing and real tests on a prototype, SOLIDWORKS Simulation provides user the chance to test the prototype virtually during the engineering phase in the project. It’s so powerful that it can help you to solve difficult engineering questions in a short period of time by using it mesh analysis and iteration functions inside the system. However, the correctness of the boundary conditions and parameters will bring a huge difference in result. Once you accidentally set the parameter incorrectly, all the computational efforts will be gone, and user needs to simulate again. Hence, due to this issue, I would like to share how to mesh modelling will affect stress convergent.

Let’s start with a basic concept which is known as principle of convergence. To further demonstrate how the convergence can be done, a simple example is used. Assume that there is a fixed geometry fixture in the two holes and a force is pushing in the counterbore hole. According to CAD2M, 5 static studies have been created to further discuss the details of convergence. Throughout the 5 studies, the mesh element size at the location where the highest stress exists. The mesh control is applied to decrease the element size at some regions such as the turning region. Below are some of the fine adjustments that have been done to further elaborate the convergence principle. As you can see in the diagram below, the mesh size becomes smaller and refined at the intersecting region. That setting is important to identify the accuracy of stresses applied to the region. After running the studies with similar forces and boundary conditions, the end results are as shown below. Maximum Von Mises Stress of different studies are as shown. The red regions are region with maximum stresses. As predicted, the stress value becomes more reliable with smaller element sizes. With a 4mm element size, the maximum stress spot quite small, like it is concentrated at an element node. After refining the meshes a couple times, the maximum stress does not really change at mesh size of 1mm, 0.5 mm and 0.25 mm. To have a clearer interpretation, a graph is plotted out. The graph above shows the convergence graph. It shows 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. Form the results, the stresses are converging to a certain value. Hence, further refinement is not necessary as the results will be almost the same and it will not influence the solution of study.

Sometimes, users might find the solution isn’t converging. This is the case known as stress singularity. It happens frequently in simulation study. A stress singularity is a point of the mesh where the stress does not converge towards a specific value. As the meshes are kept refining, the stress at certain regions keep increasing. Theoretically, the stress at the singularity is Infinite. Typically, this situation happens where the appliance of a point load, sharp corners, corners of bodies in contact and point fixtures.

If to show stress singularity in a clearer way. Let’s assume that the sharp corner has its fillet being suppressed. Once again, similar 5 studies created with same mesh controls at the sharp edges. Below are the results after running the simulation. This time the maximum stress at the sharp corner keeps increasing. In the diagram above, maximum stress is concentrating at the sharp corner (Red region becomes smaller). This is the sign for stress singularity. The plotted graph is as shown. The maximum stresses increase as the element size reduces. No sign of converging in the value. To prevent stress singularity, sharp corner can be solved by adding fillet radius at that corner. This means that the stresses at that location can converge and singularity will disappear. To allow users to better differentiate between stress singularity and convergence, a simple guideline can be applied, if the stress concentration is happened to be showing a finite value, then it’s the stress convergence. Stress singularity doesn’t mean that your study is wrong but rather a deviation created at the region. But at some distance from singularity, the stress results can be trusted also the displacement results are correct, even at the singularity point.