# SOLIDWORKS Simulation: Finding Accurate Stress Results Around a Singularity Part 2

July 7, 2017

## Example 2: Sharp corner on L Bracket

### Location of Singularity

For this example, I am going to use a model almost all SOLIDWORKS simulation users are familiar with but with a few modifications. As you can see in Figure 14, the L bracket has a sharp corner where it changes direction. This sharp corner is a definition singularity and a perfect second example to confirm my results.

### Sensor Grid and Sensor Locations

Using the same method as described in the previous example I created a grid of faces where I could place sensors. I put 10 sensors starting at the location of the singularity and placed another sensor at every intersection moving away from the corner as shown in Figure 16. For sizing reference the first and last sensors are 2 mm (0.078 in) apart. As you can see in Figure 15 the grid was placed along the entire length of the face and this was done to get a better resolution of the mesh around the sensors and have the ability to incrementally increase the mesh away from the sensors.

### Results

I was able to get all of the sensors that were not on the singularity location to converge after refining the mesh in the area as shown in Figure 17. Figure 18 is proof of all sensors convergence in a plot where the resolution is not skewed by the singularity. All of the data can be seen on Table 9 and if you look closely you can notice the eleven million degrees of freedom in run 6 which is ridiculous but I wanted one more data point and to see how far I could push the problem.

Table 8: Von Mises Stress Values at the Sensor Locations and the Degrees of Freedom for 6 Different Meshes of the L bracket with a Sharp Corner
 Von Mises Stress (MPa) Sensor Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 1 110.382 158.072 265.174 397.257 718.952 1354.51 2 139.774 123.274 99.908 97.4845 96.3525 96.6774 3 93.6944 79.6257 75.2115 74.3946 74.1601 74.3239 4 78.3395 70.1509 64.9787 64.6465 64.625 64.7646 5 74.1552 60.4152 59.3119 59.1251 59.1377 59.2961 6 58.8188 57.7936 55.634 55.5161 55.5623 55.1641 7 55.4864 54.1118 53.0916 52.979 53.0301 53.1641 8 53.2633 51.7181 51.2172 51.1173 51.176 51.3084 9 51.0229 50.0535 49.7581 49.7052 49.7728 49.8906 10 52.235 49.1785 48.6557 48.572 48.6421 48.7568 DOF 51594 64482 131232 264159 2634474 11645379

### Conclusion

Since all the sensors converged after the third run I can comfortable say that the results are independent of the mesh and I can get that independence as close to the singularity as I desire as long as I get my mesh small enough. For this example the distance of the sensors from the singularity can be seen in Table 9 and the closest sensor converged and was 0.22 mm or 0.0087 in from the singularity. This is really close and the values seem believable especially after they are compared to the same model but with a fillet instead of a sharp corner. The maximum stress I obtained with the filleted model was 102 MPa and the sensor that was .022 mm from the singularity read 96 MPa. Fairly accurate if you ask me.

Table 9: Sensors Distance from Singularity
 Sensor Distance From Singularity (mm) Distance From Singularity (in) 2 0.222221 0.008749 3 0.444443 0.017498 4 0.666666 0.026247 5 0.888887 0.034996 6 1.111111 0.043745 7 1.333332 0.052493 8 1.555553 0.061242 9 1.777777 0.069991 10 2 0.07874

As the mesh got more refined the singularity’s effect and size shrank. In Figure 19 I set the color scale to show red for the yield stress and as you can see in the image and data the effect of the singularity is very small. I zoomed in a lot for Figure 20 and the blue line is the entity separating sensor 1 and 2 and has a length of 0.22mm. So, we can see that the singularity is not affecting much further than about a third of the line.

## Final Conclusion (TLDR;)

For those of you who scrolled to the end while only looking at the pictures here is my final statement for the results. The more you refine the mesh around a singularity the less of your model it will affect. The closest location I tried to get a mesh independent value for was 0.22 mm (0.0087 in) away from the singularity and I got converging results that were below yield and of a comparable value to a similar model without a singularity.  So if your simulation has a singularity that you cannot model away this procedure can help you locate where your values are no longer being affected by the singularity.