I see a lot of misunderstandings between SOLIDWORKS Simulation results and empirical stress analysis methods. These usually are caused by a lack of understanding of what the software calculates, but always results in someone questioning if the software calculates correctly.

SOLIDWORKS Simulation goes through rigorous NAFEMS Benchmarks which are a standard set of problems with known solutions that all commercial FEA Packages use to check accuracy. As long as the solution is within set tolerances, the software is considered acceptable. These benchmark problems are available for viewing if you use the drop-down menus in SOLIDWORKS, Simulation > Help > NAFEMS Benchmarks. A new window will open that you can then select verification problems to see the reference values and the values that SOLIDWORKS Simulation calculates.

With that cleared up, I want to get to the misunderstanding. The most common misconception I see is, "I calculated the stress by hand, and SOLIDWORKS Simulation is giving me something much higher."

There are a few reasons for this:

- You only calculated a stress component and are comparing to a failure theory
- You calculated a gross stress not a localized stress
- You aren't comparing the correct plots from simulation to your hand calculation

Before we discuss the items above, let's talk about stress. In terms of stress, we can think of them as either gross, which are evenly distributed across a cross-section, or localized which are at a small particular region or point. In this case, it’s easy to calculate a gross axial stress by hand, just divide the load by the area and you’re done. It’s not easy to calculate the localized stress concentration around a hole by hand which is where the stress concentration factors comes in, relating the two together by simple multiplication so that it becomes possible to determine by hand. This method was developed with experiments before FEA was a common tool so that engineers can get their jobs done, but it is not a failure theory in itself. For an example see below:

Kstress*gross stress = localized stress. In this case Kstress is the stress concentration factor derived from a table or graph.

Once you have the localized stress for your axial direction, in this case well call it σ_{x}, the job is not over. For most general failure theories, you still need to calculate stresses in the two remaining normal directions, and the three shears. From there you can apply a general material failure theory such as von Mises to calculate a factor of safety. In this case what von Mises calculates are general state of stress in a local region using the following formula that takes all 6 stress (3 normals and 3 shears into consideration):

σ_{vm }= (0.5[(σ_{x – }σ_{y})^{2} + (σ_{z – }σ_{x})^{2} + (σ_{y – }σ_{z})^{2}] + 6*(τ_{xy}^{2} + τ_{xz}^{2} + τ_{yz}^{2}))^{1/2}

From the equation above you can then calculate a factor of safety at that particular point. FOS = σ_{yield}/ σ_{vm.}

This does not mean that von Mises is the only failure theory, there are many out there. Many companies, codes and specifications have developed internal empirical ways of determining safety in many cases to make this process less taxing on the engineer, particularly in the case where these entities existed before the FEA era.

For example, a company may say it is too time consuming for an engineer to calculate that von Mises stress by hand and thus only σ_{x }will be calculated, and as long as it is less than some factor of safety on the yield strength of the material, say 5, then it is okay. They are relating σ_{x} to a general state of stress, like a σ_{vm}, which again reduces the number of stress components that needed to compute if a failure will occur. These simplifications are perfectly fine when there is one direction of high stress and the other directions are minor, using a higher factor of safety accounts for the other stresses that weren't calculated. However, when dealing with loads that act in multiple directions, uneven distributions and many discrete anomalies, often these empirical methods fall apart, and a more general theory of material failure needs to be utilized. That's when Von Mises, Tresca, Maximum Principal Stress, and other failure theories need to be used.

If you aren't comfortable with understanding the difference between calculating a stress component and calculating material failure, read up on some of those failure theories listed at the end of the previous paragraph. I'm sure you'll find some additional clarity.

*By: Brandon Donnelly, Simulation Applications Engineer*