Sean O’Neill, Applications Engineer
Author: Sean O’Neill, Applications Engineer, Prism Engineering, Inc.
I was recently solving an FEA study for a project I was assigned, and I found myself confronted with a seemingly terrifying responsibility: I must ensure, with a high degree of accuracy, that my product design will ‘fit the bill’ in production. The product itself will hopefully stick around for a long time, so it’s important that it’s useful and done well. If a product I sign off on proves to be faulty after its release in production, the proverbial finger of blame will be pointed in my direction.
Whether I’m using SOLIDWORKS Simulation to assist in calculating my FEA results or performing calculations by hand, the goal in both instances is exactly the same: to validate the integrity of the design in question. While I could certainly run the gamut of reasons why leveraging SOLIDWORKS Simulation’s linear statics capabilities simply makes more sense, the primary focus of this blog post will be on the topic of mesh density.
In the following real world examples, we’re going to look at why and how consideration given to mesh density directly affects actual product design changes and approvals.
A friend of mine who works on the other side of Pennsylvania (I’d tell you his name, but he’s a Steelers fan) was recently asked to approve designs for hole-wielding aluminum plates intended to be featured and relied upon in his company’s job shop. The three designs above, as you can see, vary noticeably from design-to-design; the second is much wider than the first, the third much taller than both the first and second, etc. Using the configurations and multi-study capabilities of SOLIDWORKS, I’m able to compare the results of all three designs and their respective studies in a useful, quadrant-sectioned layout.
All three versions of the plate are subject to the same fixture conditions and the same applied forces. The left sides of the plates are fixed, and a 2,000 lb. pull force is applied to the opposite-side faces. The simulation is run with material properties derived from the SOLIDWORKS-provided listings for 1060 Alloy, which my friend wants to use because of its affordability and availability.
For example, in my initial run of the smallest plate design (the study in the upper left quadrant), I notice that my von Mises stress plot reports that I exceeded the yield strength of my material — around 3,999 psi for 1060 Alloy. After my first run of this study, it appears to only do so by a questionable margin, according to the plot. This begs the question: “Am I going to put all of my trust into this results plot?”
The answer is no. The mathematical model – comprised of my preset values of items like material properties, supports, and loads – has been reviewed and is sure to be accurate. The murky area resides in my mesh settings, which could quite possibly require refinements before we contemplate proceeding with any potential changes.
When performing FEA, situations like the one we encounter with version 1 of the holed plate have always struck me as intriguing. Initial returns report that I am over the yield strength of my material; to the untrained eye, this might be enough to say, “1060 Alloy is an awful idea. I need something better,” or “There is no way this plate will hold up with the hole intact; we need to add support material.” However, we are clearly very close to the yield strength of the material. I think we owe it to good old 1060 Alloy and the designer of this model (obviously a Certified SOLIDWORKS Expert (CSWE), based on the CAD-modeling prowess displayed in this part) to do some further digging.
In any FEA study with considerable ramifications, you certainly want to keep a keen eye on how you are defining your modular elements. Not doing so is careless, akin to solving complex, tight-tolerance equations while relying solely on your mental number-caching abilities as a solver. In the example below, you’ll see that, across the thickness of the model in question, we only have one solid element. If you’ve used any kind of FEA package in the past, you should quickly identify this as a major ‘no-no.’
Another thing I’ve noticed when I analyze the reported element level stresses in the given result, is that I’m seeing semi-drastic differences in localized stress areas. SOLIDWORKS Simulation presents this very clearly:
Because the color difference from the pictured red-colored, cylindrically-mapped element is so different from that of its neighboring elements, I can conclude yet again that further mesh refinements are likely required to obtain assuring results.
As a function of refining my mesh, I am technically adding more degrees of freedom to my analysis. Because a finer mesh necessitates more elements, and more elements necessitate more nodes, we are bound to gather more specific displacement data in localized modular areas such as the cylindrical face pictured above. Since our heaviest stress area is rightfully assumed to be located within and around the crevice, this is very important.
In fact, I could tell SOLIDWORKS Simulation to apply a denser mesh in the revealed areas of concern (namely, the crevice area). By applying specific mesh controls to entity areas of interest (i.e. by splitting the body into two with the Split command), we can lessen the density of the mesh in areas I’ve shown to be less important in predicting stress behavior. More importantly, we can assign the mesh in the crucial regions to be much denser. This will provide more specific results:
As stress is dependent on displacement, we can deduce that as our displacement metrics increase in reliability, stress-level accuracy can be expected to rise as well. In many cases, stress results will rise more noticeably. After applying a finer mesh to this plate, I am able to examine elemental stresses in the area of concern once again:
In my new results, I am able to get a more exacting look at the stress in the localized max-stress area. Whereas my result plot reported a maximum stress of approximately 4,560 psi in my initial study, I’m now seeing a maximum stress of 4,670 psi. After refining my mesh further, I start to see more convergence in my results, which leads me to reliably evaluate that this part cannot withstand the allotted pull it will regularly fall subject to in Mr. Pittsburgh Steelers fan’s shop. He might have to spend a little more money in the way of extra or different material, but he was able to pick this up in about 10-15 minutes. This was time and cost-efficient.
With this initial model, the test results that were first reported were far closer to the yield strength of material. Through mesh refinements and study result-comparisons, we came to realize that while the first results validly reported that the part could not withstand the load, they misleadingly informed us that we were closer to meeting the yield strength than we actually were. The results I ultimately drew were much closer to 4,700 psi than 4,500 psi. This exemplifies why exercising mesh refinement techniques is so beneficial and important – it leads us towards convergence of stress results, a huge indication that we’re getting the right answers to our analysis questions.