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 Fear is one of the most powerful emotions a human being can ever experience.  It can trigger quick thoughts and actions that will help us fight back or flee from whatever situation we perceive as danger; it can be paralyzing, as well, robbing us of valuable experiences and opportunities that we may have otherwise enjoyed.  Take me for example: I used to be afraid of driving the freeway. The thought of it was so overwhelming that I avoided at all cost going anywhere that wasn’t  “local”, and even scheduled appointments with my doctor, who had his office in Mountain View,  ONLY whenever my husband was able to drive me there.  However, as careful as I always was to avoid the freeway, and given the fact that Murphy has made my home his residence, one day I ended up on I-880 just like that, and it was then that, in the midst of my panic attack, I realized that I was not afraid of the freeway, but of not knowing my way around the freeway. I was afraid of getting lost. Well, we found an easy solution for that by equipping my van with a GPS unit. My life has improved ever since! Now I get lost in style whenever the GPS takes me to the middle of a swamp and proudly declares, “You have arrived”… but at least the fear is gone.

But why did I have to tell you all this? Well, because I’m beginning to think that for many people it’s almost the same with FEA.  I’ve always been interested in simulation. I was excited to finally have access to simulation software through SolidWorks and be able to learn how to use it, but I soon became discouraged by comments I read and heard from people that didn’t consider FEA as a useful or even reliable part of design. Their idea was something like “I won’t trust results that I can’t calculate myself”, but the more I learn about how Finite Element Analysis works (not only SolidWorks Simulation), I honestly don’t see how they are going to be able to obtain results “by hand”  without the use of the finite element method or some other form of numerical method approach, or without making use of some extremely simplified mathematical model. Unfortunately, although it’s true that most practical problems  in engineering can be represented by mathematical models of the actual physical problem, and are generally governed by differential or integral equations that represent them, it is also true that due to complexities in geometry, boundary conditions, and others,  these equations can’t be solved at all without the use of numerical methods to obtain an approximate solution to the problem. The other option, of course, is to go through the loop of the build-test-build cycle as many times as necessary, but that can be expensive and time consuming, without mentioning that it doesn’t really provide the designer with much information about the behavior of the product until near the end of the process.

So, if FEA is only a way to provide a solution for the series of equations that describe the mathematical model and if those equations derive from applying exactly the same laws and theory that we would otherwise while solving the problem “by hand”, why is it that some people out there are so afraid of it?  I think it may be perhaps that, same as me and the freeway, people aren’t precisely afraid of the finite element method per se, but of “getting lost” in the Finite Element Analysis software. After all, your results are only going to be as good as your mathematical model and the input you provide, and you still need some common sense when it comes to interpreting the results of your analysis.  With this in mind, FEA software can be a great tool for design or just another way to get lost in style.

A quick example is in the following simple problem, taken from a popular engineering textbook. In the example, we have a stepped cylindrical shaft that is rigidly clamped on one end and that has a force of 1000 N applied to the opposite end.

I meshed the model using draft quality solid elements, and the default values for element size and tolerance.

Then generated a stress plot showing the normal stress in the X direction, the stress you would usually calculate using the simple formula 

where sigma is the normal stress, F is the force and A is the cross sectional area of the shaft at the location of interest. By using Probe to investigate the value of the stress at some node in the middle along the length of each step, I realized the results for this case are very similar to those obtained “by hand”.  

Notice how the value of the stress changes, however, as we approach the ends of each step and the transition between areas.

So then I wonder what would happen if I shortened the shaft. I created a second study using a short configuration of the model in which each step was only 0.01 m, instead of the previous 0.5 m. The diameters, fixtures and force all remained the same, and so did the quality of the mesh and even the element size and tolerance.  My results, however, didn’t match those obtained applying the same formula as before.

I even refined the mesh, used high quality elements and all, but the results still didn’t match.

 Then it occurred to me that the formulas we apply for the solution of this kind of problems were derived assuming, among many other things, that we were trying to figure out the stress in a section far away from the point of application of the load, because in general, the value of the stress at any point in the section is actually given by

And this value changes across the section and is very different from the average value given by the first equation. The variation is small in a section far away from the points of application of any loads, but very noticeable in the neighborhood of these points.  When the shaft gets shortened, the steps become so thin that there is no way to be far enough from the point of application of the load, so the assumption we made before doesn’t really work here.  What I wonder is what to think of the results obtained in this case by using SolidWorks Simulation.  Are these even meaningful results? Should refining the mesh even more work better in this case? Unfortunately, I will never know because I tried to refine my mesh even more and received a message saying I had insufficient memory and needed to increase the value of my elements.  I’m still very new to FEA and SolidWorks Simulation to know if there’s a different approach to this kind of problem, so if you have any ideas on this, please let me know.  I’m just excited to finally be learning about FEA.

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