Regarding FEA, Who Are You Calling Dumb?

I like using analogies. When it comes to finite element analysis (FEA) elements, think of them as players on your football team who have a certain level of intelligence.

3D continuum elements are what I call “smart.” They understand what is happening inside their volume. Mathematically, this is through their shape functions and internal displacement responses. However, there are degrees of smartness; parabolic second-order tetrahedral elements and first-order brick elements have an acceptably high IQ. However, distort those elements and they will produce poor results. These are team members who are not playing to their full potential. They need coaching to get organized into a better mesh distribution. First-order tetrahedral elements have an unacceptably low IQ. You do not want them on your team.

A CAD design, meshed properly with 3D solid elements, will create an FEA model with a well-defined response. The intelligence of the model is really helping us out. We do not have to do so much thinking about how the elements represent the displacement or stress distribution. But as the coach, we are going to be critical about preparation and performance.

FEA solvers do not know anything about CAD geometry; they understand nodes and elements. So, the raw input file describes the 3D geometry via these smart 3D spatial elements.

Now we come to the 2D shell elements and 1D beam elements. I invariably describe these as “dumb” when describing their characteristics.

So why is a 2D shell element dumb? It has no concept of the world outside its datum mid-plane surface. I cannot directly mesh a thin shell type CAD model with 2D elements. Techniques, such as mid-surfacing, explain to the poor old shell element where its mid-plane is. We even need to tell it what thickness it has and which direction is up. Smart preprocessing can associate the CAD geometry thickness to the element, as an FEA physical property. But even then, we need to check accuracy.

The input file created for the FEA solver describes the design component as 2D surfaces mapped into 3D space, with a parametric thickness. We, the analyst, work harder to idealize the structure so that this representation will work adequately.

The 2D shell element guesses what is happening through thickness, by extrapolating from the mid-plane. Pure in-plane load assumes a constant stress variation through thickness. That’s OK for in-plane stresses, but shear stress through thickness is ignored for a plain stress element. Bending uses a linear variation of direct stress and a parabolic distribution of shear stress through thickness.

The B Team

So why have these dumb elements on our team? By now they should have been eliminated because of the limitations that we have seen. We can indeed view them as the second team, and they will struggle to perform well in a general, chunky, 3D component. However, compared with our star players, the 3D solids, they are dirt cheap. If the conditions are right, and we have thin shell-type design components, then our “poor performers” really start to shine. They have limited horizons, and will not overthink the problem, as their 3D colleagues would do in this case. Their approach is “I’ve been told it’s a shell, so I will model as a shell.” This is where our 3D superstar gets a little out of his depth, to excuse the pun. His approach is: “Space is space. What is a shell?”

So, selecting 3D solids or 2D shells is rather like picking the right team, for the right conditions. My professional football analogy is rather suspect, but there must be a comparison to pitching your multi-million-dollar star players against a scratch college team, on a muddy field with 300 spectators present. Being a Brit, maybe I should stick to rugby at this point.

So, where does that leave the 1D beam elements? They can only handle 1D concepts. They understand what happens along their axis, but have no clue about response in the cross-section. They follow simple rules to take a guess at what is going on out there. These guys are the bottom of the pay grade. However, we can afford them in large numbers; it will not put the smallest dent in our wallet. They also play to their strengths. The approach is familiar: “I’ve been told it’s a beam, and I’m going to handle it like a beam.” Their report back to you, the analyst, is straightforward. If we set the superstars onto this type of structure, we get a large salary bill, and every one of them tells a complicated story.

There we have it: another analogy. Use it to pick your team, but remember not to insult the players too much!