[Editor’s Note: In the past, when you finished designing an important model, you sent it to highly specialized professionals for finite element analysis (FEA). But with the introduction of simulation capabilities in 3D CAD systems, more and more design engineers are taking on at least some of the FEA themselves. It’s often just faster to do it yourself—at least as you rough out your design. That led us to ask FEA expert and instructor, Tony Abbey, for some tips. What should every design engineer know about FEA?]
This blog started as a very interesting challenge; could I distill everything that a designer should know about FEA into a few key topics. There are many areas that could be covered, but here are the ones that I think are the most important and have made the cut!
Part with mesh created in Creo Simulate
If you have ever worked through any FEA theory then you will probably remember that the fundamental process is to create a stiffness matrix for each element, then reassemble these into a system stiffness matrix. That matrix is inverted and multiplied by the applied loads to solve for displacements. And that’s it! No strains, no stresses, and no internal forces at this stage – just displacements at the nodes.
That seems counterintuitive – surely, we primarily want stresses. In fact, many researchers in this field beat their heads against a brick wall during the 50s and early 60s, trying to solve directly for stresses. The breakthrough came when it was realized that solving for displacements would allow much easier programming and automation. That’s what we have been stuck with ever since!
So, our solutions are reasonably accurate for displacement and therefore stiffness, provided we set up the model carefully. For a stiffness or natural frequency driven design, we are in good shape. However, if we carry out a strength assessment, we need stresses, and that’s where we can run into trouble.
To get from the continuous displacement solution to the required stresses, the FEA solver works back through the element stiffness matrices. This is done one by one - and there’s no guarantee of matching stresses across element boundaries. Think of each element putting in its own vote as to what the level of stress should be!
We need a fine mesh (lots of elements) in regions where there are high stresses and stress gradients. This gives good accuracy by providing a good sampling of the stresses present - plenty of votes available!
The accuracy of the stresses also depends on how well we set up the mesh. We need the mesh to be as regular as possible with good shaped elements. A good shape means a perfect square for a shell element, a perfect cube for a brick element and equal angles for a tetrahedral element. Any deviation away from this shape starts to reduce the accuracy of each element. Very badly distorted elements can in fact lead to contamination of the overall solution.
Everyone makes mistakes when building up an FEA model, it is just a natural part of the build process. One of the most common mistakes made is to forget to fully constrain the model down to ground. This means that one or more rigid body motions, or mechanisms, have crept into the model. Imagine a model floating around in outer space, it has six rigid body motions: three translations and three rotations. If the model is now brought down-to-earth and connected to surrounding structure, these rigid body motions must be eliminated, or the model won’t solve. This is done by constraining the structure.
There are two classic traps here. Imagine a simply supported beam. The vertical center load is balanced by the opposing vertical reactions at each end. Intuitively, we think of the only motion as being in the vertical sense, so surely, we only need to supply vertical reaction paths. This would be true of a simple hand calculation, but the FEA solver is not working in this way for linear static analysis. Remember that the assembled system stiffness matrix is inverted first. Then the loads are applied. This means that the matrix inversion is independent of the loading. The FEA solver doesn’t care whether the loads are in balance are not, it just wants to make sure all those rigid body motions are eliminated, so that it can invert the stiffness matrix. So, in the case of our beam, we have to make sure that the other two translations and the three rotations are taken care of by providing adequate constraints.
The other common trap occurs when we have a system which is completely defined by the loading which is in equilibrium. Examples include a scuba tank which resists internal pressurization, and a boat which has its weight balanced by the buoyancy up thrust. I will leave those two as challenge for you to think about! I will explain how to handle those in a later posting.
Assuming we have set up a good quality fine mesh in areas of stress and we have fully constrained our model, it is tempting to assume that we are going to be modelling reality!
Unfortunately, FEA is always an approximation to reality. The biggest area of approximation is usually in interpreting the boundary conditions of the real component. The tools we have are quite rudimentary, in that we can fully build in, simply support, put on rollers and other scenarios. None of these boundary conditions really exist in real life. There will always be some interacting stiffness between our component and its connection to the rest of the world.
Imagine a cantilever steel beam fully welded into a thick steel wall. We typically model this as fully built in; however, if we were to strain gauge the real structure we would find deflection locally throughout the wall. So, there is a natural compliance which we are ignoring. Another example occurs when the beam is a spar of a wing, and it is connected to the fuselage by a root fitting. There is a significant flexibility at the root now, and we have to find some way of modelling this.
I will be coming back to this theme, and will also discuss real-world loading, in later posts.
Well that’s my top four, but it was a struggle to pick the most important. Look out for sneaky additions to this list in upcoming posts!
Want to learn more about how to make simulation work for you and your team? Download the infographic to learn the Top 5 Best Practices for empowering design engineers. And get started realizing the potential of simulation: fantastic products.