Linear vs Nonlinear FEA

You have a staff of 10 mechanical engineers. Over the years, you paid to get them off the drawing board and into 2D CAD. That naturally led to 3D.

Then one day, a fine young engineer said, “Hey boss, we could simulate all that stuff we’re building and breaking out in the lab… right from our 3D CAD models.”┬áSay hello to FEA (Finite Element Anlaysis)… and you thought 3D CAD was expensive!

But, after a few years and lots of virtual successes, that same engineer comes back to you and says, “Hey boss, we need to spend some cash on nonlinear FEA.”

“Hold up… I thought FEA was a problem I already paid to solve?!?” You scratch your head and try to blow the fog away from rusty memories of college math. “I know there was something in there about linearizing complex systems of equations… is that what he means?”

Your son is a producer at the local TV station. He’s always talking about how cool it is to work with the non-linear video editor. Does that have something to do with this? What’s this all about? More importantly, why should you spend any money on it?

Well, your engineer may be correct. Your FEA toolset may be incomplete. It may well be worth your investment to add nonlinear FEA capabilities.

Linear FEA

You probably started down the FEA path with what’s known as simple, static, linear FEA software. Don’t feel bad! That’s what most people do. It’s the best way to get started. This level of software is meant to simulate very small part deflections in materials that aren’t being permanently deformed by forces applied. “Linear” refers to the fact that metal parts bend linearly and proportionally to the load applied… and then spring back to their original shape.

If you stand in the middle of a large I beam, the deflection is probably too small for you to even see. Linear FEA is perfect for these situations.

Nonlinear FEA

Ever see a circus strong man bend a metal bar? You’ve just witnessed what happens when you push past the yield strength of that material. The deflection achieved is no longer linearly proportional to the force applied… and the material may even permanently deform. You’ve just gone beyond the assumptions that make Linear FEA solvers valid. You’re going to need something more sophisticated to simulate these kinds of problems.

What to look for:

  • Extreme loading conditions (like a car crash)
  • Moving parts
  • Non-metallic materials like exotic composites or rubbers
  • Contact between components (both planned and unplanned)
  • Bolted connections
  • Short duration impact loads

In a nutshell, linear FEA is the simple stuff. It will get you pretty far. In fact, if your product can effectively be modeled with the assumptions of linear FEA- you should absolutely use it! Solve times will be faster and the results will be just as good as nonlinear FEA.

But, if you have a lot of contact, nonlinear materials, or forces that push past the yield strength of more mundane materials- it’s time to augment your FEA toolset.

Image by bengt-re