In short, this is what each of these study types will show you:
- Linear: This study type only analyzes a model for the linear elastic region of the stress/strain curve of a material. Any results showing that the load stress is exceeding the yield stress of the applied material invalidates the results. It would be reasonable to assume the design is a failure since yield stress was exceeded but does not reveal a true behavior of the stress and deformation for results beyond yield stress.
- Nonlinear: This study type allows for analysis of materials in the linear elastic region but expands on that to include results in the plastic region of materials. That means that for stress results beyond yield it can be made to accurately represent those stresses and displacements. Additionally, nonlinear is also capable of analyzing nonlinear material types (like rubber) which the linear elastic and buckling analysis are not capable of. Nonlinear can also be used to analyze buckling itself in place of the buckling analysis.
- Buckling: A failure due to buckling is a special case where the stiffness of the material in combination with the geometry has allowed the design to become unstable and fail before a linear study would predict. For example, hold a drinking straw from the bottom and press axially down from the top. You will find that the straw suddenly kinks and loses all ability to resist your force. This is what buckling is testing. Important to note about this study type is that "Displacements" are just qualitative representations of how the buckling failure would appear if it occurred. The numeric values of those plots do not have a real life meaning.
This all being said, your linear and nonlinear results should agree but do show a good amount of deviation. The most likely cause of this, based on your images, is that you have not meshed with enough elements across the thickness of your thin walled tube. If you were to mesh with two elements across that thickness and then rerun both the linear and nonlinear studies I believe you would see them start to agree more closely with each other.
You are much more generous than I am. I with held comments as they would have been snarky and not provided the valuable information you did. I get scared when someone wants to trust the results of their FEA analysis and has demonstrated a lack of structural knowledge. You can make costly mistakes relying on "pretty pictures" if you don't know how to accurately setup a FEA project. There are a lot of degreed engineers that don't know how to correctly do it. I consider myself marginal and wish I could spend more time learning.
Kudos to you.
I just figure it is scarier to leave the question unanswered.
Thanks Ryan. I was not intending to blindly trust my original results, hence asking here and doing some research to get multiple answers. I also figured asking broader questions would cover anything I didn't know I didn't know. That said I really appreciate your response! I refined the mesh and my nonlinear and linear analyses now agree, although I'm going to look into meshes a bit more to make sure. As is my understanding, the buckling displacement is only what it would look like at the minimum buckling load, which apparently is 14 times the force in this case; so no danger of buckling. Glad I do have a bit of time to learn this better.
I'm glad that helped. Thanks for stopping by and throwing your question up.