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# Do these linear vs nonlinear buckling plots make sense?

## Do these linear vs nonlinear buckling plots make sense?

(OP)
I am doing linear buckling analyses (where everything is linear), and nonlinear buckling analyses where you have nonlinear geometry enabled and nonlinear material behavior (hyperelastic material). Everything is done in COMSOL. The structure is fixed on one side, and a forced displacement of -0.01m in the x-direction on the opposite side. It seems the linear model buckles earlier compared to the nonlinear? What could be the reason for this, and does it look okay otherwise?

The blue lines are the nonlinear plots, and red/yellow dotted line endpoint is the buckling strain and stress - I have just made it into a line for easier visualization.

### RE: Do these linear vs nonlinear buckling plots make sense?

Usually, linear buckling analyses (LBA) overpredict buckling capacity but it’s not always the case. It largely depends on a particular structure. However, in most cases, LBA gives a very rough estimate of critical load and only nonlinear buckling analysis can provide accurate estimation.

### RE: Do these linear vs nonlinear buckling plots make sense?

(OP)
FEA way, what do you think about me applying displacement instead of load? What difference do you think it would have made if I were to apply force instead - in either the axial or transverse direction?

Because I know buckling analyses require some sort of perturbation to see which way the model will buckle, do we get this perturbation when we apply displacement to this model?

### RE: Do these linear vs nonlinear buckling plots make sense?

In most cases force is applied in buckling analyses but it’s not uncommon to load the structure with prescribed displacement, especially in the case of nonlinear buckling.

### RE: Do these linear vs nonlinear buckling plots make sense?

(OP)
Is it this displacement that provides the initial perturbation that allows the model to buckle?

### RE: Do these linear vs nonlinear buckling plots make sense?

In the case of buckling analyses, it’s important to distinguish between preloads (applied in the step prior to buckling evaluation) and actual loads causing buckling. Both might be either force or prescribed displacement. A nice description can be found in the Abaqus documentation chapter "Eigenvalue buckling prediction" (Comsol’s manuals are not that comprehensive and, from what I remember, you’ve been working in Abaqus before).

### RE: Do these linear vs nonlinear buckling plots make sense?

plot on the same axes to make it easier to see the trends.

when you "fix" a side, are you rigidly constraining all the nodes on that face ? this would not be right, if you don't allow for poisson effects.

stress vs strain is a material property ... well, it is for a complete block; and I'd've thought that it would trend for your "fill factor".

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