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Hi,

I'm trying to obtain the buckling modes of the Von Karman equations for thin plates in compression with the vertical deflection in the z-direction (https://en.wikipedia.org/wiki/F%C3%B6ppl%E2%80%93von_K%C3%A1rm%C3%A1n_equations), and no deformation on the (yz) axis.

The Foppl-Von Karman equations simplifies a lot into:

D * d^4 w /dx^4 + hSd^2 w/dx^2=P

where D is the cylindrical rigidity of the plate, h its thickness and S=sigma_xx the stress in the plate, and P the external pressure. When P=0, there are modes with oscillations in the x direction.

So I'm trying to recover those instable modes with a compressive stress inside the membrane/thin plate.

Unfortunately I do not get them. Using the membrane physics (2d model in (xy) plane), I get an instability but not the expected one. And for a 3D model with the Solid Mechanics Physics with a very slight initial curvature, I observed only a simple increase of the curvature for a very large range of stresses. I also tried with a cut of the plate (2D model in the (xz) plane) but no success either. I used the Linear Elastic Model and Hyperelastic Model (Neo-hookean). I have attached somes images for those 3 attempts.

Have you ever managed to recover the instability modes of the Foppl-Von Karman equation with Comsol ?

Thank you in advance