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Buckling Analysis of a square unstiffened plate

Buckling Analysis of a square unstiffened plate

Buckling Analysis of a square unstiffened plate

(OP)
Hello guys,

I am kind new to both Eng-tips and Abaqus, so please be patient with me..
So this is my problem. I am modelling a simply supported square unstiffened steel plate (dims 1m x 1m x 5mm thick) for my dissertation, which I know from the analytical solution that critical load should be:

stress = (k π^2 E x t^2)/(12x(1-v^2) x b^2) = in my case = 18.98 N/mm2
and thus Pcr = stress x (1000x5) = 94900 N
(k=4, E=210000n?mm2, t=5mm, v=0.3, b=1000mm)

Applying the boundary conditions (according to the theory, I get a much different result (please see attached file).

I have observed though that the only case that I get a close result to the analytical result is if I restrain the unloaded edges to all 3 directions but not the loaded edges.
Any help? Should the unloaded edges be restrained in all 3 directions and if yes, why?? How should the proper boundary conditions be for a 3D simply sup square plate?

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