Crippling: FEM vs. Closed-form solution comparison

I've done a parametric study of crippling of a plate simply supported on 3 edges with 1 free edge (the free edge is not a loaded edge). I've compared the results to a classical hand calc.

The problem is that my FEM predictions (linear eigenvalue) are about twice as high as the closed-form solution. I've double-checked the material properties, as well as the loading and boundary conditions (3 edges constrained from out of plane motion and the edge opposite the unconstrained edge is constrained perpendicular to the load direction). Does the closed-form solution use some sort of conservative energy method approach or make some other conservative assumptions?

For reference, the closed-form solution I am using is as follows:

crippling stress =3D k*E*pi/12/(1-(mu^2))*((t/h)^2)



t=3Dthickness of the flange, L=3Dlength, and h=3Dheight

k approaches about .407 for flanges with high length to height ratios (mu=3D.33).

This hand calc is based on the following reference: Bulson, P.S., =93The Stability of Flat Plates=94, American Elsevier Publishing Company, New York, 1969.

Why is there such a large discrepancy?

Thanks in advance for any advice! Dave

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Well, I found one of the errors. It should be:

crippling stress =3D k*E*pi^2/12/(1-(mu^2))*((t/h)^2) (I forgot to square pi)

Now the problem is the closed form solution is consistently over- predicting the FEM by about 25%. This is a lot closer, but is the closed-form solution really that unconservative?

Thanks in advance, Dave

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