Crippling comparison: FEM vs. closed-form solution descrepancy

[achilles03]

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), just like a typical flange. I've compared the results to a classical hand calc.

The problem is that my FEM predictions (linear eigenvalue, Abaqus 6.7) 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 (jn plane) to the load direction. No rotational constraints anywhere. 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 = k*E*pi/12/(1-(mu^2))*((t/h)^2)

where:

k=1/(L/h)+6*(1-mu)/(pi^2)

t=thickness of the flange, L=length, and h=height

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

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

Why is there such a large discrepancy?

Thanks in advance for any advice!
Dave

 

[crisb]

I have done these sort of runs before, and got very close to the theoretical elastic buckling equations.
For real life with plastic material and initial imperfections a nonlinear analysis is more appropriate. However the OP appears to be wanting to emulate the classical elastic buckling equations.
I suggest you consider:
Element type, quadratic shell elements suggested.
Element size, too course and the model will be too stiff.
Boundary conditions, are you inadvertantly constraining the plate from in plane movements.
Also try a square plate as a check.

 

[GregLocock]

Random observation: why would you expect a linear solver to give the right answer?

It may be that the element formulation in question understands elastic buckling, but... dat ain't no simple thing.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.