negative eigenvalues in buckling analysis

[ridbay]

Hi,

can anybody suggest me about what can the negative eigenvalues in bucling analysis mean?

after having performed a buckling analysis, i got the eigenvalues like:

15.394
-15.397
15.925
-15.934
-16.213
16.223

the structure is geometrically symmetric, but i applied gravity loads...

Thanks in advance

 

[SWComposites]

Eigenvalues are simply factors on the applied loads; a negative value means that the structure will buckle when the applied loads are reversed in direction.

 

[271828]

Can you further describe your structure and loads? I can't imagine a structure for which that would make sense, but I could be wrong. For example, if you have a moment frame and apply gravity loads, it certainly will not buckle if those loads are reversed and are pulling up.

Do the positive buckling loads make sense? There should be some way to approximate the buckling load, even roughly, by hand, for comparison.

Have you input a very simple structure with known buckling loads for comparison? For example, a pinned-pinned rectangular column.

 

[msquared48]

You might recheck your input to your program.

There is a reason for saying "Garbage in, Garbage out".

Mike McCann
McCann Engineering

 

[271828]

Hey, here's another idea for you. Can you make sure that the structure has some mass in your model and then do a modal analysis? It would be interesting if the program picked out negative eigenvalues for that. It would also be interested to see if the structure has any zero or veeerrrryy low frequency modes indicating rigid body motion.

And... As soon as I typed the other reply, I thought of a case that might give negative eigenvalues. Say you have a doubly-symmetric I-beam and the loading is composed of end moments. I think that should have negative eigenvalues because it will buckle at the same moment whether or not it's reversed. Also, say you had a cylinder modeled with shells and apply a torque. Shell buckling should happen for +Tcr or -Tcr if everything's symmetric. Do you have a structure similar to this?

 

[ridbay]

Thanks for all replies...

especially for the question from 271828; i had modeled a simple shell cylinder, and applied gravity loads in Z direction. The buckling analysis has delivered negative eigenvalues beside the positive ones. But any torque...

for your first suggestion about performing a modal analysis: i could not get it, which results you expect, and how they can be helpful? Can you please explain that?

 

[271828]

Hmmmm. I might have an idea that explains your +/- pairs of eigenvalues. This is just a theory, not saying I know for sure.

It sounds like you have a cylinder with load applied parallel to Z-axis (assumed to be parallel to the cylinder longitudinal axis.

Say you have this load causing compressive stress in the Z-direction. Your first mode will probably have it buckling with the waves running in the Z-direction. Now, if the load is reversed, the walls have tensile stress in the Z-direction, so no buckling is expected. However, Poisson's effect exists and you have compressive stress in the tangential direction. There might be a buckling mode with the waves running around the tangential direction. Depending on your problem, I can believe that these two loads might be similar or maybe even equal.

The higher modes probably just have different buckle wavelengths and numbers of waves.

Does this make any sense when you look at your buckling mode shapes?

Here's a test for your model. Make the shells orthotropic, with the bending stiffnesses much different the Z and tangential directions. See if this pushes the eigenvalues farther apart.

Forget the modal analysis part. That's probably not useful for this problem.