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Simultaneous buckling of beams

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TheHypnotoad

Aerospace
Jan 13, 2011
3
Hi everyone!

I'm working on a buckling problem (not my personal area of expertise) and I wanted to pick your collective brains on the topic of failure and Finite Element analysis.

So, we have two metallic plates, held apart by four angled L-beams. Everything is modeled as shells. (Abaqus S4R5 elements, if you want specifics). A uniform pressure is applied to the top plate, and a uniform displacement is applied on the bottom. Constraints against rigid body motion are applied, natch. The setup is symmetric, and all of these L-beams should be under an identical load in a mathematically perfect world.

If you're like me, you would expect all the beams to fail at the same time in the same way, with identical stress distributions . . . but they don't; one gives first and the top plate slides off toward a corner. Then the next buckling mode hits a few psi later and the top plate slides off toward another corner.

Why don't they fail simultaneously?

My best guess is that Abaqus has a certain amount of significant digits when assigning coordinates to nodes, and when you look closely enough, the beams are not perfectly straight. The rounding error causes minor imperfections in the beams, just enough to make one fail first, by a few pounds. Has anyone had this happen before?

On the other hand, my coworker, who has much more experience than me at this and is tremendously helpful, isn't buying my idea. What tests would you perform on this model to work out what's wrong (or prove/disprove my idea)?

Thank you!!
 
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Jou mentioned that "a uniform displacement is applied on the bottom."

With variations in member stiffnesses, how is that possible? Perhaps I misunderstand your statement...

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
 
If it's 4 beams on a plate then why not just model 1 beam with symmetry applied to represent the full geometry? The results should be the same for the full geometry and your 1st mode, roughly. Your hypothesis might be correct, but I'd check you've assigned all shell properties/materials correctly.

Tata but not yet tara
 
is anything being reacted by your rigid body restraints ?

i don't use ABAQUS, but it seems you're getting a progression of loading, how to you see one angle failing and the rest trying to carry on ?

i'd've thought you applied the loads, and got an answer ??

what if you apply the loads separately ?

 
Wow! Thanks for all the quick feedback on this. A few clarifications:

@msquared48: I'm sorry, I misspoke. I should have said that a uniform displacement of 0 was applied to the bottom plate in the normal direction. So, two plates, held apart by 4 angled beams, and I am trying to push the two plates together with a pressure load. Hope that makes more sense!

@corus: PEBKAC was suggested (kindly) by my coworker, too; but we've been through the material assignments and boundary conditions rigorously by now and haven't found a problem. I have done a quarter panel model to try to troubleshoot this case, but with angled beams, I'm worried I would miss a failure mode where the top panel twists on the way down . . . I'm not a structures type, so maybe I am unduly worried about this?

Anyway, once I'm satisfied this is working, the next step involves combined loads with shear, so I'd need all four beams to capture that.

@rb1957: the bottom plate is the one with the rigid body constraints, and it is showing no surprise stresses or displacements near the rigid body pinned nodes. With Abaqus, you can apply one load and extract multiple eigenvalues and their corresponding failure states; I'm not really sure how it ignores a previous failure, but it can. Never tried it before this project, but it's pretty neat!

--

Is there anything else I could try to get to the bottom of what's going on here?
 
"angled beams" = nested angles (making a C section) ?

instead on an enforced displacement of zero (sounds odd to me) constrain the lower plate out of plane (z) only. this'll take care of three rigid body motions(z, rx, ry). constrain the central node of the plate in the other three rigid body modes (x, y, rz).
 
Hi again, rb1957: I must not have explained it well, but the set of constraints I applied are exactly as you suggested. Sorry about the confusion!

As for the "angled beams", I have four L-beams. They start near the corners of the bottom plate and are angled so that they are closer to the center of the top plate. The corners of the Ls point out toward the corners of the plates.
 
ok, the L sits on one plate; how does it pick up the other plate ?

the Ls are arranged in something like a radial pattern. if all the Ls are flanged the same way, ie on the clockwise side of the upright, then the structure isn't truly symmetrical and i think the secondary effect of torsion buckling of the Ls might induce a cascade failure.
 
In the real world one leg will fail first.

Have you checked several eigenvalues to see if there is a mode where all four fail at once. Could be the math model is saying that the lowest buckling load is the one where one leg fails.

Just my 2 cents.

TOP
CSWP, BSSE

"Node news is good news."
 
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