Plate buckling via linear FEM solution 1

[mathlete7]

Hello everyone,

I'm curious about your thoughts in performing linear buckling analysis on webs (via a FEM). I have some webs that have multiple holes in them at various locations so I can't just perform a Bruhn type calc for plate buckling. These webs are stability critical (buckle before they start to yield so inelastic buckling isn't an issue). I know that linear buckling analysis has its limitations and I've heard of a couple different methods to try to "trick" a FEM into giving you a reasonable buckling load. They are as follows:

- "Jiggle" the nodes in the web to create geometric irregularities. This would simulate manufacturing tolerances and induce earlier onset of buckling.
- Apply an out-of-plane load to the web. If this method is used, any ideas on how to specify a "realistic" out-of-plane load?

Does anyone have thoughts on how to get believable results out of a FEM for a web buckling analysis?

Thanks for your input...

 

[rb1957]

are the lightening holes flanged ?

does it Really matter if the web buckles ? is it primary structure ??

i would model the webs (without holes), get the shear flow and fudge an answer from there; if the shear stress is the panel is <10ksi. if this is Primary structure and Must not buckle (Must implies more than some project weenie saying so) then i'd try to stiffen the panel so that there was one hole in each bay.

 

[mathlete7]

This is definitely primary structure and carrying loads in IDT is definitely out of the question in this case (and in this case not going to IDT isn't some project weenie call, there's actually some important reasons on this program that I won't go into).

I pose the question about this specifc case, but the question is more general and is something I've been curious about. That is, getting good buckling loads out of a linear buckling solution (again when it is known that yielding won't occur prior to buckling).

 

[SWComposites]

You can run an eigenvalue (linear) solution and design to a ~20% margin which should be sufficient for a shear web. Shear buckling is typically less sensitive to imperfections than a compression loaded plate or cylinder. Or run a non-linear analysis with an applied initial imperfection (typically derived from the displacement vector from the eigenvalue analysis).

 

[mathlete7]

Thanks for the response SWComposites. You mentioned running a non-linear analysis with an applied initial imperfection "typically derived from the displacement vector from the eigenvalue analysis".
What did you mean by this last statement? How would I go about doing this? I'm quite familiar with linear buckling runs, and have done a little non-linear, but am not quite sure what you're referring to...
Thanks much...

 

[SWComposites]

The details depends on the FE code you are using.

Basically apply the eigenvector as an initial displacement to the nonlinear analysis, with a scale factor to set the max transverse displacement to something on the order of ~ 1/2 the thickness (probably will have to run several displacement levels to evaluate the sensitivity).

Check your code documentation on how to apply an initial displacement.

Or just size to a conservative factor on the eigenvalue analysis (much easier) and validate with a test.

 

[rb1957]

eigen value works for shear buckling ?

 

[RPstress]

rb: yes. Eigenvalue analysis works for almost any structure and loading. It usually uses differential stiffness matrixes and in Nastran using plate offsets can screw that up (as it can geometric non-linear).

There are specialised non-linear buckling runs in most systems, but you still often/usually wind up putting in initial perturbations, usually based on the shape of the lowest eigenvector.

Traditionally for stiffeners and things we use 1/1000 for the initial bow/length for beam-columns, but SW's suggestion of half the plate thickness is good too.

FE is handy for buckling of composites because it takes through-thickness shear into account properly.

There are a few structures, ones which undergo pop-through (think point load on a dome), where you have to get a bit fancy and use non-Newton options, but if it's done right you can model the negative stiffness part of the process. However, for most engineering structures such as struts and plates in compression (and especially plates in shear), stiffness never goes negative unless material yield/break is included.

It does beg the question, when analysing non-linearly, as to what a non-buckling panel really is. If you put in a an initial deformed shape which is based on an eigenvector prediction of the buckled shape then you'll get some out-of-plane deflection like a buckle from the word go. At some point you will get a big increase in out-of-plane deflections, and you can usually say for sure that the structure is buckled when that happens, but defining exactly when is problematic.

 

[Andries]

As SWComposites says, a linear buckling analysis will work well. If you have a rectangular panel under pure shear, for example, apply "unit" shear loads to the panel. Multiply the load with the lowest eigenvalue to get the critical buckling load. If the edges are tapered use the average of the shears.
To gain confidence in your FE analysis it is good practice to do an FE analysis of a similar type problem for which an analytical solution exists and compare results.
Be very careful when specifying the boundary conditions!

Regards

Andries

 

[RPstress]

I said

"It does beg the question, when analysing non-linearly, as to what a non-buckling panel really is. If you put in an initial deformed shape which is based on an eigenvector prediction of the buckled shape, then you'll get some out-of-plane deflection like a buckle from the word go. ... defining exactly when [it buckles] is problematic."

I just read a paper suggesting that the buckling point in a non-linear analysis can be taken to be at the maximum of the second order derivative of the load-shortening curve, where the third order derivative is zero.

 

[mcclain]

Should the buckling point be the minimum of the sencond derivative, i.e., the point with the sharpest downward concavity on the load shortining curve?