Buckling of shells - industry practice

[trainguy]

Hello everyone.

I am wondering what the usual approach is with respect to buckling checks after linear static analysis of thin plate structures, like an airplane, for example.

When using linear static FEA, how do you go about checking that you will NOT have buckling, be it in shear, compression, etc.?

I know the usual steps in FEA involve first plotting a Von-Mises stress plot to get overall stresses and peak stresses, but from there, how do you systematically check each panel for allowable buckling?

And which quantities do you use - principal stress, von Mises, x-direction / y-direction?

tg

 

[joekm]

I know this isn't much of an answer, but I poked around here a lot yesterday and I've got real work I need to do today .

Anyway, if you can get your hands on a copy of Bruhn, a lot of what you are looking for can be found there (inter-rivet bucking, section crippling, web buckling, Needham and Gerard methods, etc.).

If I had more time, I'd point you to specific sections.

Good luck,

--
Joseph K. Mooney
Director, Airframe Structures - FAA DER
Delta Engineering Corporation

 

[corus]

Design standards usually have methods by which you check for buckling of structures. If you have a FE program you should be abe to run an euler buckling assessment which will give you the factor of the applied load to cause buckling. Euler's method isn't conservative but it's used for the basis of design standards. The correct way would be to use large displacement methods.

corus

 

[feajob]

The solution strategy is based on introducing a geometric imperfection in your structure. If details of imperfections caused in a manufacturing process are known, it is normally more useful to use this information as the imperfection. However, in many instances only the maximum magnitude of an imperfection is known. In such cases assuming the imperfections as linear combinations of the eigenmodes is a reasonable way to estimate the imperfect geometry.

The first stage in the simulation is a linear eigenvalue buckling analysis. Eigenvalue analysis is used to obtain estimates of the buckling loads and modes. The concept of eigenvalue buckling prediction is to investigate singularities in a linear perturbation of the structure's stiffness matrix. The resulting estimates will be of value in design if the linear perturbation is a realistic reflection of the structure's response before it buckles. For this to be the case, the structural response should be linear elastic. Such analysis is performed using buckling option, with the live load applied within the step.

The second stage involves introducing the imperfection into the structure using only the first buckling mode. Note that, there are two factors that significantly alter the buckling behavior:

Imperfection Shape: FEA codes (such as ABAQUS) allows us to consider a single mode or a combination of modes to construct the imperfection, and we believe that using the first buckling mode for this purpose is sufficient. Because, the first buckling mode represents some local buckling effects which is consistent with the local buckling observed in reality;

Imperfection Size: Scaling factor for the first buckling mode represents the imperfection size and it is considered as a percentage of the minimum wall thickness of your structure.

The final stage of the analysis simulates the postbuckling response of your structure for a given imperfection. The primary objective of the simulation is to determine the static buckling load. The stabilization method discussed earlier is used to obtain a solution since the loading cannot be considered proportional and the instabilities are local.

The response of some structures depends strongly on the imperfections in the original geometry, particularly if the buckling modes interact after buckling occurs. By adjusting the magnitude of the scaling factors of the various buckling modes, the imperfection sensitivity of the structure can be assessed. A number of analyses should be conducted to investigate the sensitivity of a structure to imperfections.

Cheers,
AAY

http://www.geocities.com/fea_tek/asd/