How to ascertain if a linear buckling solution exists ? 1

Hmm, why do you call this linear buckling?

Anyway, terminology aside, can you think of a test even for a simple case like a stocky column that will ascertain whether buckling is likely, without actually doing the analysis? I don't think so. In which case it seems unlikely that anything more rigorous than a rule of thumb could be generated for the far more complex model you are proposing.

Having said that a mode shape analysis might give you some clues as to which panels are likely to buckle, if loaded (in)correctly. Cheers

Greg Locock

Oh, I see why you call it linear, perhaps it would be better to call it linear elastic buckling. Cheers

Greg Locock

GregLocock

It is indeed linear elastic buckling. But I am afraid you haven't got my question! To clarify your point, here one is not trying to find an ALTERNATIVE to an FE run for buckling, but rather, is trying to ascertain (ab initio) whether a solution does exist so that the FE run is worth going for. The question pertains to any FE model that is complex enough for one to be unsure that a buckling solution exists.

Regards,
Vijay.

And that was my point - if in a hand calculation there is no way of predicting whether a given simple system will buckle or not then it seems to me that there would be no way of doing so for a very complex model. Cheers

Greg Locock

DrBVVijay,

If a structure has one or more dimensions that are small relative to the others (slender or thin-walled), and is subject to compressive loads, then a buckling analysis may be necessary. Therefore, with knowledge of the component geometry and by viewing the principal stresses (if they are negative in some regions), one can quickly identify if buckling will be a concern.

An important note is that, from a mathematical point of view, linear buckling is an eigenvalue problem and so the solution does not take into account of any initial imperfections in the structure. Therefore, the results rarely correspond with practical tests.

The outcome of any linear buckling analysis is a series of load factors which identify the danger of buckling. If one or more BLF's are greater than unity, then there is a danger that buckling will occur.

So how should we know if a linear buckling analysis is sufficient ?? Carry out both a linear static analysis and a linear (eigenvalue) buckling analysis. If the max stress is significantly less than yield, and the buckling load factor is greater than 1.0, then buckling will probably not occur. If however the BLF is less than 1.0, then the buckling analysis will be linear provided that the max stress is far below yield. In all other cases, a non-linear buckling analysis should be carried out. If the component is critical to the safe operation of a system, full displacememnt analyses should be carried out.

Hope this helps

Dermot

So are you suggesting that in order to find out whether a buckling analysis is necessary that he should do a buckling analysis?

Or have I missed something? Cheers

Greg Locock

You might want to reread his entire post carefully. He already answers that question in his first paragraph. No need for people to repeat what they already wrote well. Hope this helps.

You are right. Sorry. the last paragraph sounds a bit circular, that's all. Cheers

Greg Locock

dermotMonaghan

Thanks for your response. While you have brought out the standard facts pertinent to buckling, I am afraid you are not answering the question I have put out. I am familiar with the buckling and post- buckling theoretical aspects you have written about. To clarify, here I am not trying to figure out whether buckling is important for a given structure, or how the results would be related to imperfections. My question rather, is quite a practical one, and is addressed to the FE analyst routinely involved in analyses for buckling. The answer one would seek is either YES, a solution would exist, so you may do a run for the buckling- critical load , or NO, don't do a run, because a solution does not exist.

Hope this clarifies my query.
Regards,
Vijay.

If there is a compressive load at any point in the structure, there will be an eigenvalue that corresponds to buckling. Basically, your answer is a solution will exist. Whether or not the soution is on importance is another question. Think of it this way, if you have even one element that is compression, the code could find it and apply buckling to a single element. May not be very practical, but it exists.

If you have
[K](tangent) + P * [K] (geometric stiffness matrix) = 0
and if P is negative (compression) then you will satisfy this equation at some value of P for at least one element if there is compression in that element.

FeaGuru

I don't quite agree with what you say. The fact is buckling cannot occur merely because compression (stress/ strain/ deformation) exists somewhere in the structure- that compression needs to be kinematically uncoupled from flexure as well . Here you may recall that linear elastic buckling is a phenomenon of bifurcation where two or more alternative equilibrium paths exist in the load- deformation curve), and the flexural one is the stable one among them. For instance, compression exists throughout the length of an eccentrically loaded strut, but as any load would INDUCE the stable flexural deformation mode, apart from the unstable compressive mode, a bifurcation point does not exist. In fact, my original question may be expressed as follows: for a complex FE model, how does one figure out whether a region exists in which compression and flexure are uncoupled ?

Regards
Vijay.

Hi all,
basically, i fully agree with dermotMonaghan. As addition to hits first paragraph : buckling will also occure in slender or thin-walled through "shear load", think at aircraft skin structure. Of course this is not the case for beam element, where buckling only through pressure load and uneccentricity.
Actually, i have had the same question with DrBVVijay, but i didn't find any theoretical answer and then i though : instead of try to figure out wether the buckling (local or global) solution exist for a complex structure, just run a linear buckling FEA analysis and see the solution. It is simpler and the computer run faster and faster then i could figure out the exist of buckling solution, any suggestion?
Far more, the interesting question (practically) is what dermotMonaghan stated in his last paragraph, i.e wether a linear buckling solution is sufficient (reliable) to a structure or non-linear buckling should be carried out (cost/time). Comment to Monaghan, you say "both" linear static and linear buckling analysis. I think linear buckling needs linear static analysis, i.e. you automatically run the linear static analysis if you run linear buckling, at least this is done in ANSYS.
A nice dicussion volks!

regards

zuardy

Are you suggesting that we solve for buckling in order to confirm existence of a buckling solution ? Well, we used telescopes to confirm that the planets exist, without actually journeying out in search of them, right ? Much the same situation here. Actually, cost aside, there is another important reason one would want to ascertain existence of the buckling soln- in optimisation where the constraint or objective depends on the critical load- unless you have a solution, your optimiser will have to abort its search there!

Regards,
Vijay.

DrBVVijay,
as i told you, that i have had the same question like yours : wether linear buckling solution exist or not, because i also had to optimize at that time a structure under pressure. I used at that time SQP algorithm and had also similar problem with you. Some times, the FEA-model could not be built due to bad geometry shape and some times the FEA solution was not succesfully carried out (e.g. no buckling solution ;-)). What i do was simply give back a big value of objective to the optimizer, so it will handle it as bad search region. Of course, it is not simple if this problem occures in the vicinity of constrains, exactly active constrains.
Now, i do more complicated optimization problem, i.e. parallesized shape, topology and combination optimization of a satellite platform structure. There are many configurations, where no solution are available due to many reasons :-(. Fortunately, i use now a genetic algorithmic and do the same thing if such a problem occure, namely give back objectives with big value (bad), so the integrated penalty functions will cause this individum to be died, simpler ;-)

regards

zuardy

I have used genetic search for years now, on problems with objectives dependent on advanced criteria such as non- conservative dynamic stability boundaries. But I can't see what logic there is in declaring a search region to be bad because one can't solve for buckling for a design there- the defect is not with the design, but with the FE analysis.

From the discussions so far, I am beginning to conclude at the moment there is no established methodology to ascertain existence of the critical load in a practical structure. Perhaps one way out may be to solve for the lowest few natural frequencies under the influence of the same load distribution, and estimate (hopefully realistic) the critical load from extrapolation [/b] within the resulting frequency- load data. However this is a more expensive approach for sure, so we have to adopt it after thought and experience.

Regards,
Vijay.