Does FEM analysis correctly model buckling?
Does FEM analysis correctly model buckling?
(OP)
For finite element models, say RISA or some other program, where you have a structure under various loadings, does the PDelta analysis performed by these programs properly estimate buckling?
We've been having this disussion in our office and one view is that the PDelta certainly estimates the second order effects, but that this is not the same as Euler buckling.
The other view is that Euler buckling is simply a derivation of second order effects that uses an assumed out-of-plane initial distortion to get second order effects started. So with a finite element model with forces in two or three global directions you will, by nature, have the second order effects started and the buckling load will be at least approximated.
What do you think?
We've been having this disussion in our office and one view is that the PDelta certainly estimates the second order effects, but that this is not the same as Euler buckling.
The other view is that Euler buckling is simply a derivation of second order effects that uses an assumed out-of-plane initial distortion to get second order effects started. So with a finite element model with forces in two or three global directions you will, by nature, have the second order effects started and the buckling load will be at least approximated.
What do you think?






RE: Does FEM analysis correctly model buckling?
I don't think that the FEM programs are intended to capture buckling in that manner. The Euler buckling load is for a perfectly straight column.
I tried, with an FEM program - RAM Elements (Advanse, at the time) - to capture this behavior and I just couldn't mimic it.
Since the Euler buckling load is for a perfectly straight column such that any disturbance will cause buckling upon reaching the critical load, I had two choices in my mind.
1) I could model a straight column with a small lateral load at mid-height, or
2) I could model a column with a slight curve.
I chose option 2, and modeled a column with a half-sine wave shape. I made it like 20' long and broke it into 1' segments. I selected a column shape that should buckle elastically. I then loaded the column near the buckling load to see what kind of behavior I would get. I expected to see lateral displacements that would begin to really increase significantly as I approached the buckling load. What I found was that there wasn't a sudden increase in the lateral displacement at (or near the buckling load), but rather a more gradual increase. It wasn't linear, but it wasn't as sudden as I thought it would be.
What really threw me for a loop was when I got above the buckling load, it actually displaced in the opposite direction. I still haven't figured that one out.
At no time, however, did it fail to converge, which was also a little confusing. I didn't run this test on a lot of different column sections, heights, etc, so it's possible I could have got different results under different conditions.
To get back to the actual question......... I'm not sure I understand the question exactly. We typically use the buckling load on the design side, right? The analysis kind of is what it is. You get moments and axial forces and compare that to the capacities (which account for the possibility of buckling).
RE: Does FEM analysis correctly model buckling?
The answer to your question is yes and no.
Yes, in the sense that an elastic P-Delta analysis (if done properly) will generally capture the member's buckling or the frame's buckling.
No, in the sense that there are limitations related to modeling and results.
1) First, as Lion6 points out, there has to be some form of initial displacemnt. Either a built in out of straightness or some form of lateral load applied to your model.
2) Second, in order to capture individual member buckling you need to capture the P-Little Delta effect in addition to the P-Big Delta effect. This will often require that the member be sub-divided with additional nodes along the length of the column.
3) The results from an elastice FEM program (like RISA) can really only capture the ELASTIC buckling effects. The good news is that AISC's Direct Analysis Method (which is a pseudo-elastic method) contains adjustments to the elastic analysis which will allow it to approximately capture the inelastic member buckling.
Below is a link to a download from the RISA website. In the link is a set of "benchmark" problems from the AISC commentary which are used to determine if you analysis can adequately capture the elastic buckling effects (i.e. p-little delta). As you can see in the presentation, the RISA results match very well... but only if you sub-divide the column.
h
Hope that helps!!
RE: Does FEM analysis correctly model buckling?
Seeing that we have used 4 elements only, we have used an initial imperfection, and RISA acknowledges other deformations, particularly axial deformation, uses K=1 on segment lengths of 2.5 m for the check (quarters) it seems not initially a bad match.
For the elastic buckling, if you substitute the 0.877 by one, and do not reduce the axial limit, you also get 6.91 as the limiting axial load. So again, under that concept of the coefficients, a close match.
Yet I am not entirely satisfied since both the 0.877 in the formulation should figure instead of 1 and a reduction factor 0.85 to give the limit for the check, i.e., one would expect a lower limit load for the 1999 LRFD check, and hence a lower limit load in my model.
I upload an image then zipped model.
RE: Does FEM analysis correctly model buckling?
RE: Does FEM analysis correctly model buckling?
Keep in mind that a bending code check of 1.0 does not correspond to buckling.... When you approach the buckling limit your code check should become "infinite".
Also, in order to nicely match the "theoretical" value you would need to turn off shear deformation on the Global Parameters.
You do both of these things and you should get very close to the buckling values. Though the program will always start to "diverge" on the P-Delta analysis slightly before the actual Euler buckling value.
RE: Does FEM analysis correctly model buckling?
Lion06 - Euler buckling would require an intential out-of-plumbness so that was basically my question - with an out-of-plumbness in the model already, would buckling occur.
Josh - I did the benchmark problems (found in the back of the AISC manual) on RISA some years ago and found that (as you state) they do indeed capture the little delta effect.
My particular project involves a stainless steel sculpture about 17 feet tall - a somewhat irregular shape. So we modeled it in RISA.
Attached is a stress plot of what we were working with.
Since it has all sorts of planes and curves at odd angles to xyz we felt that there was already an intential out-of-plumbness of sorts to begin with.
I see what you are saying about the inelastic effects in the Euler buckling. RISA would assume elastic. (so when will RISA get some inelastic analysis developed? Hurry up!!
RE: Does FEM analysis correctly model buckling?
RE: Does FEM analysis correctly model buckling?
RE: Does FEM analysis correctly model buckling?
That sculpture looks like a parachutist's nightmare.
BA
RE: Does FEM analysis correctly model buckling?
It is the same slender member than above but with 6 m length.
Both the code and RISA 3D show substantial consistence in the results, even if the statement of what to do may be done better.
RE: Does FEM analysis correctly model buckling?
RE: Does FEM analysis correctly model buckling?
In my experience, FEA only captures the precipice of buckling, not the process. Once it starts, all bets are off.
RE: Does FEM analysis correctly model buckling?
I thought that the PDelta was simply a routine in the matrix solution that cycles through independantly of the type of element (i.e. two node "beam" vs. multi-node plate).
How does RISA differentiate between doing PDelta in a model that has both plates and beams? That doesn't make sense. The matrix solution is dealing with joints and their mathematical relationship between themselves (in terms of stiffness against relative movement).
RE: Does FEM analysis correctly model buckling?
RISA 3D does not account for P-Delta in plate elements even when the option P-Delta is marked.
How to ... surely is a matter of what enters equilibrium and not in the FEM setup. FEM is all mathematical manipulation, that's part of the force/nature of the method.
RE: Does FEM analysis correctly model buckling?
More importantly, it does not redistribute loads after a member
has buckled...one has to manually remove that member from the model(make it inactive).
FEA is a very good number-cruncher and rule-checker but in no way
is it a substitute for engineering judgement and experience.
RE: Does FEM analysis correctly model buckling?
There are however FEM packages very well adapted to find the buckling load of some structures in accord with the constitutive laws of the materials, restraints and other conditions that may apply, irrespective of some code formulation.
RE: Does FEM analysis correctly model buckling?
The question, I think, is: does the buckling occur prior to a portion of the model reaching an inelastic state, or can PDelta "buckling" occur - a diverging of the model - prior to inelasticity.
I thought the initial divergence, under Euler buckling, wasn't inelastic as JoshPlumb above suggests. I agree that once it begins to buckle, it eventually will reach and exceed yield stress. Just not sure if Fy must be exceeded prior to model divergence.
RE: Does FEM analysis correctly model buckling?
RE: Does FEM analysis correctly model buckling?
interprets the results based on a set of rules dictated by the applicable code. It can determine wheather it fails or is still ok
based on this criteria.
Beam/Col.....the program can easily handle the P-little Delta and after applying the loads calculate the deflections. Then it can
iterate the loads on this deflected shape thus covering P-Big Delta and check if the members are still ok.
That's as far as it goes...if the structre was initially stable, i do not believe that it will say it is now unstable because a certain member failed.....the engineer has to address the failed member himself. There is no post-buckling analysis.
Plate elements....an entirely different animal altogether.
Most of the rules pertaining to bm/cols dictated by the codes do not apply here, especially concerning stability.
So the engineer has to get really involved in interpretating the results to determine if they make sense.
Using RISA's plate elements in your model may give you a general idea of the resulting stress levels.
I always check the resulting stress levels and try to understand how they got there. Your model shows one area of peak stress which in reality may not exist as plate can easily redistribute loads as one area begins to yield.
The biggest pitfall in plate strucures are in-plane compressive stresses. So to that end I would add the following comments on your structure:
With the following assumptions....no interior steel skeleton and plate probably made out of gage ss.
Loads will gravitate towards the stiffest areas of the structure...so all the verical corners will carry the majority of the loads.
This leaves one with a skeleton of corners with a fill-in of plate that is just delivering the load to the stiff areas.
Determine axial loads in corner based on this assumption.
Check corner as an angle compression member..how big a leg?...use b/t limitations from aisc code...are these angles(corners) braced by the remaining pl?...hmmmmm..probably not.
Anyway, that is a general approach that I would look at.
JoshPlum has alot more credability and in-depth knowledge of the RISA program than I do, so I would tend to pay more attention to his remarks than my long-winded comments.
RE: Does FEM analysis correctly model buckling?
RE: Does FEM analysis correctly model buckling?
FEA analysis does correctly derive the stress levels in odd shapes and structures (assuming small enough elements).
If you take a curved shape - a really significantly curved shape: think half cylinder - and add axial load, the finite element analysis will correctly derive PDelta effects as long as it is in the elastic range.
The question is - does buckling always involve inelastic conditions?
RE: Does FEM analysis correctly model buckling?
RE: Does FEM analysis correctly model buckling?
No, Euler buckling is based on elastic behaviour. On the other hand in real structures buckling behaviour is often initiated earlier than would be indicated by Euler buckling theory because of inelastic behaviour. This is one area where a correctly set up FEA will often give a more accurate and more conservative result than application of simplified theories in a hand calculation.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Does FEM analysis correctly model buckling?
If that is the question, the answer is no. Buckling does not always involve inelastic conditions. Long columns buckle elastically. Intermediate columns buckle inelastically. Short columns don't buckle.
The buckling load of a compression member may be governed by flexural buckling, torsional buckling or torsional-flexural buckling.
I thought that the question in this thread was...does RISA or some other program properly estimate buckling? Possibly some do, but apparently RISA does not, at least not at the present time.
BA
RE: Does FEM analysis correctly model buckling?
The secondary question, with a finite element model such as the one I posted above, would be - is there any way to tell if you are in a long-intermediate-short condition with an odd, irregular plate layout.
RE: Does FEM analysis correctly model buckling?
I'm a bit staggered to read some of the above comments. It's a big world out there, not everybody gets to design to code.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Does FEM analysis correctly model buckling?
Take one of the lower panels which looks like 5'wide by,say, 5' high.
A rough guess of the effective width would be, say, 40t to each
corner. Assume 10ga...40x.135=5.4". So one is left with an effecive angle in the corners of 5.4x5.4".
What happened to the rest of the 60" wide pl....did it buckle?
Not in the sense of a col ...it just has no load carrying ability as far as compression is concerned..not a problem as long as the load can get to the corners.
Take shear loads...h/t=60/.135=444...is shear buckling a possibility?..not a problem if one can develop tension field action.
Does one look at the sides as a deep girder, etc.
These are all questions I would ask as I believe that the FEA program is not set up to handle because there are just too many variables for each different case and that only engineering judgement can address.
RE: Does FEM analysis correctly model buckling?
As you say design by the code may become difficult to attain. But real structural designers are demanded quick solutions to structures with not too much time to provide an answer, with many other perentory tasks to do concurrently and still, as usual, finding some difficulty in being economically functional. In short, real engineers, as in the vapor era, make some mistakes and some boilers explode.
It is pertinent to signal that no building is being thrown the dedication and expertise nor in hours nor in demanded technical stature of the intervening professionals than something as the automotive or aerospace or weapons industries is having; nor the price of the items are comparable.
So I instead of becoming baffled am reassured that to get to any level of quality you either throw the required means or you get not, I see logic in it and not bafflement. You get what you are paying for.
RE: Does FEM analysis correctly model buckling?
There is one exception and that's for curved archrib structures. These are laminated wood, 3 pin arch structures and I have found a close correlation with analysis and design. By making minor changes in the depth of the ribs, you can review the condition as it starts to 'buckle' or have the design moment diagram change 'wildly'.
Canadian codes require these be checked for unbalanced loadings and the effect is quite dramatic. I've used it to show some clients why a change in span or geometry has a large increase in the cross section.
Dik
RE: Does FEM analysis correctly model buckling?
Structural engineers are required by law to design to code although some might prefer to do otherwise.
BA
RE: Does FEM analysis correctly model buckling?
For frame members, you would normally only consider the lateral joint translation and axial force in the member as a contributor to the P-Delta effect. It is not difficult to modify the local element stiffness matix of the member or introduce secondary shear forces which induce an effect equivalent to the P-Delta moment.
Now, look at a plate element. You've got a two-dimensional element subject to a multi-dimensional stress state. The destabilizing effect of this system is not nearly as clear. That's why most programs do not consider P-Delta effects for plates.
The programs that do include P-Delat for plates may be using an inexact approximation of the effect (this is what RISA does for the wall panel elements). In which case, I don't know that you can expect a P-Delta analysis of a plate element to truly capture the elastic buckling effect in the way that it woudl do so for a frame model..... In my opinion, you'd probably have to do an Eigenvalue buckling analysis to have more confidence that the buckling effects of your plate element model were adequately captured.
RE: Does FEM analysis correctly model buckling?
http:/
RE: Does FEM analysis correctly model buckling?
After reading the help on this I'm a bit surprised as my own PDelta knowledge from past FEA studies - both two node and multi-node elements - the PDelta analysis was performed on the deflections of the joints - and not as RISA does, by adding shears to two-node elements only. I'm not sure I like that (despite liking a lot about RISA).
RE: Does FEM analysis correctly model buckling?
Running 1 with P-Delta as it is 175 hypothesis in RISA 3D for a Portal Frame Building 25x50 m long takes about 15 mins in my now becoming midrange PC. Now imagine the same for iterative reconstruction of the matrix stiffness in each of the hypotheses and cycles ... no wonder the sellers of structural analysis shy from such approach.
RE: Does FEM analysis correctly model buckling?
Use the Wall panel element in RISA rather than pure plate elements. Then you should get your P-Delta effects. Though I should point out that it is a P-Big delta effect.
P-Little Delta effects for walls generally have to deal with a code based iterative procedure that considers the cracking of the wall (see masonry and concrete codes). In RISA, this is taken care of the wall force and code check calculations rather than being considered directly in the analysis.