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# Linear Buckling Analysis

Experimenter

Hey guys,

I have a simple model that I have been trying to test in compression on NX simulation. But when I fix my bottom face and apply a load to the top I get this (which makes sense because the bottom is fixed in translation and rotation):

This is not what I am looking for...

So then I realized that since I am in compression, the most relistic solution type is Linear Buckling. Because I want to see the middle part of my part bowing outward. But I am still having trouble with my constraints and getting a displacement where the middle of the part is bowing. Does anyone have an idea?

Thank you!

9 REPLIES 9

# Re: Linear Buckling Analysis

Phenom

What kind of elements are you using?  Looks like 1 layer of bricks, that's not going to be enough to represent bending properly, you'd need at least 2-3...  I'd do a shell mesh on that or refine the mesh quite a bit, you're not representing the stiffness accurately...

Linear buckling is only going to give you the load multiplier to buckle, it's an eigenvalue solution...

# Re: Linear Buckling Analysis

Experimenter

Hey!

Thank you for that response. I think you are totally right. I was using cube (brick) elements. Only 1 through the cross section.. And you're saying that is not enough correct?

I will switch to shell because it's a little bit more simplified.

For my own knowledge can you clarify somethings for me.. I think I am getting confused on what stiffness exactly is. I understand its a K value that describes the stiffness, or the resistance to deformation. And it decreases with an increase in force. Is that a good physical respresentation?

Also, you said, "Linear buckling is only going to give you the load multiplier to buckle, it's an eigenvalue solution..." Does that mean I should switch to a non-linear solution type?

Thank you.

# Re: Linear Buckling Analysis

Phenom

If you have only one element through the thickness, then you are not modeling the bending stiffness (among other things) correctly, your FE model is much stiffer than reality.  You could simply had a couple of layers of bricks.  If you're planning on shell mesh, then make sure to mesh at the midplane if you want to perform buckling analysis...

As for linear vs non-linear, I don't think it makes a difference.  The output of a buckling analysis is a set of eigenvalues corresponding buckling modes.  Each of these are load multipliers to your applied load to reach buckling instability.

Do you know for fact that your load is sufficient to buckle the structure?  Seems to me that you could do a linear static analysis first, then possibly a non-linear static on (with arc-length method if buckling is anticipated) to see what happens...

# Re: Linear Buckling Analysis

Experimenter

Hey thank you for replying again.

Definetely food for thought. But as I am moving forward, before I run down the nonlinear buckling / linear buckling (any buckling for that matter), I should consider if this is even a buckling problem. This specimen is very small. Like 2 inches tall. And it is compressed. It shouldn't buckle it should compress right (assuming on material)... Would it still be smart to run a buckling analysis if it's supposed to purely compress?

Thnk you.

# Re: Linear Buckling Analysis

Experimenter

Also can you explain the arc-length method a little more?

# Re: Linear Buckling Analysis

Phenom

Before jumping into any FEA, I would do handcalcs to know what to expect in terms of defelction and buckling...  That would give you an idea of what you need to run: are you expecting small deformations or not, is it at risk of collapsing, could it permanently deform?  Once you have these answers, you will be able to pick and choose what solution is more appropriate...

# Re: Linear Buckling Analysis

Experimenter

Hey there!

I just decided to join, so I might as well drop my 2 cents

There are several things here you should consider.

1. The 1 layer brick mesh was already mentioned - simply do the shell FE as you wrote - In my opinion the only reasonable approach.

2. I do not think this will buckle... I mean by the look of things your "column" is quite short, and plate is relatively thin - you might expect local stability issues (or do you call that buckling?) in the web (the middle part) of the section.

3. The above is simplest to verify by LBA (also referred to as buckling or linear buckling) - in many cases the answer is "wrong" in terms of actual capacity and shape of the deformation (you can read about it here on my blog), but it will show you where the stability issues most likely will occur.

4. Arc length method that was mentioned is used for a snap-threw (and other strongly nonlinear phenomenon) analysis. Not all (but many) nonlinear buckling analysis is performed with arc length methods (Riks or Crisfield algorithms mostly). You can also use the "general approach" (so without arc-length) - this may lead to convergence problems near the load where model looses stability, but for the start it is a bit easier to set and analyze.

5. If you will decide to go with nonlinear buckling consider loading your model with displacement rather than force (it's not exactly the same, but close in many cases). This should help with convergence a bit.

6. If you are unsure if the mesh size is ok you can always do a convergence study.

This are all the things that come to mind - if you have any more questions I will do my best to drop in and try to help out

Have a great day!

Łukasz

# Re: Linear Buckling Analysis

Phenom

Us old people and our linear buckling "wrong" results still managed to get it right on many space programs...  15% over-predicting is not "wrong", it's a conservative 15% margin

# Re: Linear Buckling Analysis

Experimenter

I have nothing against overestimation , nor will I deny how many incredible things were made only with linear calculations (and how many were made without any calculations at all)! There are however some other things to consider:

The "famous" 15% I believe origins in prof. Yoshimuras article where he pointed out that linear vs nonlinear buckling of shells tends to be 15% apart (1984 if my memory serves, perhaps there were earlier texts I haven't found - this article is cited however). I'm quite certain however that this do not have to be positive factor - since LBA actually over predicts capacity this is a 15% under predictive margin at the least.

Since then several researchers have pointed out, that this margin can actually be higher (this is still not a huge issue) but also that LBA can predict buckling in wrong places (and this is problematic).

There are a lot of other problems involved - in LBA you cannot take into account "elephant foot buckling" (influence of plastic capacity of material on stability) - many silo failures had to happen to get that one clear - this can easily be the case here (I do not know the thickness of the web in relation to its width).

Other things like contacts are most likely not an issue here.

I totally respect linear analysis - there is a lot you can do with a simple approach - I often use it myself. However nonlinear analysis of this case will take what... 3 minutes instead of 15 seconds? I do not see any gain in linear approach to this problem, since the model is small. You do not have to use any additional licenses (Sol 106 will do the trick), and you can simply get a better result at the cost of setting 4 parameters and 3 minutes of waiting... in this case I'm happy with this trade - this is why I did advice it.

Cheers

Łukasz