Buckling Imperfection Factor

[sushi75]

Hello,

I've started a thread in another forum, but following advice of one of the member I post it here as my analysis is applicable to a pressure vessel.

So here is the summary of the problem, hope someone can give me guidances and good information to progress!!

Thanks!

I'm currently going through buckling analysis, for a hemispheric shell. So it a basically a portion of a sphere.

It is subjected to a pressure load on the external surface, therefore it can buckle.

From handbooks I could calculate the thickness, radius and angle using handcalcs.

But I have to include a knock down factor to account for imperfection.
And the problem begins!!

I don't clearly see the method to do that. I can run a FE model using linear buckling, which will give me a buckling load factor.
Then maybe run a non linear buckling analysis to measure the actual displacement to make sure there is no snap through.
This is the idea I have, it's a bit reproducing a test from where we usually derive the imperfection factor.

But I'm not sure to get it right with this strategy... so if someone knows a good (or better) way of deriving this factor (basically a KDF to be applied to the Young's modulus to account for stiffness reduction).

Thanks a lot for any help you can provide me!

Cheers

 

[TGS4]

Thanks for bringing the discussion over here.

A few thoughts:
1) If there is nothing extraordinary about this hemispherical shell, then I would suggest that you simply follow the design rules in either ASME Section VIII, Division 1 (UG-28) or Division 2 (4.4).

2) If you have something that isn't covered by the rules, then you would be into a Design By Analysis, in which case you should be following the rules in ASME Section VIII, Division 2, Part 5, Section 5.4 Protection Against Collapse From Buckling.

In the previous thread, I mentioned a threshold of 0.55*Sy. Below that threshold, it can be assumed that the buckling mode will be linear-elastic. Above that threshold, the failure mode will be a mixed elastic-plastic buckling. This is addressed in the Division 1 Code Case 2286, which forms the basis of Division 2 Section 4.4.

If you would like, I can also discuss design-by-analysis approaches.

 

[sushi75]

Thanks TGS4, I was not aware of ASME design rules, so I'll have a look I guess there will be relevant information for this buckling assessment!!

From your experience, what range of KDF do you expect? 2-3 ish?

 

[TGS4]

For heads, the design margin required based on elastic eigenvalue buckling analysis is on the order of 16.

 

[sushi75]

Hi TGS4,

I had a look at the ASME design rule but i'm still a bit puzzled about the rationale I should take.

I'm using the NASA handbook 8032 for doubly curved shell.

So what I've got assess is the hemispherical cap under pressure (imagine a bottle with the cylinder ending with a curved shell).

the critical buckling load is presented in the NASA handbook; and there is no imperfection factor recommended, but I'm asked to find one...
usually for buckling 3 is a common value.

to account for imperfection I have a FE model, but I don't how I can make any conclusion from that!
for the pressure case I'm running, linear buckling predicts a BLF=9.36.

So can this factor be considered as the knock down factor for imperfection?

I'm not sure of the logic behind this analysis. So if anybody has a better or more consistent idea to progress, I'll be hapy to follow your advice!!

Thanks a LOT!

 

[TGS4]

Here's what I do:

Perform an eigenvalue buckling analysis. Forget about the eigenvalue - the important bit of information is the eigenvector (bucking mode shape). You will then introduce an imperfection/perturbation of a magnitude equal to the manufacturing tolerances of your component - unless otherwise specified, I would tend towards 1% of the diameter - in the shape of the eigenvector that you just calculated. Then, perform an elastic-plastic analysis (with non-linear geometry). If it collapses before the design loads, then you have a problem - otherwise you should be fine.

The ASME Code right now doesn't tell you how to introduce the imperfection/perturbation. That's what I've shown you above.

Forget everything that you think you know about evaluating the results of an eigenvalue buckling analysis with the eigenvalue. If the membrane stress at the buckling load is greater than 0.55Sy, then your into the mixed elastic-plastic buckling region, a region where elastic eigenvalue buckling is completely inadequate, regardless of how big the knock-down factor is. I have been bitten in the butt to many times in the past by trying to do eigenvalue buckling - My company's standard approach now is to only do elastic-plastic buckling.

 

[sushi75]

Hi TSG4,

Thanks a lot for these guidance. So I've followed your advice, run t a buckling analysis for a spehrical cap under pressure. I've got a BLF of 10 and the shape of the first mode. it's not really the one I expected at it shows a direction opposite to the load.

So from that, I will amend the geometry and create an modified profile based on the the first mode shape. that will be the baseline for the imperfection of the surface inducing buckling.

From this stage I should then be running a non linear analysis with an incremental load, and check if snap through occurs looking at the displacements?

However, how is the imperfection factor derived from that? If we need to adjust the load to make sure no collapse occurs, then the factor is based on the ratio?

Many thanks for your support, with your help I can have a better understanding of buckling.

Cheers

 

[TGS4]

The magnitude of the imperfection should be equal to the manufacturing tolerances on your sphere. Or, if you are so inclined, you could measure (think laser scanning) and impose tgs4 imperfection based on the magnitude of the actual imperfections.