Buckling Imperfection Factor

[sushi75]

Hello!

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

 

[MotorCity]

In order to come up with a factor to account for imperfections, I think you will need to define and limit the imperfection. You probably cannot come up with a single factor to account for all imperfections of all sizes, locations, etc. For example, would a dent be considered an imperfection? If so, what is the maximum diameter and depth that you are willing to allow in your shell. One of the ways this is done in steel is to assume that the maximum imperfection is the fabrication or erection tolerance and go from there.

 

[TGS4]

The answer is that it depends on what the stress is at your buckling load? if it is more than 0.55*Sy, then you are no longer into an elastic buckling analysis, but an elastic-plastic buckling analysis.

What is done in the pressure vessel industry (based on what you have described, this industry might be more relevant) is that a mode SHAPE is derived from the eigenvalue buckling analysis. Then, using the manufacturing tolerances as a displacement scale factor, the "perfect" sphere is perturbed based on the mode shape from the eigenvalue analysis. Then, an elastic-plastic analysis (full true stress-true strain, non-linear geometry, etc) is performed.

 

[WARose]

I don't remember those types of shells being very imperfection sensitive. However, for a safe allowable pressure/stress.......you probably need to find a code like ASME's code. What you are describing sounds like it might be analogous to a pressure vessel head. I don't know if you have a pressure vessel handbook around (I can recommend one if you want), but many of them handle internal/external pressures and point loads. A code allowable is always a good basis for a situation like that.

 

[sushi75]

Hello,

Thanks for your quick feedback, and the information provided.

TGS4, the structure is a pressure vessel, so I believe it's worth following your strategy.

I'm not aware of the 0.55*Sy as a limit, what is it based on?

So based on the mode shape, How do you perform the non linear analyis?

To run the non linear analysis, my intention was to run a static non linear with a ramp function for the pressure case, rather than a constant load.

Is it the idea you started to develop?

Thanks a lot!!

 

[TGS4]

sushi75 - let's continue the discussion over in forum794. There will be lots of additional knowledgeable people who can chime in over there (who don't frequent the Structural Forum).

 

[mike20793]

What kind of shell is it? Steel? I've done quite a few concrete ones (truncated hemispherical domes) recently and there are provisions for determining the snap buckling strength. I'm not sure about any other materials, though.