Buckling of an Externally Pressurised Cylinder 2

[Jack Devlin 1998]

Hello,
I’m currently carrying out an FEA study looking at the elastic-plastic buckling of externally pressurised cylinders (loaded radially).
In order to verify my analysis, I’d like to compare with analytical equations, however I am struggling to find equations for a cylinder pressurised radially, all I can find are examples of an axially loaded cylinder.
The outer diameter of the pipe is 170mm and the thickness is 10mm.
Thanks in advance for any help.

 

[r6155]

Do you know ASME code for pressure vessel?

Regards

 

[chicopee]

I know how to find the wall thickness of a pressure vessel under external pressure using the ASME code VIII, however, I am not confident that it could apply to cylinders unless we are dealing with ASME cylinders.

 

[Jack Devlin 1998]

Sorry, I wasn’t clear in my original post. I’m looking for an equation that finds the critical buckling pressure of a radially loaded cylinder.
For example, the computer model is telling me that my cylinder will buckle when the external pressure is 106MPa, in order to verify the simulation is accurate, I’d like to compare this with theoretical calculations.

 

[prex]

Google Buckling of circular cylinders and you'll find many papers dealing with your problem. I guess that also on eng-tips you can find what you are looking for.

prex
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[Jack Devlin 1998]

Hi Prex,

Believe me, I have googled every combination of “Buckling” “Cylinder” and “Externally Pressurised”.
I would not have came here to ask for the forums help if I had not exhausted all other means.
If you google “buckling of circular cylinders” all that is returned are papers discussing cylinders loaded axially.
The cylinder I am analysing is subject to an external pressure, loaded around it’s circumference, as shown in the attached photo.

 

[3DDave]

I used Google and "buckling of circular cylinders from external pressure"

Got a lot of hits exactly what you describe.

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690013955.pdf

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19660001966.pdf

https://www.thejot.net/login/?page_id=837&show_article_preview=84&jot_download_article=84

paid:

https://www.sciencedirect.com/science/article/abs/pii/026382319390006V

https://asmedigitalcollection.asme....Steel-Cylinders-Under?redirectedFrom=fulltext

 

[Jack Devlin 1998]

That third one looks to be a god send, no idea why it never came up when I searched for it. Thank you very much!

 

[r6155]

See the classic book; ROARK`S 7th edit "Formulas for stress and strain", Table 15.2

Regards

 

[JStephen]

Pretty sure that is covered in Roark, that and combinations of axial and external pressure.
Theory should be in Timoshenko, "Theory of Elastic Stability". If I remember right, in some of these cases, the theoretical buckling strength can be double the actual or so.
I'm thinking a lot of that research was motivated by submarine design, so the problem's been around a while.
Just looking back at your question, I see "elastic-plastic" and the theoretical is generally all-elastic.

 

[EdStainless]

The real world problem with these is eccentricity. If you have a cylinder with perfect dimensions and properties then you come very close to the theoretical values. But if the roundness, wall thickness, or properties very at all then you may buckle at 1/10th the value. I used to assist building deep well equipment, we cared about this.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy

 

[Jack Devlin 1998]

That’s actually one of the things the study is going to look at, I plan to model some geometrically perfect cylinders on ANSYS and see what it churns out, compare with theoretical calculations in order to verify ANSYS isn’t handing me nonsense, and then I plan to carry out a buckling analysis on cylinders with some imperfections modelled into them.

 

[HTURKAK]

I will suggest you to look the following books regarding the buckling of cylindrical shells under the action of uniform external pressure :

1-Stephen P. Timoshenko, Theory of elastic stability (1936)

2- Jawad, Maan H, Design of plate and shell structures

3-Dr.Ing. E. h. Alf Pflüger ,Stabilitätsprobleme der Elastostatik (1975)

Good Luck..

 

[CuMo]

Maybe the following could help you somehow:

PD 5500 3.6 Vessels under external pressure
Also 3.6.2.1
and
PD 5500 Annex M Requirements for establishing the allowable
external pressure for cylindrical sections outside
the circularity limits specified in 3.6

Also referenced are:
a) C187/72, Buckling under external pressure of cylinders with either
torispherical or hemispherical end closure, by G.D. Galletly and R.W.
Aylward.

Also worth reading is
PD 5500 - Enquiry Case 33.
Verification of shape of vessels subject to external
pressure

https://pdfs.semanticscholar.org/e15d/7358be18b27dcc372e98a97177ff6bae8620.pdf

https://www.researchgate.net/public...ressure_Vessel_Subjected_to_External_Pressure

https://www.sciencedirect.com/science/article/abs/pii/S0263823118302994

 

[mskds545]

I'm not sure comparing equations for elastic instability of a cylinder to an elastic-plastic analysis of a perfect cylinder is meaningful. Remember, buckling happens because perfection is not real. If you model perfection, you might not pick up on buckling. The elastic-plastic analysis might pick up buckling if you have some non-uniformities in your mesh that act like shape imperfections, but if you have a nicely structured mesh it might not collapse until the hoop stress reaches the plastic limit. This is kind of arbitrary.

You should compare the textbook equations to an eigenvalue buckling analysis of a perfect cylinder, both of which can be non-conservative compared to a real imperfect cylinder. Compare your elastic-plastic model results with an imperfection to both of those, and look at it as a function of imperfection magnitude. You can use ovality, or a multi-lobed shape, or a small notch, or a peak, or a local thin area, or whatever as the imperfection. But I wouldn't ascribe much meaning to instabilities induced by arbitrary mesh imperfections that you can't define physically.

-mskds545