Hello Amir

Generally the problem of buckling does not have a single solution, in direction and amplitude; especially for the forms with symmetry.

For certain designs and loading, the direction of buckling will determine the continuation and the behavior in post buckling and in this case the local curvatures are  prévalent  to determine  the  critical cases and  or the stability  behavour.

Imaginations will be much better than the usual theory and methods.

I could better help you according to the form of your structure.

Good luck.  

Thank you dear Naceur

Your explanation are very useful in physical comprehension of the problem, but, actually I am trying to write a finite element code to capture the post-buckling path of plate and shell structures and I do not know how to do this.

Thanks a lot anyway

Hello Amir,

I transmit your question to my colleague  Khalil Mansouri ( ENIT) , he works on similar problems  and uses XFEM methods for non linear problems.

I appreciate your consideration Dear Naceur

Thank you

Hello

I'm not an expert of post buckling but for numerical techniques to perform postbuckling you refer to the help of abaqus (Abaqus theory guide)  where a modified Riks algorithm is detailed, there are some references in this section

* http://abaqus.software.polimi.it/v6.14/books/stm/default.htm

you can see also some abaqus examples (Buckling and posbuckling analysis  here :

* http://abaqus.software.polimi.it/v6.14/books/usb/default.htm?startat=pt03ch06s02at03.html#usb-anl-apostbuckling

Good luck