Hi, everyone,

I am new here. Now I am doing a research which is related to the Euler's buckling formula.  It is known that when the cylinder is thick enough, Euler's buckling formula is no longer valid. I want to know in which region of slenderness(aspect ratio) of a cylinder or column that the Euler's buckling formula is valid. Is there any analytical study or numerical results about it? Is there any suggestion or paper I can find?

 Thank you very much!