Numerical analysis of the branching of solutions to nonlinear equations for cylindrical shells

A nonlinear boundary-value problem for shells is formulated. The problem statement permits us to analyze the behavior of the postbuckling solutions in a finite-dimensional space with the dimension independent of the discretization technique. A branching pattern is established for the solutions of the problem in the case of a uniform external pressure. Four characteristic types of solution are recognized in the case of an arbitrary external pressure. The associated buckling loads are determined. It is found out that five significant parameters are sufficient for a qualitative analysis of a cylindrical shell __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 103–112, January 2006.