On the nonlinear buckling and post-buckling analysis of thin elastic shells
The aim of the paper is to determine the critical and post-critical behaviour of elastic structures in the frame of a geometrically nonlinear shell theory with moderate rotations. For the fundamental equilibrium path, critical points and post-critical path, a variational method is used, and the equilibrium equation and boundary conditions are obtained in a compact form using an appropriate operator description. The problem of determining the critical values and post-critical path is solved by using the static perturbation technique in the neighbourhood of a critical point. The example refers to a shallow circular cylinder panel with two opposite edges hinged and the other two free, loaded by a central point and axial compression. For a symmetric deformation, it is shown that the collection of critical points is a cusp catastrophe.
scientific article; zbMATH DE number 3880204
scientific article