Secondary branching and the post critical behaviour of thin-walled shells during non-uniform deformation

Abstract

The non-linear behaviour and post-critical behaviour of thin walled shells during non-uniform deformation due to a non-uniform load or inhomogeneous structure are analysed. The branching equations are constructed and, for the non-linear equations for Newton's method, the singular points are classified. The results of calculations and an analysis of the post-critical behaviour for cylindrical and spherical. shells with inhomogeneities of different forms are given. It is shown that localized patterns of stability loss and fracture are due to the eidstence of isolated equilibrium branches and secondary branching of non-linear solutions.