SECONDARY BRANCHING AND THE POSTCRITICAL BEHAVIOR OF THIN-WALLED SHELLS DURING NONUNIFORM DEFORMATION

The non-linear behaviour and post-critical behaviour of thin-walled sh ells during non-uniform deformation due to a non-uniform load or inhom ogeneous structure are analysed. The branching equations are construct ed 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 locali zed patterns of stability loss and fracture are due to the existence o f isolated equilibrium branches and secondary branching of non-linear solutions. (C) 1997 Elsevier Science Ltd. All rights reserved.