Stability of Doubly Periodic Deformed Configurations of Plates and Shallow Shells

Abstract

Presented here is a nonlinear analysis of infinite plates and shallow shells, subjected to doubly periodic surface loadings. The drastically different behaviors predicted by the linear and the nonlinear theories are analyzed and discussed. It turns out that the transition from the small to the large deflection behavior involves nonlinear bifurcation and the existence of multiple equilibrium configurations, and it entails the question of stability. Seen in this light, it is easy to explain various features special to problems in this class, including the jump phenomenon. From the viewpoint of stability analysis, this class of problems is distinct and interesting in that the perturbations which can lead to instability have actually a higher degree of symmetry than the unperturbed configurations.