Dynamical models for plates and membranes. An asymptotic approach

Abstract

We examine the asymptotic expansion of a time-dependent displacement field defined over a three-dimensional elastic body whose shape corresponds to a thin plate. We show that under simple assumptions it is possible to derive from the principles of virtual work two known plate equations and three membrane models. Our results modify the displacement-stress method used by P.G. Ciarlet to derive von-Karman plate equations. The modified algorithm allows one to employ techniques of algebraic geometry which simplify the computational aspects of the analysis.