Dynamics of Geometrically Nonlinear Elastic Nonthin Anisotropic Shells of Variable Thickness

Abstract

A theory of dynamic elastic geometrically nonlinear deformation of nonthin anisotropic shells with variable thickness is constructed. Shells are assumed asymmetric about the reference surface. Functions are expanded into Legendre series. The basic equations are written in a coordinate system aligned with the lines of curvature of the reference surface. The equations of motion and appropriate boundary conditions are obtained using the Hamilton–Ostrogradsky variational principle. The change in metric across the thickness is taken into account. The theory assumes that the refinement process is regular and allows deriving equations including products of terms of Legendre series of unknown functions of arbitrary order. The behavior of a square metallic plate acted upon by a pressure pulse distributed over its face is studied.