Symbolic computation of potential energy functions

Abstract

We derive potential energy functions for a shallow cylindrical panel. The starting point is a system of two coupled partial differential equations based on Donnell's shallow shell theory. The total potential energy is approximated using a finite number of degrees of freedom. All calculations are performed by computer algebra routines. Two applications of potential energy functions are discussed: the analysis of shell buckling and the derivation of systems of ordinary differential equations that govern dynamic behaviour.