Elastodynamics and Elastostatics by a Unified Method of Potentials for x 3-Convex Domains

Abstract

A new general solution in terms of two scalar potential functions for classical elastodynamics of x3-convex domains is presented. Through the establishment and usage of a set of basic mathematical lemmas, a demonstration of its connection to Kovalevshi–Iacovache–Somigliana elastodynamic solution, and thus its completeness, is realized with the aid of the theory of repeated wave equations and Boggio’s theorem. With the time dependence of the potentials suppressed, the new decomposition can, unlike Lame’s, degenerate to a complete solution for elastostatic problems.