Fundamental solutions for the generalised plane strain theory

Abstract

This paper presents some fundamental solutions of the three-dimensional stress distribution pertaining to a point force and an edge dislocation in an infinite plate of arbitrary thickness. These solutions are obtained using the generalised plane strain theory, which assumes that the through-the-thickness extensional strain is uniform in the thickness direction. These solutions recover, as special cases, the plane-strain solutions of the classical theory of elasticity close to the source and the plane-stress solution at large distance away from the source. Using these new solutions, the problem of a through-crack in an infinite plate of arbitrary thickness has been solved analytically. © 2002 Elsevier Science Ltd. All rights reserved.