GREEN-FUNCTION FOR THE ELASTIC FIELD OF AN EDGE DISLOCATION IN A FINITE ORTHOTROPIC MEDIUM

A fundamental solution of plane elasticity in a finite domain is devel oped in this paper. A closed-form Green's function for the elastic fie ld of an edge dislocation of arbitrary Burger's vector at an arbitrary point in an orthotropic finite elastic domain, that is free of tracti on, is presented. The method is based on the classical theory of poten tial fields, with an additional distribution of surface dislocations t o satisfy the free traction boundary condition. A solution is first de veloped for a dislocation in a semi-infinite half-plane. The resulting field is composed of two parts: a singular contribution from the orig inal dislocation, and a regular component associated with the surface distribution. The Schwarz-Christoffel transformation is then utilized to map the field quantities to a finite, polygonal domain. A closed fo rm solution containing Jacobi elliptic functions is developed for rect angular domains, and applications of the method to problems of fractur e and plasticity are emphasized.