A dislocation in a nearly polygonal isotropic domain

This paper describes the singular solution of a plane elasticity problem associated with a dislocation or a concentrated load in a polygon with rounded corners. The solution is constructed using a transformation that maps the nearly polygonal domain into a circular ring. The solution is in the form of an infinite series that reduces to a closed form when the approximate polygon is a square with rounded corners. For the singularity associated with a dislocation, the self-energy outside the dislocation core is finite. When the dislocation occurs near the boundary, this energy can be significantly lower than that of a dislocation which occurs far from the boundary. When the domain is large, the self-energy approaches that commonly used for an infinite domain.