Singular solutions of a plane elasticity problem that was associated with a dislocation or a concentrated load in a polygon with rounded corners were studied. The solutions were constructed by using a transformation which mapped the almost polygonal domain onto a circular ring. The solutions were in the form of infinite series which reduced to a closed form when the polygon was a square with rounded corners. In the case of the singularity which was associated with a dislocation, the self-energy outside of the dislocation core was finite. When the dislocation was located near to the boundary, this energy could be significantly lower than that of a dislocation which was located far from the boundary. When the domain was large, the self-energy approached the value that was generally assumed for an infinite domain.

A Dislocation in a Nearly Polygonal Isotropic Domain. P.Tong, T.Y.Zhang: International Journal of Fracture, 1996, 78[3-4], 241-60