Continuation of some solutions in potential theory and their applications to elastic contact and crack problems (Q1309439)

The following mixed boundary value problem is considered: arbitrary tangential displacements are prescribed inside a circle, while the tangential and normal stresses outside the circle are zero. In this case, a direct and simple formula is derived for the tangential displacements outside the circle in terms of prescribed displacements inside, thus making the tangential displacement known all over the boundary. Another solution for the case, when arbitrary tangential displacements are prescribed outside a circle, is derived in a similar manner. The reciprocal theorem is used to derive the continuation formulae for the tangential stresses inside and outside a circle.