Analytic solutions for the problems of an inclusion of arbitrary shape embedded in a half-plane

摘要

We study the problems of an inclusion of arbitrary shape embedded in the half-plane y<0, with fixed and rigid, frictionless boundaries y=0 by using complex variable function method. With the help of the techniques of analytic extension, analytic continuation and conformal mapping, analytic expressions of solution are obtained. The results show that for a rigid frictionless boundary, the mean stress remains constant inside the thermal inclusion and vanishes outside regardless of the shape of the inclusion, and this is not true of the case for the fixed boundary.