Green's function of the displacement boundary value problem for a heat source in an infinite plane with an arbitrary shaped rigid inclusion

Summary Green's functions of the displacement boundary value problem are derived within two-dimensional thermoelasticity for a heat source in an infinite plane with an arbitrary shaped rigid inclusion. The following two cases are considered: either rigid-body displacements and rigid-body rotations of the inclusion are allowed or no rigid-body displacements and no rigid-body rotations of the inclusion are possible. To solve these problems, fundamental solutions are developed for a point heat source, for rigid-body rotations of the inclusion, and for concentrated loads acting on the inclusion. Complex stress functions, temperature function, a rational mapping function and the thermal dislocation method are used for the analysis. In analytical examples, distributions of stresses are developed for an infinite plane with a rectangular rigid inclusion. Received 5 August 1998; accepted for publication 1 December 1998