Deriving exact Green’s functions and integral formulas for a thermoelastic wedge

In this paper an exact Green’s function and a Poisson-type integral formula for a boundary-value problem (BVP) for a thermoelastic wedge are derived in elementary functions. The thermoelastic displacements are generated by a heat source distributed in the inner points of the wedge. On the boundary half-planes the temperature is given, the mechanical boundary conditions being locally-mixed and homogeneous. Similar results for a quarter-space and for a half-space as particular cases of the wedge also are included. According to the well-known analogy between thermoelasticity and poroelasticity, the obtained results can be extended to poroelasticity problems, by making use of changes in respective constants. This paper introduces an approach for deriving new thermoelastic and poroelastic influence functions and Poisson-type integral formulas in closed form not only for wedge, quarter-space and half-space but also for many other canonical domains.