Exact Elementary Green’s Functions and Integral Formulas in Thermoelasticity for a Half-Wedge

Abstract

AbstractIn this study new exact Green’s functions and a new exact Poisson-type integral formula for a boundary-value problem (BVP) in thermoelasticity for a half-wedge with mixed homogeneous mechanical boundary conditions are derived, in which the boundary angle is rigidly fixed and the normal displacements and tangential stresses or the normal stresses and tangential displacements are prescribed on the boundary quarter-planes. The thermoelastic displacements are subjected to a heat source applied to the inner points of the half-wedge and to mixed nonhomogeneous boundary heat conditions, in which the temperature is prescribed to the boundary angle or to one boundary quarter-plane and the heat flux is given on the other boundary quarter-plane. When the thermoelastic Green’s function is derived, the thermoelastic displacements are generated by an inner unit point heat source, described by the δ-Dirac function. All results are obtained in elementary functions that are formulated in a special theorem. Analogo...