NEW 3D THERMOELASTIC INFLUENCE FUNCTIONS, CAUSED BY A UNITARY POINT HEAT SOURCE, APPLIED IN A QUARTER OF LAYER

Abstract

The aim of this paper consist in the constructing of the main thermoelastic displacements Green’s functions (MTDGFs) for a generalized 3D BVP of uncoupled thermoelasticity for a quarter of layer. To reach this aim are derived structural formulas for MTDGFs, expressed via respective Green’s functions for Poisson’s equation (GFPE) by using harmonic integral representations method (HIRM). These structural formulas are validated by the checking the equations of thermoelasticity with respect to point of response in which the thermoelastic displacements appeared and with respect to point of application the heat source and the nonhomogeneous Poisson’s equation. In addition, they satisfy the homogeneous mechanical boundary conditions for MTDGFs with respect to point application the displacements and to mechanical boundary conditions and temperature Green’s function with respect to point of application the heat source. The thermoelastic volume dilatation (TVD) derived separately from respective integral representations has been equal to the TVD derived by using structural formulas for MTDGFs. The final analytical expressions for MTDGFs obtained on the base of mentioned above structural formulas for sixteen new 3D BVPs of thermoelasticity within quarter of layer contain Bessel functions of the zero-order of the second type. These results are presented graphically.