Solution of some boundary value thermoelasticity problems for a rectangular parallelepiped taking into account micro-thermal effects

摘要

A three-dimensional system of differential equations is considered that describes a thermoelastic equilibrium of homogeneous isotropic elastic materials, microelements of which, in addition to classical displacements and thermal fields, are also characterized by microtemperatures. In the Cartesian system of coordinates the general solution of this system of equations is constructed using harmonic and metaharmonic functions. Some boundary value micro-thermoelasticity problems are stated for the rectangular parallelepiped. An analytical solution of this class of boundary value problems is constructed using the above-mentioned general solution. When the coefficients characterizing microthermal effects are zero, the obtained solutions lead to the solutions of corresponding classical boundary value thermoelasticity problems, the majority of which have been solved for the first time. It should be noted that the aim of the given work is to construct an effective (analytical) solution for a class of boundary vale problems rather than to investigate the validity or applicability of the involved theory.