Some Non-Classical Boundary Value Problems of Thermoelasticity and a Three-Dimensional Analogue of Muskhelishvili's Thermal Effect

The present article deals with special thermoelastic equilibrium of the rectangular parallelepiped; some non-classical thermoelasticity problems are stated and analytically solved. In particular, in the Cartesian system of coordinates thermoelastic equilibrium of an isotropic homogeneous rectangular parallelepiped is considered. Symmetry or antisymmetry conditions are defined on four lateral facets of the parallelepiped, while the remaining upper and lower facets are free of stress. The problem is to define the temperature on the upper and lower facets of the parallelepiped, so that normal displacements or tangential displacements on these facets would take a priori defined value (note that since zero values have been already defined on the upper and lower facets, on each of these facets instead of three conditions four or five conditions should be satisfied). It should be emphasized that at the end of the paper a three-dimensional thermal effect is stated, similar to Muskhelishvili's two-dimensional thermal effect.