Some non-classical thermoelasticity problems for a rectangular parallelepiped

In the Cartesian system of coordinates, thermoelastic equilibrium of an isotropic homogeneous rectangular parallelepiped is considered. On the lateral faces of a parallelepiped either symmetry or anti-symmetry conditions are defined while the top and bottom faces are free of stress. The problem is that to define the temperature on the top and bottom faces of a parallelepiped so that the normal displacement or the tangential displacements would take a priori fixed values on some two planes parallel to the bases. The problems are solved analytically using the method of separation of variables. The problems are non-classical, but they differ from other non-classical problems known in literature and are of a practical importance.