Tsitskishvili Z.
Academically Doctor of Mathematical Sciences,Professor
Museridze R.
Academic Doctor of Construction Sciences, assistant professor.
Chkheti V.
PhD student. Georgian Technical University

Abstract
Determining the complete picture of the stress-strain state (SSS) of massive elements (bodies whose overall dimensions are of the same order) requires the use of three-dimensional models.
A special case of a massive element—a parallelepiped-shaped plate—is one of the most common objects used in technology.
A large number of works have been devoted to the problem of the equilibrium of a loaded elastic parallelepiped, but it remains relevant to the present day, since a closed solution has not yet been obtained.
Existing analytical solutions for three-dimensional problems of the theory of elasticity do not allow satisfying arbitrary boundary conditions on the faces of a parallelpiped.
In the work under consideration, for one class of boundary value problems using the method of separation of variables and double series, solutions to static boundary value problems of thermoelasticity  for a rectangular coordinate parallelepiped are constructed.

Keywords: boundary value problem of thermoelasticity, stress-strain state, isotropic plate, equilibrium equations (without taking into account body forces), Equation of state (physical law or Hooke’s law), heat equation, Sturm-Liouville problem, method of separation of variables, double series, convergence.