Analytical solution of classical and non-classical boundary value contact problems of thermoelasticity for a rectangular parallelepiped consisting of compressible and incompressible elastic layers and numerical example of the solution of such problems

Abstract

The paper deals with a static thermoelastic equilibrium of an N-layer rectangular parallelepiped. The layers of the considered body are made of an isotropic homogeneous elastic material. A case when some of the layers consist of incompressible elastic materials, which are also assumed to be isotropic and homogeneous, is considered as well. Boundary conditions of symmetric or antisymmetric continuous extension of the solution are imposed on the lateral facets of the parallelepiped. Between the layers contact conditions of rigid, sliding or other type of contact can be defined. On the upper and lower facets of the parallelepiped, arbitrary boundary conditions are defined. Solution of the stated problems is made analytically using the method of separation of variables. The solution of the problems is reduced to the solution of systems of linear algebraic equations with block diagonal matrices. In the conclusion, a practical example establishing the elastic equilibrium of a three-layer rectangular parallelepiped is given.