The solution of uncoupled thermoelastic problem with first kind boundary conditions

In this paper the method of calculation of the stress strain state of a homogeneous isotropic body of arbitrary shape with a piecewise smooth surface is offered. The behavior of the body is described by an uncoupled quasistatic thermoelastic problem, boundary conditions of the first kind are considered. The offered method allows to find the analytical solution of a considered problem of thermoelasticity and to define components of a displacement vector and temperature as functions of body point’s coordinates and time. In order to obtain the solution the considered problem decomposed to an initial boundary value problem of heat conductivity and a boundary value problem of the linear theory of elasticity. The solution of a heat conductivity problem is built by support functions method. The non-uniform problem of the linear theory of elasticity is reduced to the homogeneous problem by means of Kelvin–Somigliana’s tensor; its solution is obtained by means of the theory of potential and Fourier’s transformation.

boundary thermoelastic problem, first kind boundary conditions, heat conduction problem, volume potential, Fourier transform