Construction of three-dimensional solutions of the equations of the theory of thermoelasticity in the cylindrical coordinate system

A linear model of the theory of thermoelasticity for an isotropic body in the cylindrical coordinate system is considered. The stationary temperature satisfies a three-dimensional Laplace equation. The general solution of the system of Navier’s differential equations, which describes the thermoelastic stress state of the body, is presented as a sum of homogeneous and partial solutions. The partial solution, which does not contain the elastic displacements, is called the temperature solution. The theory is written that the sum of normal temperature stresses is zero. To solve the Navier’s equations the temperature is presented in the form of Bessel series, according to which properties the temperature solution of the Navier’s equations is constructed. Analytical formulas for the description of temperature displacements and stresses in explicit form are given. The general solution of the equations of the theory of thermoelasticity in terms of four harmonic functions is presented.