First fundamental axisymmetric problem of thermoelasticity for a compressed spheroid with a concentric spherical cavity

An axisymmetric boundary-value problem of thermoelasticity for a compressed spheroid with a concentric spherical cavity is studied by the generalized Fourier method. The problem is reduced to an infinite system of linear algebraic equations with the Fredholm operator under the condition that the boundary surfaces are not crossed. Results of a numerical analysis of stresses in the case of load-free boundary surfaces in the presence of a temperature field caused by a constant temperature distribution on the boundary surfaces are presented.