Generalized two-dimensional thermoelastic problems in spherical regions under axisymmetric distributions

Two-dimensional thermoelastic problems under axisymmetric temperature distributions are considered within the context of the theory of generalized thermoelasticity with one relaxation time. The general solution is obtained in the Laplace transform domain by using a direct approach without the customary use of potential functions. The resulting formulation is used to solve two problems of a solid sphere and of an infinite, space with a spherical cavity. The surface in each case is taken to be tractionfree and subjected to a given axisymmetric temperature distribution. The inversion of the Laplace transforms are carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical methods are used to accelerate the convergence of the resulting series to obtain the temperature, displacement, and stress distributions in the physical domain. Numerical results are represented graphically and discussed. A comparison is made with the solution of the corresponding coupled problem.