The effect of fractional thermoelasticity on two-dimensional problems in spherical regions under axisymmetric distributions

Abstract

Two-dimensional axisymmetric problems are considered within the context of the fractional order thermoelasticity theory. The general solution is obtained in the Laplace transform domain by using a direct approach without the 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 traction free and subjected to a given axisymmetric temperature distribution. The inversion of the Laplace transforms is 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. Some comparisons are shown in figures to estimate the effect of the fractional order parameter on all studied fields.