Generalized three-dimensional thermoelastic treatment in spherical regions

Abstract

In this work, the 3D problems of the generalized theory of thermoelasticity in spherical regions are investigated. The main aim is to obtain the form of the temperature, displacement components and stress tensor components in a closed form in the Laplace transform domain. To the author’s knowledge, this work is the first attempt to solve the full system of equations of generalized thermoelasticity in spherical regions. In the previous attempts some parts of the governing equations were neglected. Laplace transform techniques together with eigenfunction expansion are utilized to get the solution in the form of an infinite series using a new direct approach without the customary use of potential functions. An application is considered to illustrate the method. The inverse Laplace transforms are obtained using a numerical method. The solutions are represented graphically and discussed.