Generalized thermoelasticity problem of a hollow sphere under thermal shock

Abstract

This problem deals with the thermo-elastic interaction due to step input of temperature on the boundaries of a homogeneous isotropic spherical shell in the context of generalized theories of thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector-matrix differential equation which is then solved by eigen value approach. The inverse of the transform solution is carried out by applying a method of Bellman et al. Stresses, displacements and temperature distribution have been computed numerically and presented graphically in a number of figures for copper material. A comparison of the results for different theories (CTE, CCTE, TRDTE(GL), TEWOED(GN-II), TEWED(GN-III)) is presented. When the outer radius of the shell tends to infinity, the corresponding results agree with that of existing literature.