Magnetothermoelastic stress and perturbation of magnetic field vector in a functionally graded hollow sphere

Abstract

In this article, a closed-form solution for one-dimensional magnetothermoelastic problem in a functionally graded material (FGM) hollow sphere placed in uniform magnetic and temperature fields subjected to an internal pressure is obtained using the infinitesimal theory of magnetothermoelasticity. Hyper-geometric functions are employed to solve the governing equation. The material properties through the graded direction are assumed to be nonlinear with an exponential distribution. The nonhomogeneity of the material in the radial direction is assumed to be exponential. The temperature, displacement and stress fields and the perturbation of magnetic field vector are determined and compared with those of the homogeneous case. Hence, the effect of inhomogeneity on the stresses and the perturbation of magnetic field vector distribution are demonstrated. The results of this study are applicable for designing optimum FGM hollow spheres.