Electro-magneto-thermo-mechanical Behaviors of a Radially Polarized FGPM Thick Hollow Sphere

Abstract

In this study an analytical method is developed to obtain the response of electro-magneto-thermoelastic stress and perturbation of a magnetic field vector for a thick-walled spherical functionally graded piezoelectric material (FGPM). The hollow sphere, which is placed in a uniform magnetic field, is subjected to a temperature gradient, inner and outer pressures and a constant electric potential difference between its inner and outer surfaces. The thermal, piezoelectric and mechanical properties except the Poisson’s ratio are assumed to vary with the power law functions through the thickness of the hollow sphere. By solving the heat transfer equation, in the first step, a symmetric distribution of temperature is obtained. Using the infinitesimal electro-magnetothermo-elasticity theory, then, the Navier’s equation is solved and exact solutions for stresses, electric displacement, electric potential and perturbation of magnetic field vector in the FGPM hollow sphere are obtained. Moreover, the effects of magnetic field vector, electric potential and material in-homogeneity on the stresses and displacements distributions are investigated. The presented results indicate that the material in-homogeneity has a significant influence on the electro-magneto-thermo-mechanical behaviors of the FGPM hollow sphere and should therefore be considered in its optimum design.