Time Dependent Electro–Magneto–Thermoelastic Stresses of a Poro Piezo Functionally Graded Material Hollow Sphere

Abstract

In this paper, analytical solution for timedependent electro–magneto–thermoelastic stresses of a hollow sphere made of a fluidsaturated functionally graded porous piezoelectric material (FGPPM) is presented. All material properties, except Poisson's ratio, vary through the radial direction of the FGPPM spherical structure according to a simple powerlaw. The general form of thermal, mechanical, and electric potential boundary conditions is considered on the internal and external surfaces of the sphere, and the sphere is under constant electrical and magnetic fields. Stress–strain and strain–displacement relations are used to obtain stress–displacement equations, and then by putting stress–displacement equations in the equilibrium equation, Navier equation is acquired. The homogenous differential heat conduction equation is solved. The nonhomogenous differential Navier equation is solved for two cases. At first, creep strains are ignored and the initial electro–magneto–thermoelastic stresses are obtained. Then considering creep strains singly, the creep stress rates are obtained. Finally, timedependent creep stress distributions at any time ti are attained.