Time-dependent behaviors of a FGPM hollow sphere under the coupling of multi-fields

Abstract

This paper presents an analytical solution for time-dependent behaviors of a hollow sphere made of functionally graded piezoelectric material (FGPM) under the coupling of multi-fields. Material properties, electric parameters, permeability, thermal conductivity and creep parameters vary smoothly through the radial direction of the FGPM spherical structure according to a simple power-law. Using equations of equilibrium, stress–strain and strain-displacement in a differential equation, containing creep strains, for displacement are obtained. Firstly, ignoring creep strains in the differential equation, a closed form solution for the initial electromagnetothermoelastic stresses at zero time is presented, and considering Von Mises stress balance equation, the effective electromagnetothermoelastic stresses are also presented. Secondly, considering only creep strains, creep stress rates are obtained by using the Prandtl–Reuss equations and Norton’s law. Finally, time-dependent creep stress redistributions at any time ti are obtained iteratively. The aim of this research is to understand the effects of the graded index on creep behavior of hollow spherical structures and design optimum FGPM hollow spherical structures.