Tensor spherical harmonics analysis of electro-elastostatic fields in a spherically isotropic multiphase functionally graded piezoelectric medium

Abstract

This paper is devoted to the study of the electro-elastostatic fields of a multiphase concentric spherical piezoelectric ensemble under general electromechanical loading in the presence or absence of body forces and body electric charges. Each phase is assumed to be spherically isotropic and at each point the poling direction is radially oriented. Thanks to the robustness of spherical harmonics, in this work we will obtain the exact solutions for the three-dimensional displacement and electric potential when the elastic, piezoelectric and dielectric constants of each phase vary as power-law functions of the radial distance.