Elasticity Solution Approach for Functionally Graded Spherical Shell with Piezoelectric Properties

Abstract

Based on elasticity approach, 1D analytical method is adopted in radial direction to analyze spherical shell made of FGPM. The mechanical properties are regulated by volume fraction as a function of radial coordinate. Loading can be internal and external pressures, or electric field. All mechanical and piezoelectric properties except the Poisson's ratio are assumed to be power functions of radius. The 3D governing equations are reduced to a 1D second order nonlinear differential equation in terms of radial displacement, which then is solved analytically. By satisfying four different sets of boundary conditions and incorporating them into governing equation, a system of algebraic equations is obtained that delivers the unknown constants. Static responses of FG shell to electro-mechanical loads with different powers of material in-homogeneity ‘n' as well as the effects of size are investigated. The accuracy and computational efficiency of the proposed approach are verified by comparing the results with those obtained for homogenous material in the literature. The induced stresses are compared to the residual stresses locked in the homogeneous sphere.