Elasticity Solution Approach for Functionally Graded Spherical Shell with Piezoelectric Properties

In this paper, an analytical method is adopted, based on elasticity approach to analyze the hollow FGM sphere with piezoelectric properties. The electro-mechanical properties except the Poisson’s ratio are assumed to be power functions of radius. Loading is a combination of pressures and a distributed electric field. For axisymmetric problem, 3-D governing equations are reduced to a 1-D second order nonlinear Cauchy-type differential equation, in terms of radial displacement. The solution of nonlinear differential equation is opted as a power law function. By satisfying five 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 ‘n’ and the effect of size are investigated. The induced radial and circumferential stresses of an imposed electric potential are compared to the residual stresses locked in the homogeneous sphere.