Analytical Solution for the Thermopiezoelastic Behavior of a Smart Functionally Graded Material Hollow Sphere Under Radially Symmetric Loadings

Abstract

An analytical study of the piezothermoelastic behavior of a functionally graded material (FGM) hollow sphere with integrated piezoelectric layers as a sensor and actuator under the effect of radially symmetric thermoelectromechanical loading is carried out. The material properties of the FGM layer are assumed to be graded in the radial direction according to a power law function. Governing differential equations are developed in terms of the components of the displacement field, the electric potential and the temperature of each layer of the smart FGM hollow sphere. The resulting differential equations are solved analytically. Numerical examples are given and discussed to show the significant influence of grading index of material properties and feedback gain on the mechanical–electrical responses. This will be useful for modern engineering design.