The static response of functionally graded radially polarized piezoelectric spherical shells as sensors and actuators

This paper analyzes the static response of a functionally graded spherical shell made of piezoelectric materials. A hollow piezoelectric sphere is polarized in the radial direction. Spherically symmetric problems of piezoelectric spherical shells as sensors or actuators are considered. For the gradient of power-law behavior, closed-form explicit expressions for the electroelastic field are derived. These solutions can serve as benchmarks for functionally graded piezoelectric hollow spheres. For arbitrarily varying gradient, an analytic approach for reducing the problem to a Fredholm integral equation is suggested to obtain the responses of the electroelastic field. Numerical results for a spherical piezoelectric vessel are obtained for special radial nonhomogeneity, and the distribution of the radial and circumferential stresses as well as the response of the electric potential for sensors and actuators are presented graphically under electrical and mechanical stimuli, respectively. Our results indicate that the gradient index strongly affects the stress distribution and electric response. The obtained results are helpful for optimizing the design of hollow spherical piezoelectric transducers.