3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loadings

Abstract

The problem of a piezoceramic hollow sphere is investigated analytically based on the 3D equations of piezoelasticity. The functionally graded property of the material along the radial direction can be taken arbitrarily in the paper. Displacement and stress functions are introduced, and two independent state equations with variable coefficients are derived. By employing the laminate model, the two state equations are transformed into ones with constant variables from which the state variable solution is easily obtained. Two linear relationships between the state variables at the inner and outer spherical surfaces are established. Numerical calculations are performed for different boundary conditions imposed on the spherical surfaces.

Meshless Local Petrov-Galerkin Method for Solving Contact, Impact and Penetration Problems

“…Shulga (1984, 1990)]. Analytical solution for stationary and transient dynamic load of a nonhomogeneous spherically isotropic piezoelectric hollow sphere is given by Chen et al (2002) and Ding et al (2003), respectively. The laminate model with radial dependence of physical fields is transformed to 1D problem.…”

“…The inner 0.4 a m = and outer radii 1 b m = are considered, respectively. The analytical solution is given by Chen et al (2002) and Ding et al(2003) and it is used as a benchmark to test the accuracy of the present method. The boundary conditions with prescribed pressures and vanishing electrical displacements on both surfaces correspond to pressured sphere embedded into nonconductive media (the open-circuit electric condition).…”

A complete set of equations for piezo-magnetoelastic analysis of a functionally graded thick shell of revolution

“…They proposed an analytical solution for the coupled large deflection analysis of mentioned structures. A spherical shell made of homogenous materials subjected to mechanical and electrical loads has been studied by Chen et al (2002). Liu et al (2002) developed an analytical model for free vibration analysis of a cylindrical shell under mechanical and electrical loads using Mindlin's theory.…”

The transient piezothermoelastic problem of a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply

“…In addition, exact treatments for functionally graded piezoelectric materials have been carried out. The piezoelectric problems of functionally graded piezoelectric spherical shells whose material properties vary according to a power product form in the radial direction were treated in [17,18]. The three-dimensional piezoelastic problem of a simply supported functionally graded piezoelectric plate whose material properties vary exponentially in the thickness direction was treated in [19].…”

“…(42), C 1J and C 2J are unknown constants.In order to obtain the particular solution we use the series expansions of the Bessel functions as shown in Appendix B. Since the order of the Bessel function in Eq (18). is not an integer in…”