3D elasticity solution for static analysis of functionally graded piezoelectric annular plates on elastic foundations using SSDQM

Three-dimensional elasticity solution for static analysis of functionally graded piezoelectric (FGP) annular plates with and without elastic foundations through using state-space based differential quadrature method (SSDQM) at different boundary conditions is presented in this paper. The material properties are assumed to have an exponent-law variation along the thickness. A semi-analytical approach which makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is utilized to obtain the mechanical behavior of FGP annular plates. The state variables include a combination of electric potential, electric displacement, three mechanical displacement parameters and three stress parameters. Numerical results are given to demonstrate the convergency and accuracy of the present method. Both closed circuit and open circuit effects are studied and the influences of the Winkler and shearing layer elastic coefficients of the foundations, the material property graded index, radius, thickness, mechanical load and boundary conditions on the deflection response of the FGP annular plates are investigated. The new results can be used as a benchmark solutions for future researches.