Analytical Analysis for a Uniformly Loaded Circular Plate of Functionally Graded Piezoelectric Materials Using Mian and Spencer Theory

Mian and Spencer developed a procedure for constructing exact solutions to the equations of linear elasticity in thick isotropic functionally graded plates. In this study, the Mian and Spencer plate theory is extended from elastic material to piezoelectric material by incorporating intrinsic electro-elastic coupling. An electric potential function is constructed by analogy with the displacement components, and the corresponding functions are obtained through stepwise integration using the mechanical and electrical boundary conditions on the top and bottom surfaces of the plates. Exact 3D elasticity solutions are then derived for a uniformly loaded FGPM circular plate under simply supported and clamped boundary conditions, with the material coefficients allowed to vary arbitrarily along the thickness direction z. The analytical solutions are validated through comparison with results reported in the literature. Finally, a systematic parametric study is performed to investigate the effects of the material gradient index, boundary conditions, thickness-to-radius ratio, and piezoelectric effect on the electro-elastic effect of FGPM circular plates.