Three-Dimensional Piezoelectricity Solutions for Uniformly Loaded Circular Plates of Functionally Graded Piezoelectric Materials With Transverse Isotropy

This paper considers the bending of a uniformly loaded transversely isotropic piezoelectric circular plate with material properties being arbitrary functions of the thickness coordinate. The displacements and electric potential are expressed in terms of appropriate polynomials of r, the radial coordinate, with coefficients being undetermined functions of z, the axial coordinate. The differential equations satisfied by eight z-dependent functions are derived for the general case. For the uniform load, the eight functions can be obtained through a step-by-step integration with properly incorporating the boundary conditions at the upper and lower surfaces of the plate. The three-dimensional solutions for functionally graded piezoelectric circular plates with simply-supported or clamped boundary are presented. These solutions can be readily degenerated into those for a homogenous circular plate. Three numerical examples are finally given to show the validity of the analysis, the effect of material heterogeneity and the merits of the present analyses. Since no ad hoc hypotheses on the distribution of the elastic and electric fields are introduced, the present three-dimensional solutions could provide a useful way for checking the validity of various approximate theories and numerical methods.