Analytical solutions of functionally graded piezoelectric circular plates subjected to axisymmetric loads

Based on the three-dimensional theory of piezoelectricity, this work analytically investigates the axisymmetric bending of circular plates whose material properties vary along the thickness. The transverse loads are expanded in terms of the Fourier–Bessel series, and the solutions corresponding to each item of the series are derived by a semi-inverse method. The overall results are then obtained through the superposition principle. The exact solutions are obtained for two unusual boundary conditions if the material properties obey an exponential law. Meanwhile, a layerwise model is employed for the case of arbitrary and independent distribution of each component of material properties and the approximate solutions are proposed for simply supported and clamped boundaries. Finally, the numerical examples are illustrated, and the results are compared with those of the finite element method to demonstrate the present method.