Analytical solutions for axisymmetric bending of functionally graded piezoelectric annular plates

Abstract

The bending of piezoelectric annular plates is the classic problem in theory of piezoelectric elasticity. The solution of axisymmetric bending of FGPM annular plates subject to arbitrarily transverse loads is not available in the literatures though some solutions for special loads have been derived. For this purpose, this paper analytically studies the axisymmetric bending of functionally graded piezoelectric annular plates subjected to arbitrary transverse loads. Based on the three-dimensional theory of piezoelectricity, this work derives analytical solutions for the axisymmetric bending of piezoelectric annular plates. The transverse loads are expanded in terms of the Fourier-Bessel series, and the solutions corresponding to each item of the series are obtained by the semi-inverse method. The total solutions are then obtained through the superposition principle. The present solutions rigorously satisfies the governing equations when the material properties obey the exponential law along the thickness of the plates. The boundary conditions on the top and bottom surfaces are completely satisfied while the boundary conditions at the circumferential edges are approximately satisfied based on Saint-Venant's principle.