Closed-Form Solutions of Three-Dimensional Functionally Graded Plates

Abstract

Three-dimensional analysis of a functionally graded plate is presented in this paper. The plate is subjected to normal and shear tractions of arbitrary form on the lower and upper surfaces while edge boundary conditions are given as simply supported. The problem is formulated on the assumption that the elastic modulus depends on the z-coordinate along the thickness direction. Plevako's solution of the general three-dimensional governing equations is used and the corresponding physical quantities are expanded into Fourier series. Closed-form solutions are obtained for some specific variations of material modulus. The influence of different functionally graded models and plate configurations on the stress and displacement fields is studied through numerical examples.