Bending of functionally graded plates via a refined quasi-3D shear and normal deformation theory

Abstract

Bending of functionally graded plate with two reverse simply supported edges is studied based upon a refined quasi three-dimensional (quasi-3D) shear and normal deformation theory using a third-order shape function. The present theory accounts for the distribution of transvers shear stresses that satisfies the free transverse shear stresses condition on the upper and lower surfaces of the plate. Therefore, the strain distribution does not include the unwanted influences of transverse shear correction factor. The effect of transverse normal strain is included. Unlike the traditional normal and shear deformation theories, the present theory have four unknowns only. The equilibrium equations are derived by using the principle of virtual work. The influence of material properties, aspect and side-to-thickness ratios, mechanical loads and inhomogeneity parameter are discussed. The efficiency and correctness of the present theory results are established by comparisons with available theories results.