Analysis of the mechanical behavior of functionally graded plates: Effect of boundary conditions and micromechanical models

The novelty of this manuscript is the use of a simple refined higher order shear deformation theory for micromechanical behavior analysis of functionally graded (FGM) plates. To achieve this purpose, a new shear deformation shape function is employed. Furthermore, the present refined theory considers a new displacement field that includes undetermined integral terms and contains fewer unknowns 'variables while considering the effect of transverse shear stresses and strains. The plate's material properties are assumed to be graded in the thickness direction according to various micromechanical models, starting with the Voigt's model, which is commonly used in most functionally graded plates studies, to the Reus's, LRVE's and Mori-Tanaka's models. The principle of virtual displacement is used to determine the equilibrium equations and several numerical results are given to validate the precision of the present method for the bending behavior of FGM plates. Afterwards, a parametric study is conducted to determine the effect of different parameters on the deflection of the FGM plates, where we found out that the mechanical behavior of these FGM plates is significantly influenced by the type of micromechanical model considered to determine the plate's stiffness and the type of boundary conditions. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and micromechanical models on the displacements and stresses. In the light of the present research, it can be concluded that the present theory is accurate and simple in predicting the deflection behavior of functionally graded plates under mechanical effects and micromechanical models.