Finite element analysis of functionally graded plates under transverse load

Abstract

The nonlinear behaviors of functionally graded material (FGM) plates under transverse distributed load are investigated here using a high precision plate bending finite element. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of the constituents. The effective material properties are then evaluated based on the rule of mixture. The formulation is developed based on the first-order shear deformation theory considering the physical/exact neutral surface position. The shear correction factors are evaluated employing the energy equivalence principle. The transverse shear stresses and transverse normal stress components are obtained using the in-plane stresses evaluated from the constitutive equations and the three-dimensional equilibrium equations. The nonlinear governing equations are obtained following a standard finite element procedure and solved through Newton–Raphson iteration technique to predict the lateral pressure load versus central displacement relationship.