Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov–Galerkin method

Abstract

Static deformations, and free and forced vibrations of a thick rectangular functionally graded elastic plate are analyzed by using a higher-order shear and normal deformable plate theory (HOSNDPT) and a meshless local Petrov–Galerkin (MLPG) method. All components of the stress tensor are computed from equations of the plate theory. The plate material, made of two isotropic constituents, is assumed to be macroscopically isotropic with material properties varying in the thickness direction only. Effective material moduli are computed by using the Mori–Tanaka homogenization technique. Computed results for static and free vibration problems are found to agree well with their analytical solutions. The response of the plate to impulse loads is also computed for different volume fractions of the two constituents. Contributions of the work include the use of the HOSNDPT and the MLPG method for the analysis of functionally graded plates.