Effect of micromechanical models on structural responses of functionally graded plates

Abstract

This paper examines the influence of alternative micromechanical models on the macroscopic behavior of a functionally graded plate based on classical and shear-deformation plate theories. Several micromechanical models are tested to obtain the effective material properties of a two-phase particle composite as a function of the volume fraction of particles which continuously varies through the thickness of a functionally graded plate. The static, buckling, and free- and forced-vibration analyses are conducted for a simply-supported functionally graded plate resting on a Pasternak-type elastic foundation. The volume fraction of particles are assumed to change according to the power-law, Sigmoid, and exponential functions. The governing partial differential equations are solved in the spatial coordinate by Navier solution, while a numerical time integration technique is employed to treat the problem in the time domain. Finally, the numerical results are provided to reveal the effect of explicit micromechanical models such as Voigt, Reuss, Hashin–Shtrikman bounds, and LRVE as well as the semi-explicit model of self-consistent on the static and dynamic displacement and stress fields, critical buckling load, and fundamental frequency.