A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

Abstract

In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

A Review on Buckling Analysis of Functionally Graded Plates Under Thermo-Mechanical Loads

“…The second approach in the group of linear equation approach is adjacent (neighboring) equilibrium criterion, which considers the equilibrium configuration at the buckling (bifurcation) point and an adjacent configuration that is very close just after buckling point [84]. Many published works used this method, examples can be found at [39,42,50].…”

An Edge-Based Smoothed Finite Element for Free Vibration Analysis of Functionally Graded Porous (FGP) Plates on Elastic Foundation Taking into Mass (EFTIM)

“…Duc et al [20] presented the analysis of nonlinear thermal dynamic response of shear deformable functionally graded plates on the EF. Mahmoudi et al [21] developed a refined quasi-three-dimensional shear deformation theory to analyze the functionally graded Sandwich plates resting on the two-parameter EF under thermomechanical loading. Duc et al [22] used an analytical method to calculate static bending and free vibration of FG carbon nanotube-reinforced composite plate resting on Winkler-Pasternak foundations.…”

Dynamic Analysis of Functionally Graded Porous Plates Resting on Elastic Foundation Taking into Mass subjected to Moving Loads Using an Edge-Based Smoothed Finite Element Method

“…Duc et al [7] studied the nonlinear thermal dynamic response of the shear deformable functionally graded (FG) plates. Mahmoudi et al [8] developed a refined quasi-three-dimensional shear deformation theory for analyzing FG sandwich plates under thermomechanical load. Recently, Tran et al [9] also investigated the free vibration of the FGP plates resting on the EFTIM.…”