A three-dimensional exact solution is presented for free and forced vibrations of simply supported functionally graded rectangular plates. Suitable displacement functions that identically satisfy boundary conditions are used to reduce equations governing steady state vibrations of a plate to a set of coupled ordinary differential equations, which are then solved by employing the power series me...

WE DERIVE FIELD EQUATIONS for a functionally graded plate whose deformations are governed by either the first-order shear deformation theory or the third-order sheardeformation theory. These equations are further simplified for a simply supported polygonal plate. An exact relationship is established between the deflection of the functionally graded plate and that of an equivalent homogeneous Ki...

An equivalent continuum model based on the Eshelby-Mori-Tanaka approach was employed to estimate the effective constitutive law for an elastic isotropic medium (i.e., the matrix) with oriented straight carbon nanotubes (CNTs). The two-dimensional generalized differential quadrature method was an efficient and accurate numerical tool for discretizing equations of motion and for implementing vari...

This paper deals with the dynamic response of Functionally Graded Material (FGM) plates resting on a viscoelastic foundation under loads. The governing equations are derived by using Hamilton’s principle classical plate theory and higher-order shear deformation theory. Using state-space methods to find closed-form solution functionally graded rectangular foundation. Numerical examples given for...

In this paper, the flexural response of functionally graded plates with porosities is investigated using a novel higher order shear deformation theory, which considers the influence of thickness stretching. This theory fulfills the nullity conditions at the top and bottom of the plate for the transverse shear stresses, thus avoids the need of a shear correction factor. The effective material pr...

An exact solution is obtained for three-dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and/or bottom surfaces. Suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical defo...

Static deformations, and free and forced vibrations of a thick rectangular functionally graded elastic plate are analyzed by using a higherorder 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 assum...

Abstract The first-order shear deformation theory (FSDT) was used to explore the natural frequency response of functionally graded piezoelectric plates subjected static electrical and mechanical strain in this present study. A monomorph model for a plate with material properties that change according sigmoid law respect thickness has been considered. three-dimensional finite element free tetrah...