An inverse problem for a functionally graded elliptical plate with large deflection and slightly disturbed boundary

Abstract

This paper deals with the inverse problem of a functionally graded material (FGM) elliptical plate with large deflection and disturbed boundary under uniform load. The properties of functionally graded material are assumed to vary continuously through the thickness of the plate, and obey a simple power law expression based on the volume fraction of the constituents. Based on the classical nonlinear von Karman plate theory, the governing equations of a thin plate with large deflection were derived. In order to solve this non-classical problem, a perturbation technique was employed on displacement terms in conjunction with Taylor series expansion of the disturbed boundary conditions. The displacements of in-plane and transverse are obtained in a non-dimensional series expansion form with respect to center deflection of the plate. The approximate solutions of displacements are solved for the first three terms, and the corresponding internal stresses can also be obtained. (c) 2005 Elsevier Ltd. All rights reserved

Free vibration analysis of functionally graded coupled circular plate with piezoelectric layers

“…1) Based on the given form of the electric potential across the thickness direction Eq. (17), the components of electric field intensity, E i and electric flux densities D i , can be obtained as [30]: (23) in which, r E , E θ , z E are the electric field intensity in the r, θ and z directions, respectively. Also, D r , D θ and D z are the corresponding electric displacements in indicated directions; ∆ is the Laplace operator in the polar coordinate given by:…”

“…Also, [22] investigated the nonlinear vibration of functionally graded plates with imperfection sensitivity so that equations of motion were derived with attention to initial stress and geometric imperfection size, and solved using perturbation technique, Galerkin method and Runge-Kutta method. In [23] an inverse problem of a functionally graded material for elliptical plate with large deflections based on the classical nonlinear Von Karman plate theory is presented. In [24] by using finite element analysis the asymmetric free vibration and thermoelastic stability of FGM circular plates are analyzed with due regard to field-consistency principle.…”

Nonlinear bending analysis of FGM circular plates based on physical neutral surface and higher-order shear deformation theory

“…Cheng and Batra [35] carried out a new solution in closed form for the thermo-mechanical deformations of an isotropic linear thermo-elastic FGM elliptic plate rigidly clamped at the edges. Hsieh and Lee [36] studied the inverse problem of a FGM elliptical plate with large deflection and disturbed boundary under uniform load based on the classical plate theory. Kumar et al [37] presented parametric studies on the prediction of vibro-acoustic response from an FGM elliptic disc.…”

Shape Effect on Free Vibration of Functionally Graded Plates

“…Patel et al [19] investigated the free vibration characteristics of functionally graded elliptical cylindrical shells using finite element. Hsieh et al [20] investigated static behavior of FGM elliptical plate using approximation method. Zhang D-G. [21] investigated non-linear bending analysis for super elliptical thin plates with Ritz method.…”