Bending analysis of thin functionally graded plates using generalized differential quadrature method

Abstract

In this paper, the differential quadrature (DQ) method is presented for easy and effective analysis of isotropic functionally graded (FG) and functionally graded coated (FGC) thin plates with constant Poisson's ratio and varying Young's modulus in the thickness direction. The bending of FG and FGC plates under transverse loading has been studied using the polynomial differential quadrature (PDQ) and the harmonic differential quadrature (HDQ) methods. A three-dimensional elasticity solution for a moderately thick FG plate with exponential Young's modulus is used as the benchmark. Two examples, including a thin FG rectangular plate and a thin FGC rectangular plate with sigmoidal Young's modulus, are investigated. The numerical results of PDQ and HDQ methods reveal good agreement with other solutions. Also, it is shown that the formulations for thin FG plates and homogeneous plates are similar, except that the plane strain components of the middle surface in FG plates are not zero.

Accurate free vibration analysis of Euler functionally graded beams by the weak form quadrature element method

“…For the purpose of comparisons, the material properties of the functionally graded beam are assumed to vary along the thickness direction according to the power-law form defined by [10] 1 ( ) ( )+ 2 k c mm z P z P PP h aeö = -+ ç÷ èø (5) where subscripts c and m denote the ceramic and metal, P(z) is either the elasticity modulus E(z) or the mass density () z r , and the power-law exponent k is a non-negative variable. It is easy to see that the material of the lower surface of the beam ( /2 zh =- …”

“…The classical finite element method (FEM) can be used [4], however, its solution accuracy is not so high as compared to other efficient numerical methods, such as the differential quadrature method (DQM) and harmonic differential quadrature (HDQM) method [5,21,22], discrete singular convolution (DSC) [23,24], and the weak form quadrature element method (QEM) [8,[25][26][27]. These numerical methods have been proved accurate and computationally efficient when they are used to analyze problems in structural mechanics.…”

“…Various methods are employed, including analytical method [2], semi-analytical method [3] and numerical methods such as finite element method (FEM) [4], differential quadrature method (DQM) and harmonic differential quadrature method (HDQM) [5], various meshless methods [6,7], and quadrature element method (QEM) [8]. A vast body of literature exists.…”

“…Since the behavior of structural members with FGMs are of importance thus has been received great attention in the last decades. Studies have been devoted to understand the static, buckling and dynamic behavior of the functionally graded structural components [1][2][3][4][5][6][7][8][9][10].…”

Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

“…As extended applications, various two-dimensional (2D) plate theories have been used to investigate the static bending of functionally graded plates in the past years, such as the thin plate theory with Kirchhoff hypothesis [2] , the first-order shear deformation theory [3][4] , the thirdorder plate theories [5][6][7] , and the refined higher-order theories [8][9][10] . Due to the hypotheses and simplification concerning the deformation field along the thickness direction, the applicability of the 2D plate theories is always confined to the plates with lower thickness-to-length ratios.…”