In this paper, a thick functionally graded plate based on three-dimensional equations of elasticity and subjected to nonuniform transverse loading is considered. The Young’s modulus of the plate is assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents and the Poisson’s ratio is assumed to be constant. Three-dimensional graded finite element method based on Rayleigh–Ritz energy formulation has been applied to study the static response of the plate. The plate deflection and in-plane stress for different values of the power law exponent, thickness-to-length ratio, and various boundary conditions have been investigated. To verify the presented method and data, the results are compared to published data.
KoizumiM. The concept of FGM. Ceram Trans Funct Grad Mater1993; 34: 3–10.
2.
JhaDKKantTSinghRK. A critical review of recent research on functionally graded plates. Compos Struct2012; 96: 833–849.
3.
ReddyJN. Analysis of functionally graded plates. Int J Numer Meth Eng2000; 47: 663–684.
4.
FerreiraAJMBatraRCRoqueCMC. Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos Struct2005; 69: 449–457.
ZenkourAM. Generalized shear deformation theory for bending analysis of functionally graded plates. Appl Math Model2006; 30: 67–84.
7.
TalhaMSinghBN. Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Appl Math Model2010; 34: 3991–4011.
8.
XiangSKangG. A nth-order shear deformation theory for the bending analysis on the functionally graded plates. Eur J Mech A/Solids2013; 37: 336–343.
9.
MantariJLOktemASSoaresCG. Bending response of functionally graded plates by using a new higher order shear deformation theory. Compos Struct2012; 94: 714–723.
10.
MantariJLOktemASSoaresCG. A new higher order shear deformation theory for sandwich and composite laminated plates. Compos Part B2012; 43: 1489–1499.
11.
KaramaMAfaqKSMistouS. A new theory for laminated composite plates. Proc IMechE, Part L: J Materials: Design and Applications2009; 223: 53–62.
12.
ReddyJNLiuCF. A higher order shear deformation theory of laminated elastic shells. Int J Eng Sci1985; 23: 319–330.
13.
SoldatosKP. A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mech1992; 94: 195–220.
14.
TouratierM. An efficient standard plate theory. Int J Eng Sci1991; 29: 901–916.
15.
PendhariSSKantTDesaiYM. Static solution for functionally graded simply supported plates. Int J Mech Mater Des2012; 8: 51–69.
16.
WenPHSladekJSladekV. Three dimensional analysis of functionally graded plates. Int J Numer Meth Eng2011; 87: 923–942.
17.
KashtalyanM. Three-dimensional elasticity solution for bending of functionally graded plates. Eur J Mech A/Solids2004; 23: 853–864.
18.
KashtalyanMMenshykovaM. Three dimensional elasticity solution for sandwich panels with a functionally graded core. Compos Struct2008; 87: 36–43.
19.
LiewKMTeoTMHanJB. Three dimensional static solutions of rectangular plates by variant differential quadrature method. Int J Mech Sci2001; 43: 1611–1628.
20.
VaghefiRBaradaranGHKoohkanH. Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov–Galerkin (MLPG) method. Eng Anal Bound Elem2010; 34: 564–573.
21.
Rezaei MojdehiADarvizehBBastiA. Three dimensional static and dynamic analysis of thick functionally graded plates by the meshless local Petrov–Galerkin (MLPG) method. Eng Anal Bound Elem2011; 35: 1168–1180.
22.
KimJHPaulinoGH. Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. J Appl Mech2002; 69: 502–514.
23.
ZhangZPaulinoGH. Wave propagation and dynamic analysis of smoothly graded heterogeneous continua using graded finite elements. Int J Solids Struct2007; 44: 3601–3626.
24.
Ashrafi H, Asemi K, Shariyat M, et al. Two-dimensional modelling of heterogeneous structures using graded finite element and boundary element methods. Meccanica 2012; 48: 663–680.
25.
DhondtG. The finite element method for three-dimensional thermo mechanical applications, UK: John Wiley & Sons Ltd, 2004.
26.
ZienkiewiczOCTaylorRL. The finite element method for solid and structural mechanics, 6th ed. Oxford: Elsevier Butterworth-Heinemann, 2005.
27.
EslamiMR. A first course in finite element analysis, 1st ed. Tehran: Amirkabir University of Technology Press, 2003.
