ARTICLE IN PRESS UNCORRECTED PROOF Please cite this article in press as: M. Tahani, S.M. Mirzababaee, Nonlinear analysis of functionally graded plates in cylindrical bending under thermomechanical loadings based on a layerwise theory, European Journal of Mechanics A/Solids (2008), doi:10.1016/j.euromechsol.2008.05.002 JID:EJMSOL AID:2438 /FLA [m5G; v 1.43; Prn:12/06/2008; 22:34] P.1 (1-9) European Journal of Mechanics A/Solids ••• (••••) •••–••• Contents lists available at ScienceDirect European Journal of Mechanics A/Solids www.elsevier.com/locate/ejmsol 1 67 2 68 3 69 4 70 5 71 6 72 7 73 8 74 9 75 10 76 11 77 12 78 13 79 14 80 15 81 16 82 17 83 18 84 19 85 20 86 21 87 22 88 23 89 24 90 25 91 26 92 27 93 28 94 29 95 30 96 31 97 32 98 33 99 34 100 35 101 36 102 37 103 38 104 39 105 40 106 41 107 42 108 43 109 44 110 45 111 46 112 47 113 48 114 49 115 50 116 51 117 52 118 53 119 54 120 55 121 56 122 57 123 58 124 59 125 60 126 61 127 62 128 63 129 64 130 65 131 66 132 Nonlinear analysis of functionally graded plates in cylindrical bending under thermomechanical loadings based on a layerwise theory Masoud Tahani a,∗ , Seyed Mahdi Mirzababaee a,b a Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran b Khorasan Research Center for Technology Development (KRCTD), Quchan Highway, Mashhad, Iran article info abstract Article history: Received 8 September 2007 Accepted 16 May 2008 Keywords: Functionally graded material Geometric non-linearity Plate Analytical solution Layerwise method A layerwise theory is used to analyze analytically displacements and stresses in functionally graded composite plates in cylindrical bending subjected to thermomechanical loadings. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The non-linear strain–displacement relations in the von Kármán sense are used to study the effect of geometric non-linearity. The equilibrium equations are solved exactly and also by using a perturbation technique. Numerical results are presented to show the effect of the material distribution on the deflections and stresses.  2008 Published by Elsevier Masson SAS. 1. Introduction In conventional laminated composite materials, there is a high chance that debonding will occur at some extreme loading condi- tions. On the other hand, gradually varying the volume fraction of the constituents can resolve this problem. Functionally graded ma- terials (FGMs) are composite materials which exhibit a progressive change in composition, structure, and properties as a function of spatial direction within the material. Many studies for thermal stress and linear thermal bending of FGM plates are available in the literature (e.g., see Noda and Tsuji, 1991; Tanigawa et al., 1996; Reddy and Chin, 1998). However, in- vestigations in non-linear analysis of FGM plates under thermal or mechanical loading are limited in number. For example, Praveen and Reddy (1998) investigated the response of functionally graded (FG) ceramic-metal plates using a plate finite element that ac- counts for the transverse shear strains, rotary inertia and moder- ately large rotations in the von Kármán sense. Reddy (2000) pre- sented solutions for rectangular functionally graded plates based on the third-order shear deformation plate theory. The formula- tion accounted for the thermomechanical coupling, time depen- dency, and the von Kármán-type geometric non-linearity. Using an asymptotic method, the three-dimensional thermomechanical deformations of functionally graded rectangular plate were investi- gated by Reddy and Cheng (2001) and the distributions of temper- * Corresponding author. Tel.: +98 511 876 3304; fax: +98 511 882 9541. E-mail address: mtahani@ferdowsi.um.ac.ir (M. Tahani). ature, displacements and stresses in the plate were calculated for different volume fraction of ceramic constituent. Shen (2002) analyzed non-linear bending of a simply sup- ported, functionally graded rectangular plate subjected to a trans- verse uniform or sinusoidal load and in thermal environments. The governing equations were obtained based on Reddy’s higher-order shear deformation plate theory and these equations were solved by a mixed Galerkin-perturbation technique. Based on the von Kár- mán theory, Woo and Meguid (2001) derived an analytical solution expressed in terms of Fourier series for the large deflection of functionally graded plates and shallow shells under transverse me- chanical loading and a temperature field. Yang and Shen (2003) using a semi-analytical approach analyzed the non-linear bend- ing and post-buckling behaviors of FG rectangular plates subjected to combined action of transverse and in-plane loads. Tahani et al. (2006) analytically analyzed functionally graded beams subjected to thermomechanical loadings based on a first-order shear defor- mation theory. Hsieh and Lee (2006) solved the inverse problem of a functionally graded elliptical plate with large deflection and dis- turbed boundary under uniform load. They derived the governing equations of a thin plate with large deflection based on the clas- sical non-linear von Kármán plate theory. Then they employed a perturbation technique on displacement terms in conjunction with Taylor series expansion of the disturbed boundary conditions to solve the non-classical problem. Agarwal et al. (2006) used the ex- isting statically exact beam finite element based on the first order shear deformation theory to study the geometric non-linear effects on static and dynamic responses in isotropic, composite and func- tionally graded material beams. They utilized both von Kármán strain tensor and Green’s strain tensor in the static case, whereas, 0997-7538/$ – see front matter  2008 Published by Elsevier Masson SAS. doi:10.1016/j.euromechsol.2008.05.002