Differential quadrature analysis of functionally graded circular and annular sector plates on elastic foundation Sh. Hosseini-Hashemi a , H. Akhavan a , H. Rokni Damavandi Taher b, * , N. Daemi c , A. Alibeigloo c a School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran b School of Engineering, University of British Columbia Okanagan, Kelowna, Canada BC V1V 1V7 c Department of Engineering, Bu-Ali Sina University, Hamadan 65178, Iran article info Article history: Received 21 September 2009 Accepted 29 October 2009 Available online 31 October 2009 Keywords: A. Composites F. Elastic behavior I. Buckling abstract The main purpose of this study is to investigate buckling and free vibration behaviors of radially function- ally graded circular and annular sector thin plates subjected to uniform in-plane compressive loads and resting on the Pasternak elastic foundation. In-plane compressive loads may be applied to either radial, circumferential, or all edges of circular/annular sector plates. Based on the classical plate theory (CPT), critical buckling loads and fundamental frequencies of the circular/annular sector plates under simply- supported and clamped boundary conditions are obtained by using differential quadrature method (DQM). The inhomogeneity of the plate is characterized by taking exponential variation of Young’s mod- ulus and mass density of the material along the radial direction whereas Poisson’s ratio is considered to be constant. Convergence study is carried out to demonstrate the stability of the present method. To con- firm the excellent accuracy of the present approach, a few comparisons are made for limited cases between the present results and those available in literature. Critical buckling load and fundamental fre- quency parameters of the circular/annular sector thin plates are computed for different boundary condi- tions, various values of the material inhomogeneity constants, sector angles, and inner to outer radius ratios. Crown Copyright Ó 2009 Published by Elsevier Ltd. All rights reserved. 1. Introduction Sectorial thin plates are the essential structural components in civil, mechanical, and aerospace engineering. Buckling and free vibration characteristics of such components must be known to achieve an appropriate design. Buckling and free vibration behav- iors of loaded sector thin plates have been studied by only few re- search groups, whereas free vibration analysis of corresponding sector plates in the absence of an external load have been widely investigated by using analytical solutions [1–5] and numerical methods such as Ritz method [6,7], the hierarchical finite element method [8], the finite difference method [9], the variational approximation procedure [10], and Fourier p-element method [11,12]. Relatively little research work has been carried out on the buck- ling analysis of sector plates. Buckling analysis of laminated sector plates is studied by Singh et al. [13] using analytical solutions employing Chebyshev polynomials and finite element method. A semi-analytical solution was presented by Sharma et al. [14] to study the buckling behavior of a laminated composite sector plate with various boundary conditions on the basis of Chebyshev polynomials. Pawlus [15] used a finite difference method to inves- tigate the buckling of a three-layered annular sector plate with a soft core. Wang et al. [16] employed the Rayleigh–Ritz method to give buckling solutions for isotropic in-plane loaded Mindlin plates of regular polygonal, elliptical, semi-circular, and annular plates. Zhou et al. [17] developed a semi-numerical method of solution for the buckling problem of simply-supported sector plates sub- jected to in-plane pressure along the radial edges. Wang and Xiang [18] presented a relationship between the buckling loads of Mind- lin and Kirchhoff circular sectorial plates with simply-supported radial edges. Recently, a simple analytical formulation for the eigenvalue problem of buckling and free-vibration analysis of Mindlin sector plates was deduced by Sharma et al. [19] using two-dimensional Chebyshev polynomials. Plates resting on elastic foundations have found considerable applications in structural engineering problems. Reinforced-con- crete pavements of highways, airport runways, foundation of stor- age tanks, and swimming pools together with foundation slabs of buildings are well-known direct applications of these kinds of plates. The underlying layers are modeled by a Winkler-type elas- tic foundation. The most serious deficiency of the Winkler founda- tion model is to have no interaction between the springs. The Winkler foundation model is fairly improved by adopting the Pas- ternak foundation model, a two-parameter model, in which the 0261-3069/$ - see front matter Crown Copyright Ó 2009 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2009.10.060 * Corresponding author. Tel.: +1 250 807 9652; fax: +1 250 807 8723. E-mail address: hossein.rokni@ubc.ca (H. Rokni Damavandi Taher). Materials and Design 31 (2010) 1871–1880 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes