Keywords: functionally graded materials, aspect ratio, finite strip method, garland curve, initial postbuckling stiffness.

In this paper the effects of aspect ratio of rectangular plates constructed of functionally graded materials (FGM) on their buckling performance and reduced postbuckling stiffness is investigated. FGMs are heterogeneous materials usually made from a mixture of metals and ceramics. The composition is assumed to be varied in such a way that the top surface of the plate is ceramic-rich, whereas the bottom is metal-rich. To formulate the material properties of a FGM plate the simple power law is used [1]. It is assumed that the mentioned FG plates are loaded uniformly in the axial direction. The effects of aspect ratio on buckling properties of common rectangular plates with a vast variety of boundary conditions and material properties has been extensively presented in the literature as the curves so called garland [2]; however, according to the authors' literature survey such a kind of analyses for investigating the effects of aspect ratio on initial postbuckling stiffness of FG plates has not been recorded. In the current work the critical buckling load of some FG rectangular plates has been evaluated using a Rayleigh-Ritz approach for different aspect ratios and the related garland curves obtained. In the next step by incorporating two versions of finite strip methods (FSM) namely full-energy as well as semi-energy FSM the initial post buckling behavior of mentioned FG plates has been outlined. Full-energy FSM is a fairly conventional approach that has been used by many reaserchers in the past decades for buckling and postbuckling analysis of plates and prismatic plate structures [3,4,5]. The latter approach is a rigorous scheme based on the closed form solution of von-Kármán's compatibility equation that was originally developed by the authors [6]. The analyses of the results revealed that the postbuckling stiffness ratio of the FG plates demonstrates a universal saw shape curve, which is independent of volume fraction index of base materials for FG plates, which considered in this study. Moreover, the postbuckling stiffness ratio is highly influenced by the buckling mode shape of the rectangular FG plates and by increasing the aspect ratio, a transition in the buckle shape of the plate will occur that leads to a drastic drop in the initial postbuckling stiffness ratio. Finally, it may be concluded that where the design of FG rectangular plates for initial postbuckling behavior is concerned the aspect ratio of the plate will play an important role in this behavior; however, the fraction of the base materials in the FGM composition may be of less importance.

1

H.S. Shen, "Functionally Graded Materials: Nonlinear Analysis of Plates and Shells", CRC Press, 2009.

2

H.G. Allen, P.S. Bulson, "Background to Buckling", London, McGraw-Hill, 1980.

3

Y.K. Cheung, "Finite strip method in structural analysis", Oxford, Pergamon Press, 1976.

4

D.J. Dawe, V. Peshkam, "A buckling analysis capability for use in the design of composite prismatic plate structures", Composite Structures, 16, 33-63, 1990. doi:10.1016/0263-8223(90)90066-N

5

H.R. Ovesy, S.A.M. Ghannadpour, G. Morada, "Geometric non-linear analysis of composite laminated plates with initial imperfection under end shortening, using two versions of finite strip method", Composite Structures, 71, 307-314, 2005. doi:10.1016/j.compstruct.2005.09.030

6

H.R. Ovesy, H. Assaee, M. Hajikazemi, "An investigation on post buckling behaviour of functionally graded plate using a semi energy finite strip approach", Proceedings of IJSSD symposium on Progress in Structural Stability and Dynamics, Hong Kong, 2009.

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