A full compatible three-dimensional elasticity element for buckling analysis of FGM rectangular plates subjected to various combinations of biaxial normal and shear loads K. Asemi a , M. Shariyat b,n , M. Salehi a , H. Ashrafi b a Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran b Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran 19991-43344, Iran article info Article history: Received 15 November 2012 Received in revised form 14 March 2013 Accepted 21 May 2013 Keywords: Buckling Three-dimensional elasticity Functionally graded materials Shear Compression Hermitian finite element abstract In the present paper, a three-dimensional elasticity approach is employed to investigate buckling of heterogeneous functionally graded plates under biaxial compression, shear, tension-compression, and shear-compression load conditions. In this regard, a formulation that employs a full compatible three- dimensional Hermitian element with 168 degrees of freedom and guarantees continuity of the strain and stress components is used. It is known that all of the available famous commercial finite element softwares and the proposed series solutions satisfy continuity conditions of the displacement rather than the stress components. Buckling occurrence is detected based on checking both the instability onset and equilibrium criteria. Results are extracted based on a Galerkin-type orthogonality. Therefore, they are more accurate than those obtained based on the traditional Ritz method. The presented three- dimensional finite element analysis and the extracted results are quite new. A vast variety of results including results of biaxial compression, compression-tension, shear, and shear-compression load cases is considered and discussed in detail. & 2013 Elsevier B.V. All rights reserved. 1. Introduction Plate-type structural components are extensively used in majority of the engineering structures, among them, those employed in aerospace, naval, power plant, mechanical, civil, and ground vehicle structures. Due to the optimization targets frequently considered in these components, to minimize the costs, weights, fuel consumption, etc., these components may be vulnerable to sever in-plane loads (e.g., compression, shear, or a combination of them). Therefore, reliability of design of such components requires carefully evaluating the buckling loads which can heavily limit the allowable bearing capacity. Majority of the available researches on the buckling of the rectangular plates have mainly been performed for isotropic or composite plates. Shariyat investigated static and dynamic mechanical, thermal, and thermo-electromechanical buckling and postbuckling of the composite and sandwich plates, employ- ing higher-order, layerwise, and global–local plate theories [1–6]. Shen [7,8] and Shen et al. [9,10] used the classical plate theory and a perturbation technique for buckling and postbuckling analysis of the simply supported, laminated rectangular composite plates under biaxial compressive loadings. They used a Galerkin pertur- bation technique to determine the buckling and post-buckling equilibrium paths of laminated plates with or without elastic foundations. Zhong and Zhang [11] studied dynamic buckling, post-buckling, and mode jumping behaviors of clamped angle-ply laminated composite plates under biaxial compression. Majority of the available buckling studies on flat plates under- going mechanical loads have been accomplished under axial or biaxial compressive loads. Nevertheless, some few researchers have investigated buckling of plates under shear loads. Budiansky [12] studied shear buckling of the isotropic clamped rectangular plates. Smith et al. [13] presented a Rayleigh–Ritz method for local buckling analysis of rectangular unilaterally restrained plates in pure shear, using the classical plate theory. Azikov [14] investi- gated buckling of composite plates subjected to combined in-plane compression and shear. Loughlan [15] examined effect of the bend-twist coupling on the shear buckling behavior of the lami- nated composite plates using a finite strip procedure and the classical plate theory. Kim et al. [16] carried out a buckling and postbuckling analysis for composite plates under pure shear. Han et al. [17] studied postbuckling behavior of laminated composite plates under the combination of in-plane shear, compression and lateral loading, using a Lagrangian finite element-based formula- tion and the first-order shear-deformation plate theory. Lopatin and Korbut [18] studied buckling of clamped orthotropic Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/finel Finite Elements in Analysis and Design 0168-874X/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.finel.2013.05.011 n Corresponding author. Tel.: +98 9122727199; fax: +98 21 88674748. E-mail addresses: m_shariyat@yahoo.com, shariyat@kntu.ac.ir (M. Shariyat). Finite Elements in Analysis and Design 74 (2013) 9–21