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H. Nguyen-Xuan, Loc V. Tran, T. Nguyen-Thoi, H.C Vu Do, Analysis of functionally graded plates using an edge-based smoothed finite element method, Composite Structures, Vol. 93, p. 3019-3039,  doi:10.1016/j.compstruct.2011.04.028, 2011.

Abstract:
An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap (DSG) technique using triangular meshes (ES-DSG) was recently proposed to enhance the accuracy of the existing FEM with the DSG for analysis of isotropic Reissner/Mindlin plates. In this paper, the ES-DSG is further formulated for static, free vibration and buckling analyses of functionally graded material (FGM) plates. The thermal and mechanical properties of FGM plates are assumed to vary across the thickness of the plate by a simple power rule of the volume fractions of the constituents. In the ES-DSG, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains associated with the edges of the elements. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to demonstrate the performance of the present formulation for FGM plates.

Keywords: FGM Reissner/Mindlin plates; Mesh-free methods; Finite element method (FEM); Edge-based smoothed finite element method (ES-FEM); Discrete shear gap (DSG) method; Stabilization technique