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C. Thai-Hoang, N. Nguyen-Thanh, H. Nguyen-Xuan, T. Rabczuk, An alternative alpha finite element method with discrete gap technique for analysis of laminated composite plates, Applied Mathematics and Computation, Vol. 217, p. 7324–7348,  doi:10.1016/j.amc.2011.02.024, 2011.

Abstract:
This paper presents an alternative alpha finite element method using triangular meshes (AαFEM) for static, free vibration and buckling analyses of laminated composite plates. In the AαFEM, an assumed strain field is carefully constructed by combining compatible strains and additional strains with an adjustable parameter α which can produce an effectively softer stiffness formulation compared to the linear triangular element. The stiffness matrices are obtained based on the strain smoothing technique over the smoothing domains and the constant strains on triangular sub-domains associated with the nodes of the elements. The discrete shear gap (DSG) method is incorporated into the AαFEM to eliminate transverse shear locking and an improved triangular element termed as AαDSG3 is proposed. Several numerical examples are then given to demonstrate the effectiveness of the AαDSG3.

Keywords: Finite element method; Alpha finite element method (AαFEM); Discrete shear gap (DSG); Transverse shear locking; Laminated composite plates