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N. Nguyen-Thanh, T. Rabczuk, H. Nguyen-Xuan, S. Bordas, An alternative alpha finite element method with discrete gap technique for analysis of isotropic Mindlin-Ressner plates, Finite Element Analysis and Design, Vol. 47, No. 5, p. 519-535, Doi:10.1016/j.finel.2011.01.004, 2011.

Abstract: An alternative alpha finite element method (AαFEM) coupled with a discrete shear gap technique for triangular elements is presented to significantly improve the accuracy of the standard triangular finite elements for static, free vibration and buckling analyses of Mindlin–Reissner plates. In the AαFEM, the piecewise constant strain field of linear triangular elements is enhanced by additional strain terms with an adjustable parameter α which results in an effectively softer stiffness formulation compared to the linear triangular element. To avoid the transverse shear locking, the discrete shear gap technique (DSG) is utilized and a novel triangular element, the Aα-DSG3 is obtained. Several numerical examples show that the Aα-DSG3 achieves high reliability compared to other existing elements in the literature. Through selection of α, under or over estimation of the strain energy can be achieved.

Keywords: Finite element method; Smooth finite element method (SFEM); Discrete shear gap (DSG); Transverse shear locking; Plate bending.