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See detailA node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates
Nguyen-Xuan, H.; Rabczuk, T.; Nguyen-Thanh, N. et al

in Computational Mechanics (2010), 46(5), 679-701

In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates. The discrete ... [more ▼]

In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates. The discrete weak form of the NS-FEM is obtained based on the strain smoothing technique over smoothing domains associated with the nodes of the elements. The discrete shear gap (DSG) method together with a stabilization technique is incorporated into the NS-FEM to eliminate transverse shear locking and to maintain stability of the present formulation.Aso-called node-based smoothed stabilized discrete shear gap method (NS-DSG) is then proposed. Several numerical examples are used to illustrate the accuracy and effectiveness of the present method. [less ▲]

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See detailA three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics
Rabczuk, Timon; Bordas, Stéphane UL; Zi, Goangseup

in Computational Mechanics (2007), 40(3), 473-495

This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is ... [more ▼]

This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is based on a local partition of unity. An extrinsic enrichment of the meshfree shape functions is used with discontinuous and near-front branch functions to close the crack front and improve accuracy. The crack is hereby modeled as a jump in the displacement field. The initiation and propagation of a crack is determined by the loss of hyperbolicity or the loss of material stability criterion. The method is applied to several static, quasi-static and dynamic crack problems. The numerical results very precisely replicate available experimental and analytical results. [less ▲]

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