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Title: Additional properties of the node-based smoothed finite element method (NS-FEM) for solid mechanics problems
Authors: Nguyen-Thoi, T.
Liu, G.R. 
Nguyen-Xuan, H.
Keywords: Compatible model
Equilibrium model
Finite element method (FEM)
Meshfree methods
Node-based smoothed finite element method (NS-FEM)
Numerical methods
Upper bound
Issue Date: Dec-2009
Citation: Nguyen-Thoi, T., Liu, G.R., Nguyen-Xuan, H. (2009-12). Additional properties of the node-based smoothed finite element method (NS-FEM) for solid mechanics problems. International Journal of Computational Methods 6 (4) : 633-666. ScholarBank@NUS Repository.
Abstract: A node-based smoothed finite element method (NS-FEM) for solving solid mechanics problems using a mesh of general polygonal elements was recently proposed. In the NS-FEM, the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh, and a number of important properties have been found, such as the upper bound property and free from the volumetric locking. The examination was performed only for two-dimensional (2D) problems. In this paper, we (1) extend the NS-FEM to three-dimensional (3D) problems using tetrahedral elements (NS-FEM-T4), (2) reconfirm the upper bound and free from the volumetric locking properties for 3D problems, and (3) explore further other properties of NS-FEM for both 2D and 3D problems. In addition, our examinations will be thorough and performed fully using the error norms in both energy and displacement. The results in this work revealed that NS-FEM possesses two additional interesting properties that quite similar to the equilibrium FEM model such as: (1) super accuracy and super-convergence of stress solutions; (2) similar accuracy of displacement solutions compared to the standard FEM model. © 2009 World Scientific Publishing Company.
Source Title: International Journal of Computational Methods
ISSN: 02198762
DOI: 10.1142/S0219876209001954
Appears in Collections:Staff Publications

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