Please use this identifier to cite or link to this item: https://doi.org/10.1142/S0219876209001796
Title: A normed G space and weakened weak (W2) formulation of a cell-based smoothed point interpolation method
Authors: Liu, G.R. 
Zhang, G.Y.
Keywords: Cell-based smoothing
Finite element method (FEM)
Meshfree method
Numerical methods
Point interpolation method (PIM)
Weakened weak form (W2)
Issue Date: 2009
Citation: Liu, G.R., Zhang, G.Y. (2009). A normed G space and weakened weak (W2) formulation of a cell-based smoothed point interpolation method. International Journal of Computational Methods 6 (1) : 147-179. ScholarBank@NUS Repository. https://doi.org/10.1142/S0219876209001796
Abstract: This paper presents a normed G1 space and a weakened weak (W2) formulation of a cell-based smoothed point interpolation method (CS-PIM) for 2D solid mechanics problems using three-node triangular cells. Displacement fields in the CS-PIM are constructed using the point interpolation method (polynomial PIM or radial PIM) and hence the shape functions possess the Kronecker delta property facilitating the easy enforcement of Dirichlet boundary conditions. The edge-based T-schemes are introduced for selecting supporting nodes for creating the PIM shape functions and an adaptive coordinate transformation (CT) technique is proposed to solve the singularity problem for the moment matrix. Smoothed strains are obtained by performing the generalized smoothing operation over each triangular background cell. Because the nodal PIM shape functions can be discontinuous, a W2 formulation of generalized smoothed Galerkin (GS-Galerkin) weak form is then used to create the discretized system equations. Numerical examples including static, free and forced vibration problems have been studied to examine the present method in terms of accuracy, convergence, efficiency and temporal stability. © 2009 World Scientific Publishing Company.
Source Title: International Journal of Computational Methods
URI: http://scholarbank.nus.edu.sg/handle/10635/84798
ISSN: 02198762
DOI: 10.1142/S0219876209001796
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