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Title: A gradient smoothing method (GSM) with directional correction for solid mechanics problems
Authors: Liu, G.R. 
Zhang, J. 
Lam, K.Y.
Li, H.
Xu, G.
Zhong, Z.H.
Li, G.Y.
Han, X.
Keywords: Gradient smoothing method (GSM)
Meshfree method
Numerical analysis
Numerical methods
Solid mechanics
Issue Date: Feb-2008
Citation: Liu, G.R., Zhang, J., Lam, K.Y., Li, H., Xu, G., Zhong, Z.H., Li, G.Y., Han, X. (2008-02). A gradient smoothing method (GSM) with directional correction for solid mechanics problems. Computational Mechanics 41 (3) : 457-472. ScholarBank@NUS Repository.
Abstract: A novel gradient smoothing method (GSM) is proposed in this paper, in which a gradient smoothing together with a directional derivative technique is adopted to develop the first- and second-order derivative approximations for a node of interest by systematically computing weights for a set of field nodes surrounding. A simple collocation procedure is then applied to the governing strong-from of system equations at each node scattered in the problem domain using the approximated derivatives. In contrast with the conventional finite difference and generalized finite difference methods with topological restrictions, the GSM can be easily applied to arbitrarily irregular meshes for complex geometry. Several numerical examples are presented to demonstrate the computational accuracy and stability of the GSM for solid mechanics problems with regular and irregular nodes. The GSM is examined in detail by comparison with other established numerical approaches such as the finite element method, producing convincing results. © 2007 Springer Verlag.
Source Title: Computational Mechanics
ISSN: 01787675
DOI: 10.1007/s00466-007-0192-8
Appears in Collections:Staff Publications

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