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Title: A mesh-free minimum length method for 2-D problems
Authors: Liu, G.R. 
Dai, K.Y. 
Han, X.
Li, Y.
Keywords: Interpolation function
Mesh-free method
Meshless method
Minimum length method
Radial basis function (RBF)
Issue Date: Nov-2006
Citation: Liu, G.R., Dai, K.Y., Han, X., Li, Y. (2006-11). A mesh-free minimum length method for 2-D problems. Computational Mechanics 38 (6) : 533-550. ScholarBank@NUS Repository.
Abstract: A mesh-free minimum length method (MLM) has been proposed for 2-D solids and heat conduction problems. In this method, both polynomials as well as modified radial basis functions (RBFs) are used to construct shape functions for arbitrarily distributed nodes based on minimum length procedure, which possess Kronecker delta property. The shape functions are then used to formulate a mesh-free method based on weak-form formulation. Both Gauss integration (GI) and stabilized nodal integration (NI) are employed to numerically evaluate Galerkin weak form. The numerical examples show that the MLM achieves better accuracy than the 4-node finite elements especially for problems with steep gradients. The method is easy to implement and works well for irregularly distributed nodes. Some numerical implementation issues for MLM are also discussed in detail.
Source Title: Computational Mechanics
ISSN: 01787675
DOI: 10.1007/s00466-005-0003-z
Appears in Collections:Staff Publications

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