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Title: A linearly conforming radial point interpolation method for solid mechanics problems
Authors: Liu, G.R. 
Li, Y.
Dai, K.Y. 
Luan, M.T.
Xue, W.
Keywords: Gradient smoothing
Interpolation function
Meshfree method
Meshless method
Nodal integration
Radial basis function
Radial point interpolation method (RPIM)
Stress analysis
Issue Date: Dec-2006
Citation: Liu, G.R., Li, Y., Dai, K.Y., Luan, M.T., Xue, W. (2006-12). A linearly conforming radial point interpolation method for solid mechanics problems. International Journal of Computational Methods 3 (4) : 401-428. ScholarBank@NUS Repository.
Abstract: A linearly conforming radial point interpolation method (LC-RPIM) is presented for stress analysis of two-dimensional solids. In the LC-RPIM method, each field node is enclosed by a Voronoi polygon, and the displacement field function is approximated using RPIM shape functions of Kronecker delta function property created by simple interpolation using local nodes and radial basis functions augmented with linear polynomials to guarantee linear consistency. The system equations are then derived using the Galerkin weak form and nodal integration techniques, and the essential boundary conditions are imposed directly as in the finite element method. The LC-RPIM method is verified via various numerical examples and an extensive comparison study is conducted with the conventional RPIM, analytical approach and FEM. It is found that the presented LC-RPIM is more stable, more accurate in stress and more efficient than the conventional RPIM. © World Scientific Publishing Company.
Source Title: International Journal of Computational Methods
ISSN: 02198762
DOI: 10.1142/S0219876206001132
Appears in Collections:Staff Publications

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