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| Fundamental and application of generalized-node mesh-free collocation method |
| Revised:November 28, 2005 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20081014 |
| KeyWord:mesh-free method,radial interpolation function,generalized-node-based mesh-free method |
| LUAN Mao-tian YE Xiang-ji LI Yong YANG Qing |
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| Abstract: |
| In this paper,the concept of generalized node in manifold method is incorporated together with the mesh-free method to establish the interpolation functions with polynomials of arbitrary order.Based on the generalized-node interpolation functions,the generalized-node mesh-free method is developed to improve the conventional mesh-free method.At the same time,the radial basis function is used to construct the approximation functions with the feature of interpolation and the collocation method is employed to develop the discrete formulation of governing partial differential equations of the system.Therefore,the radial basis function(RBF) is applied to a direct collocation procedure and the generalized node is embedded in the RBF approximation.Then the mathematical formulation of the proposed method is developed with numerical implementation.The proposed generalized-node collocation mesh-free method is a truly mesh-free method which combines the generalized node in manifold method with point collocation discretization of the governing partial differential equations.When the zero-order displacement interpolation function of the generalized node is chosen,the proposed method will be reduced to the conventional mesh-free point collocation method.In order to improve the accuracy with less supporting nodes,a higher-order displacement interpolation function is required.As numerical examples,a cantilever beam under end shear and an infinite plate with a hole subjected to uniform tensile load are respectively analyzed by the proposed method.It is shown that the numerical results computed by the proposed method can well agree with the solutions obtained by the theory of elasticity. |
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