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Structural Engineering and Mechanics Volume 21, Number 3, October20 2005 , pages 315-332 DOI: https://doi.org/10.12989/sem.2005.21.3.315 |
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A Moving Least Squares weighting function for the Element-free Galerkin Method which almost fulfills essential boundary conditions |
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Thomas Most and Christian Bucher
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| Abstract | ||
| The Element-free Galerkin Method has become a very popular tool for the simulation of mechanical problems with moving boundaries. The internally applied Moving Least Squares interpolation uses in general Gaussian or cubic weighting functions and has compact support. Due to the approximative character of this interpolation the obtained shape functions do not fulfill the interpolation conditions, which causes additional numerical effort for the application of the boundary conditions. In this paper a new weighting function is presented, which was designed for meshless shape functions to fulfill these essential conditions with very high accuracy without any additional effort. Furthermore this interpolation gives much more stable results for varying size of the influence radius and for strongly distorted nodal arrangements than existing weighting function types. | ||
| Key Words | ||
| interpolation; Moving Least Squares; meshless discretization; boundary conditions | ||
| Address | ||
| Institute of Structural Mechanics, Bauhaus-University, Weimar, Marienstr. 15, D-99423 Weimar, Germany | ||