Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

A hybrid element-free Galerkin and natural element meshfree method for direct imposition of boundary conditions and faster three-dimensional computations

J. Yvonnet*, F. Chinesta
LMSP (Laboratoire de Mécanique des Systèmes et des Procédés) – UMR CNRS-ENSAM-ESEM Ecole Nationale Supérieure d'Arts et Métiers, 151 boulevard de l'Hôpital, F-75013 Paris, France

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The natural neighbor meshfree method, or natural element method (NEM) provides equivalent quality compared to quadrangular or hexahedral finite elements but is based on the automatic technology of Delaunay triangulation arithmetic. Since the NEM shape functions possess the Kronecker delta property as well as strict linearity over the boundaries of the domain, the essential boundary conditions can be directly implemented with ease as in the conventional finite element method (FEM). Nevertheless, the extension of the method in 3D is complex and costly, involving many geometric constructions in the Vornoi diagram of the set of nodes. In this paper a new method combining the methodology of element-free Galerkin and natural neighbors is proposed to simplify the implementation and reduce the costs of 3D NEM, as well as to provide automatic connectivity in the element-free Galerkin. A 3D Poisson problem is proposed to evaluate the numerical solution as well as the computational costs.

Keywords:  Natural element method; Element-free Galerkin; Meshfree methods; 3D

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