Interpolation naturelle sur les domaines non convexes par l’utilisation du diagramme de Voronoï contraint: Méthode des éléments C-naturels - Yvonnet, Julien; Ryckelynck, David; Lorong, Philippe; Chinesta, Francisco (European Journal of Computational Mechanics, 2003)
The natural elements method (NEM) is a new technique considered as a “meshless method” based on Sibson co-ordinates for the solution of partial differential equations. The NE shape functions are strictly interpolant which makes easy the imposition of essential boundary conditions. However, issues occur over non-convex boundaries : interpolant is not stricly linear over the whole boundary and interaction between nodes over close boundaries, like cracks, can also occur. Solutions proposed so far fail in cases like these. We propose a methodology to compute the shape functions by mean of a modified constrained Voronoï diagram. Respect of all main properties of the natural elements methods by this way without regard on the gometry of the domain is discussed