Based On The Voronoi Structure Of The Distribution Algorithm And Its Implementation Techniques

Meshless method is a kind of numerical method developed in the recent decades. In meshless method, the the problem domain is discretized only with nodes and meshes are not required. The nodal placement will strongly affect the accuracy of meshless analysis. Thus, it is necessary to study point displacement method in mshless methods.Based on the known investigations, and resorting to Voronoi tessellations and numerical integral, a point placement method is proposed based on the Voronoi tessellation in this paper. The theory of this method can be summarized as follow: Given a domain and a set of points on domain, corresponding Voronoi tessellations are constructed. Through area coordinates method, centroids of Voronoi tessellation are computed. If the centroids meet some convergent theorem, they are regarded as the nodes of the domain. Then by cutting boundary technique, algorithm of points placement can be realize in arbitrary areas. Accoding to points placement algorithm of the paper, a software package is developed. Discretized models in different domains are obtained, adding nodes around hole or shape-angle or crack is also realized.By using the proposed method, different points placement schemes can be achieved. To study the proposed method in meshless analysis, several numerical examples are analyzed using meshless natural neighbour Petrov-Galerkin method. The results are in- great agreement with the exact solutions, which proves the proposed method is very accurate and reliable in meshless methods. The influence of number of nodes and different points placement schemes on the results are also studied.