中文摘要：

以初始点的Voronoi结构为基础，建立基于质心Voronoi结构的布点算法。该算法通过区域上的初始离散点构造Voronoi结构，利用面积坐标法确定Voronoi结构的质心点，以成本函数作为质心Voronoi结构的收敛准则。若质心点满足收敛准则，则将该质心点作为区域的离散节点。然后利用切边处理技术，实现复杂区域内的布点算法，即给出不同区域的均匀布点和非均匀布点。以长圆筒为例，采用基于Voronoi结构的布点算法对求解域进行点的离散，利用自然邻近Pctrov-Galerkin无网格法计算其应力值，求得的应力值与精确值比较吻合，这证明了将质心Voronoi结构的质心点作为无网格法区域离散节点进行无网格法分析是比较精确、可靠的。

英文摘要：

Based on the Voronoi tessellation of initial points, an algorithm with centroidal Voronoi tessellation for construction of nodes used in meshless discretization is proposed. Voronoi tessellations are constructed corresponding to a given set of initial points on the domain. By using natural coordinates of triangles, the centroids of Voronoi tessellations are determined, and the cost function is used as convergence theorem. If the centroids of Voronoi tessellations meet the convergence theorem, those centroids are final obtained nodes placed in the domain and on the boundary. Then by cutting boundary technique, points can be placed in arbitrary domains. Uniform and non-uniform nodal arrangements can be realized by this algorithm. A numerical example of cylinder with hole subjected to uniform intemal pressure is presented by using the natural neighbour Petrov-Galerkin method and the proposed algorithm. The numerical results are in great agreement with the exact solutions, which indicates that the proposed algorithm is very accurate and reliable in meshless methods.