A local search scheme in the natural element method for the analysis of elastic-plastic problems

Natural element method (NEM) is a meshless method based on the Voronoi diagram and Delaunay triangulation. It has the advantages of the meshless method, and simplifies the imposition of essential boundary conditions. NEM has great potential to solve the problems with large deformation. However, the high computational cost for searching natural neighbors is one of the main problems in NEM. In this paper a local algorithm based on K -Nearest Neighbor is presented for searching natural neighbors. Compared with the global sweep algorithm and other local search algorithms, the proposed algorithm introduces K to reduce the search scope. The value of K can be adjusted adaptively with the distribution characteristics of local neighbors of the calculation point and so the search can reach the global optimal value. The search scope changes with the flow of nodes, avoiding the problem that the natural neighbors exceed the search scope and reducing the calculation error. The proposed approach realizes the meshless characteristic in the natural neighbor searching process. The approach was used to solve the elastic deformation of a cantilever beam and a porous structure and the large plastic deformation in metal forming process. The results show that the proposed approach has great significance to solve problems in the elastic-plastic large deformation of metals and it is efficient.