Research On Delaunay Mesh Generation Algorithm And Its Application In Dynamic Large Deformation

The improvement and application of finite element method are greatly promoted by various calculation methods and the rapid development of computer technology.And various finite element software have emerged as the times require,which greatly facilitates industrial production.Grid generation technology is one of the important links.As we all know,before using the finite element method for numerical analysis,the analysis model needs to be meshed.Therefore,the research and implementation of finite element mesh generation algorithm is very important.First of all,the paper studies two-dimensional and three-dimensional Delaunay mesh generation algorithms in details.The traditional algorithm is improved and new grid generation strategy is proposed to achieve more satisfactory results.The advantage of Delaunay principle is successfully applied to metal forming to solve the problem of grid degradation.The main work of this paper are summarized as follows:(1)Research on Delaunay triangular mesh generation method in arbitrary plane domain.Delaunay triangulation is an optimal mesh construction method which based on point set.But may cause boundary loss or extra-domain triangles.This leads to the conflict between optimization criteria and boundary consistency.Many scholars have studied this problem and proposed solutions.This paper presents a more reliable and general method based on a comprehensive study of the existing research schemes.On this basis,an optimization algorithm for grid node generation is proposed.This algorithm can avoid the generation of abnormal elements and ensure the quality of meshes.Application the Delaunay principle to metal forming.The advantages of Delaunay principle are applied to metal forming successfully.And the phenomenon of mesh degradation(distortion)in large metal deformation is solved.(2)Research on Delaunay triangular mesh generation method of spatial surface.In this paper,the algorithm of triangular mesh generation for surface is realized by mapping method.Firstly,the nodes of the discrete surface is meshed in the two-dimensional parameter domain by using the optimization mesh node generation algorithm proposed above.Then the mesh elements in the pa rameter domain are mapped back to the space surface by corresponding mapping method to fulfil triangulation of the surface.Finally,through the research and analysis of the mapping method,the principle of surface partitioning in mapping method is analyze d rationally.Both the quality of the mesh and the computational efficiency are considered.It has been applied in metal forming.(3)Research on Delaunay tetrahedral mesh generation method.Extending the Delaunay principle to the three-dimensional field has been an important work for researchers.In this paper,the key problem in the algorithm are replaced equivalently,and make the calculation easier,and the feasibility of this method is proved.In order to improve the quality of the grid,in this paper,the growth algorithm is fused with the three dimensional Delaunay grid generation method.Combining this two methods,and then a new mesh generation strategy is proposed,and related tests were carried out.The result shows that this method can effectively extend Delaunay theory to three dimensional space.