The Research On Technology Of Unstructured Mesh Generation And Optimization

Mesh generation is one of important research fields for the Finite Element Method(FEM)analysis and computation.FEM is an effective numerical analysis method.It becomes an important part of the technology of Computer Aided Engineering(CAE)combining with the Computer Aided Design(CAD).So how to generate adaptive finite element mesh that can reflect physical and geometric characteristics of the structure is a necessary step to apply the Adaptive Finite Element Analysis(AFEA).Unstructured adaptive finite element mesh generation and optimization method are studied in this dissertation,and also has made innovative progress in the (?)ollowing respects.1)Proposing an improved high efficiency algorithm of Delaunay riangulation generation.Delaunay triangulation has been widely used in manifold fields and is a long (?)me researched content in computer graphics & image and visualization in scientific omputing.After studying on the compound algorithm which is based on divide-onquer and incremental insertion algorithms,the higher efficiency compound lgorithm is proposed in order to modify and optimize the first compound one. (?)elaunay triangulating on random data domains can be realized by combining both. With the modified method,mesh generation in some complex domains can be easily arried.So the higher efficiency compound algorithm has better stability and fficiency.2)Presenting a new approach to three-dimensional high-quality mesh using adical basis function neural networks(RBFNN).Surface reconstruction from point cloud data is a key technology of reverse (?)gineering.It includes three steps:first,the cloud data are preprocessed for noothing;second,feature lines are extracted and the cloud data are segmented;at st,NURBS surface patches are created over rectangular mesh and trimmed to form an entire surface using radical basis function neural networks RBFNN.A specific application of this technique to the geometric mesh reconstruction is then outlined, which aims on boundary reconstructing surface model with inherent continuity.This method can improve the quality of mesh greatly and thus the precise reconstruction of data cloud is realized.The experiment result testifys that the approach is feasible.3)Putting forward a new algorithm for mesh optimization based on energy minimization.The dissertation analyses properties of the mesh and classifies mesh curvatures. Based on it,the methods for mesh optimization are studied and a mesh optimization algorithm is presented.Key vertices of the mesh are firstly calculated and the model is converted into a linear system.The mesh points are optimized and approach the scattered data points using the algorithm based on energy minimization.At the same time the mesh approaches the surface more accurately.Some simulation results are given which show that the method presented is effective for getting a good fairness and the approach is very efficient.4)Proposing a new algorithm for fast and accurately Loop subdivision surfaces with boundary.In this dissertation,the idea of subdivision is introduced,and the theory and method of Loop subdivision based triangular mesh is elucidated.It proposes an adaptive subdivision scheme for subdivision surfaces based on triangular meshes and exploits the local smoothness information of a surface for adaptive refinement of a model.Based on the flatness testing of each triangular mesh's edge,it could avoid generating cracks on subdivision surface.With this approach,it can avoid unnecessary subdivision in relative smooth areas and represents surfaces with lower cost when compared with those obtained by uniform subdivision schemes.The limit surfaces of the two Loop's models with the same subdivision format are C~2 continuous on boundary,but they are C~1 continuous at the singular point.In chapter sixth,Practical examples are given to show the high efficiency of the algorithm.In the last chapter,main contributions of the dissertation are summarized and further work is suggested.This dissertation is supported by National Natural Science Foundation of China under Grant(No:60173046,50274080),Natural Science Foundation of Hubei province under Grant(No:2005ABA227),Natural Science Foundation of Hunan province under Grant(No:05JJ40111),and also supported by the science foundation of Hunan province ministry of finance and education(No:02C643 and 04C717).