The Research Of Tetrahedral Mesh Generation Algorithm For Finite Element

Finite element method disperses continuous substance into a batch of elements, and this can transform the problem of infinity freedom degree into the problem of finite freedom degree, and then solves it by computers. It is a powerful numerical analysis method in solving engineering problems. Before analysis using finite element method, the model to be calculated must be meshed. So, the research and implementation of algorithms for finite element mesh generation is quite important. To the problem of two-dimensional models, the existing methods of finite element mesh generation have achieved much success and on the whole fulfil the requirement of actual engineering. However, to the problem of three-dimensional models, mesh generation methods only have received a little bit of effect, so they must be researched and developed farther.At first this paper discusses several common algorithms of tetrahedralization, Octree, Advancing Front Technique and Delaunay Triangulation method and in-depth study of them. And then compared their principles and characteristics. Since Delaunay Triangulation method based on sophisticated mathematical theory, good flexibility, easy to control and strict criterion, so it applies to the tetrahedralization of three-dimensional models. The main contents include:(1)Based on theories of computational geometry about Delaunay triangulation, this paper studies the concepts and criterions of Convex Hull, Voronoi and Delaunay triangulation and researches their relationships.(2)By introduction of three-dimensional qualification-Piecewise Linear Complexes(PLC) to describe the geometrical boundary, export the concept of three-dimensional Constrained Delaunay Tetrahedralization. This paper submits an initial Delaunay tetrahedralization algorithm which is Randomized Incremental Flip Algorithm.The algorithm based on the classical Delaunay triangulation algorithms: incremental algorithm and local transformational algorithm. We adopt the algorithm that increasing points while changing, so that the mesh that has been generated always meets the Delaunay criterion. This algorithm without considering the order of insertion point, effectively generate the initial tetrahedral mesh.(3)The problems about constrained Delaunay algorithm to be resolved are researched:the conforming of the boundary edges and boundary facets in specified area, and the problem of sliver element. Based on the initial tetrahedral mesh, this paper adopts the method of recovering the constrained edge firstly, and then recover the constrained face, in order to ensure the complete consistency of the boundary. Using edge recovery algorithm by adding steiner points to recover missing segments and does not add steiner points to recover missing facets by cavity regenerate tetrahedral method. Removed the sliver elements by decomposing, complete the tetrahedral mesh generation, and improve the quality of the mesh element, to further meet the requirements of finite element analysis.According to the study above, the algorithm is carried out by C++ language and applied to practical engineering application of finite element. The experiments show that the algorithm proposed in this paper, which are improved initial tetrahedral mesh generation algorithm and boundary recovery algorithm, the algorithm generates high quality mesh, through the elimination of sliver cells, the quality of the generated finite element mesh has a large extent improvement, and the mesh quality has been guaranteed.