Research On The Algorithm For 3D Hexahedral Mesh Adaptive Generation And Its Applications

With the development of computer technology and numerical method, numerical simulation methods such as finite element method, finite volume method, and finite difference method, etc. play more and more important roles in the fields of the science researches and engineering applications. The common ground of these numerical methods is to generate a desired mesh or grid system of the analyzed model. The main steps of numerical analysis or numerical simulation include geometric molding, mesh generation, computation and post-process, etc. According to the research and Stat., the step of mesh generation takes eighty percent of all the times and expenses. The accuracy and effectiveness of numerical analysis is strongly dependent on the density and quality of mesh model. In three-dimensional numerical analysis, tetrahedron, hexahedron and a combination of them are used. At present, the method and commercial software of tetrahedron have been fully mature. However, the generation of an all-hexahedral element mesh is algorithmically much more complex than that of an all-tetrahedral element mesh, so the development of hexahedral element mesh generator is still in the research stage. Many numerical simulation results show that hexahedral element mesh is better than tetrahedral element mesh because it can increase the analysis accuracy and decrease the overall element count. According to the geometrical complex of three-dimensional solid model, the automatic generation method of the conformal and adaptive mesh in all the three-dimensional space was studied. And the software for three-dimensional hexahedral element mesh generation was developed for large complex mesh model construction in many science and engineering researching fields, such as metal forming, geo-technical engineering, hydrodynamics, biological physic, et al. It will directly impel the commercial course of the engineering analysis software.In this dissertation, grid-based method for hexahedral element mesh generation was used as the basic approach. The method for adaptive hexahedral element mesh generation based on the geometric characters of solid models was studied. The identification technique for the geometrical characters of three-dimensional solid model based on STL file was presented. The technique for the generation of hexahedral element mesh refinement field based on the geometric characters of solid models, the rules for refinement, and the templates for refinement were described. The geometric adaptive technique was directly introduced to the generation of hexahedral element mesh with grid-based method. On the base of the research of initial hexahedral element mesh adaptive generation, the technique of hexahedral element mesh remeshing was studied. Quality metrics for hexahedral element mesh constructed to track timing. The methods for hexahedral element mesh quality improvement were proposed, such as mesh topologic optimization and shape quality improvement. Some key techniques about computer graphics, such as the hidden vision technique, arbitrary section, and et al. were studied. As a result, the software AUT0MESH-3D for three-dimensional hexahedral element mesh automatic generation was developed.Firstly, the advantage of hexahedral element mesh in three-dimensional finite element analysis was dissertated by an example of metal forming from the sides of mechanics and computation. The typical methods of hexahedral element mesh generation were compared. Grid-based method is highly automatic and easy to refine, so it is suitable for the adaptive generation and remeshing of hexahedral element mesh. Therefore, an algorithm for hexahedral element mesh adaptive generation with grid-based method was studied deeply in this dissertation.The STL file generated with the well-known CAD software UG was used to transfer the surface geometrical data information. A new STL data file with topological connection was constructed for the calculation in the next. The geometric characters of the solid models were correctly identified based on the curvature of the surface triangle facets in the new STL file. The technique for the element refinement information field construction based on the geometric characters of the solid model was proposed. The methods and steps of the refinement source point field construction based on the surface curvature and local thickness of the solid model were described in detail. A set of refinement templates was proposed. Compared with the templates of Schneiders, the number of the mesh elements can decrease with the modification of the face refinement template and node refinement template. As a result of our two added corner refinement templates, the refinement field extending problem was solved successfully.To combine the geometric adaptive technique and grid-based mesh for hexahedral element mesh generation, a modified grid-based algorithm for adaptive hexahedral element mesh generation based on the geometrical characters. The basic algorithms and key techniques of the outside-in grid-based method and inside-out grid-based method for hexahedral element mesh generation were studied. An interlude method for the boundary match and the corresponding match rules were proposed in the dissertation. The surface-gap filling method with hexahedral elements based on the surface quadrilateral elements was proposed. The precise boundary match between the hexahedral element mesh generated with inside-out grid-based method and the solid model was carried out with the Jacobian-based approach according to the relative position of boundary elements and the characteristic boundaries of the solid model.Automatic remeshing process is an unavoidable necessity in numerical simulation of metal bulk forming. On the base of the research of initial hexahedral element mesh adaptive generation, the technique for hexahedral element mesh remeshing was studied. Two remeshing criteria, i.e. the conditions under which remeshing should be done, were given in this dissertation. One was about geometrical interference of the finite element mesh with the die. Another is about severe distortion of the elements. The algorithm about node container test and transformation of state variables between the new and old mesh system in three-dimensional 8-node hexahedral element mesh is established, and its advantage is effective and accuracy.The mesh quality directly impacts on the accuracy and effectiveness of the results of numerical simulations. In the dissertation, the quality metric and improvement technique for three-dimensional hexahedral element mesh were studied. On the base of the determinant and condition number of Jacobian matrix, the quality metrics of hexahedral element mesh were constructed. The Jacobian matrix of element could reflect the quality of mesh, such as angle, area, volume and length. The metrics quantified the quality of hexahedral element mesh and made it easy and accurate to measure timing. On the base of the analysis of the topological connection of hexahedral element mesh generated with grid-based method, new element inserting technique and old element collapsing technique were proposed to improve the topological quality of hexahedral element mesh. The proposed six new element inserting modes and three old element collapsing modes are suitable for the topological connection improvement of the hexahedral elements on the convex edges and concave edges, respectively. The curvature-based Laplacian smooth method for the elements on the characteristic boundaries was proposed. It not only could improve the boundary element quality but also capture the geometrical characters after optimization. An approach, which took the condition number of the normalized Jacobian matrix as the objective function, was introduced to improve the quality of the surface and interior nodes. After the optimization, the mesh could preserve the geometrical characters and satisfy finite element numerical simulation. To combine the quality metric and improvement techniques of hexahedral element mesh, a quality optimization program for three-dimensional hexahedral element mesh was compiled with C++ language. With the applications to the adaptive hexahedral element meshes generated with grid-based method, the effectiveness and accuracy of the proposed algorithm and the developed program in the dissertation were validated.In the dissertation, the fundamentals of computer graphics, OpenGL technique and visualization technique were studied. The framework and function of the self-developed software AUT0MESH-3D for hexahedral element mesh adaptive generation were presented. A reasonable in-out data interface was designed. As a result, the data joints with other numerical simulation software were carried out, such as three-dimensional CAD software, three-dimensional simulation software DF0RM-3D, and etc. The visualization in arbitrary section was realized with the study of the hidden technique and cutting technique for three-dimensional hexahedral element mesh. Through following the track of the mesh quality measure, the mesh quality could be examined in time, and the generated mesh, which satisfied finite element simulation, was insured. OpenGL technique and computer graphics were introduced into the development of the software for three-dimensional hexahedral element mesh generation. Three-dimensional hexahedral element mesh generation software AUT0MESH-3D was developed. It could be a current platform for three-dimensional mesh model constructions of the researches in science and engineering fields, such as metal forming, geo-technical engineering, hydrodynamics, biological physic, and et al.