Research On The Algorithm For Adaptive Grid-based3D Hexahedral Element Mesh Generation And The Technique For Quality Improvement

Finite element method is a general-purpose method used for numerical analysis of computational science and engineering problems. It is the important part of computer-aided design. The basic idea of finite element method is discretization and slice interpolation. That is, using mesh elements to describe the space of analyzed object. Finite element method can simulate various types of complex material structures, load relationships and boundary conditions. It is widely used in metal forming, mechanics, architecture, geotechnical engineering, solid and fluid mechanics, biomedical engineering, rapid prototyping and manufacture, computer graphics and other fields. For three-dimensional issues, tetrahedra, hexahedra and a combination of them are usually used. Three-dimensional hexahedral element mesh expresses much more advantages than tetrahedral element mesh in computational accuracy, the element count, mesh distortion and re-meshing number, etc., thus receiving significant attentions. However, due to the complexity of adaptive hexahedral mesh generation itself, there remain a lot of problems yet to be further resolved. Therefore, it has important theoretical significance and engineering application values to study automatic hexahedral element meshing algorithms in arbitrary space and establish reliable and efficient discretion software platform for three-dimensional models.In this dissertation, grid-based method was used as the basic algorithm for automatic creation of hexahedral element meshes. According to the research situations, existent problems and development trends of grid-based method, we carried out the deep research on adaptive generation algorithm of three-dimensional hexahedral mesh so as to enhance the stability, reliability and robustness of the method. The key technique of geometric feature identification based on the STL files of solid models was studied. A relative perfect set of refinement templates was built. The main criteria for establishing refinement fields were proposed on the basis of the geometric characteristics of the solid model. The characteristic edge (C-edge) match technique was studied deeply. A new method combined priority nodes with relative position relationships was proposed for C-edge match. This dissertation also made an intensive study of quality improvement techniques, including two aspects:topological optimization and node position smoothing. In addition, a relative complete technique of local refinement was put forward, and the refinement level could be self-controlled arbitrarily.The STL files generated using CAD modeling software were used to reflect the surface geometry information of three-dimensional solid models. We established the STL files containing topological connections to avoid the repeated appearance of redundant data and further improve the computing efficiency. The essential technique of geometric feature identification was set up based on the curvature change of adjacent STL triangle facets. The identification methods of C-edges, characteristic points (C-points), sub-surfaces and boundary lines were given. The judgement methods of concave-convex and curve-straight attributes of C-edges and boundary lines, as well as the determination methods of the attributes of C-points, were also proposed. In order to achieve the conformal transition of the elements between refined regions and non-refined regions, this dissertation proposed a relatively perfect set of refinement templates on the basis of the research of Ito. The templates for two-face refinement and two-edge refinement were modified for the quality improvement and size uniformity of subdivided elements. The isolated node refinement template was added to refine the isolated nodes existing on the surface of the solid model or selected for local refinement. The insertion of these three templates avoided the expansion of refinement fields and implemented the effective control of refinement mesh areas.Four adaptive refinement criteria were proposed according to the geometric features of model surface, such as curvature characteristics, local thickness and small features, etc. In order to take both of the curvature change of the solid model and the density distribution of STL triangle facets into consideration, the definition of relative curvature was proposed. And on the basis of that, the refinement source point fields and element fields were constructed. Cases verified that the relative curvature criterion could allow more reasonable distribution of mesh density and obtain better refinement results. A new criterion based on local thickness was proposed according to the status properties and distribution patterns of the mesh elements in small thickness regions of the solid model. Aiming at some of the straddling elements, a supplementary refinement criterion was proposed in order to realize the accurate judgement and reasonable identification of refinement domains.Boundary matching is an important problem in automatic generation of three-dimensional finite element meshes. In this dissertation, the research and investigation of the C-edge matching technique of grid-based hexahedral element meshing method were performed. We made a deep study on the basic algorithm and key technique of relative position relationship method. A C-edge matching algorithm which combined priority nodes with relative position relationships was proposed by introducing priority nodes into the relative position relationship method. The geometric and topologic conditions for C-edge match were concluded and summarized. Eight types as well as five complementary types of free facet configurations were established, and their corresponding matching rules were also provided. The identification method for each level of priority nodes was presented, containing the identification of the first two levels and some of the third levels of priority nodes before C-edge match and the level-updated identification of priority nodes during C-edge match. The basic algorithms and implementation strategies of the combined method of priority nodes and relative position relationships were introduced in detail. An effective method for C-point match was also proposed based on geometric topology and priority nodes. A correction method was proposed to handle the irrational phenomenon where a small number of nodes were fitted to undesired C-edges. A method for treating the special sub-surface that intersected itself on a boundary line was proposed to ensure the effective match of special boundary line. For the C-edge matching problem on concave curves, this dissertation proposed a method to adjust the matching properties of the surface nodes associated with unreasonable degenerate elements. This method could unify the orientations of the degenerate facets fixed on a common concave curve in order that they pointed to the same sub-surface. Several examples demonstrated that the combined method proposed in this dissertation and the treatment methods for corresponding problems especially for concave curve matching problems could achieve accurate match between the surface of the solid model and the surface of the mesh. More than that, the geometric and topologic characteristics of the boundary elements and matched nodes could fully conform to the basic conditions of C-edge match, and the meshing accuracy was improved significantly.The quality of the mesh directly impacts on the accuracy and efficiency of numerical analysis. In this dissertation, we deeply studied the quality improvement techniques of three-dimensional hexahedral element meshes. The quality metric was constructed based on the minimal determinant value of Jacobian matrix, which quantified the quality of hexahedral meshes and made the evaluation of mesh quality easier and more accurate. We studied the topological connections of boundary elements in the hexahedral mesh created by inside-out grid-based method, and analyzed the reason why geometric and topologic problems of boundary mesh were created and the necessity of topological optimization. New element inserting technique, old element collapsing technique and the mixed technique which combined the inserting and collapsing techniques were employed. These three techniques improved the geometric topology of surface mesh remarkably. On the base of the current topological optimization modes, five inserting modes, four collapsing modes and three mixed modes were newly proposed. We also summarized all of the eleven inserting modes, seven collapsing modes and six mixed modes in the pattern of tables to show their geometric characteristics, types and the change of element number. The coordinate application rules of topological optimization modes especially mixed modes and the treatment methods of conformal problems were given. For node position smoothing technique, the Laplacian smoothing algorithm was studied in detail. Aiming at the issue that the conventional Laplacian method could not conserve volumes of solid models, modified methods were proposed accordingly. The curvature-based Laplacian method was used to smooth the nodes fitted on C-edges to prevent the deviation of the mesh nodes from the boundary line of the solid model. In order to resolve the geometry distortion and volume error that usually appeared while using conventional Laplacian method, a projection-based Laplacian method was proposed for the smooth of the remaining boundary nodes. A node-and area-based Laplacian equation was proposed to adjust the position coordinates of interior nodes in order that the interior nodes and the remaining boundary nodes had the same smoothing amplitude so as to further improve the quality of the surface elements.The research on local refinement technique was conducted. This technique could achieve the effective local refinement for individual or groups of nodes, elements, element-surfaces, element-edges, mesh-boundaries, mesh-faces and local regions, etc. This dissertation stated the reason why each category of local refinement was needed. For the technique of node refinement, this dissertation gave the judgement criterion and refinement method of the isolated nodes. For the technique of mesh-boundary or-face refinement, it was required first to identify the mesh-boundaries or-faces of the resulting mesh. For that reason, this dissertation proposed the basic algorithms and detailed procedures of mesh-boundary or-face identifications. Multi-level local refinement technique was also proposed. The levels of local refinement could be self-controlled effectively. The multi-level local refinement technique was able to perform arbitrary times of local refinement for certain geometric domains of the solid model, so that the final mesh could capture the geometric and physical features of the solid model more accurately and further increase the accuracy of finite element analysis.On the basis of the research on grid-based hexahedral element mesh generation algorithms and key techniques described above, the hexahedral mesh automatic generation software AUTOMESH-3D previously developed by our groups was modified and improved. The reliability, stability and versatility of AUTOMESH-3D were further enhanced, which built a general-purpose platform to generate three-dimensional hexahedral element meshes for various science and engineering problems. In this dissertation, the module structure and function properties of this software were introduced. Several hexahedral element meshing examples for solid models with complex geometric shapes were provided to demonstrate the accuracy and reliability of the developed software.