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

Finite element mesh generation is an important intersection research field combined with engineering science and computer science. At present, mesh generation is still very active after about forty years of development. As the engineering and scientific problems getting more and more complex, how to generate well-shaped mesh in the analyzed model efficiently has become an important issue. According to the arbitrary geometric and topological complexity of three-dimensional solid model, the automatic generation method of the conformal and adaptive mesh in the three-dimensional space was studied. The research has great practical significance and theoretical value for solving complex scientific and engineering problems. It will directly impel the commercial course of the engineering analysis software.In this dissertation, the algorithm for adaptive hexahedral mesh generation and regeneration based on grid-based method was studied. The identification technique for the geometric characters of three dimensional solid model based on STL file was presented. The refinement field was generated based on the geometry features, the physics of the problem and the user specification, etc. The technique of density control based adaptive generation algorithm of hexahedral meshes using improved grid-based method was introduced. On the base of the research of initial hexahedral element mesh adaptive generation, the technique of hexahedral element mesh regeneration was studied. The relationship between the accuracy of finite element analysis and the density of the mesh was established. The quality metric and optimization technique for three-dimensional hexahedral element mesh were studied. From the aspect of generality and automation, the software AUTOMESH-3D for three-dimensional hexahedral element mesh automatic generation was developed.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 by combining the edge-based method and face-based method. A method for the mesh density generation and control was presented. This method can automatically generate a reasonably optimized refinement field according to the geometry features, mechanical conditions and the density windows users specified. In order to improve the mesh quality of hexahedral elements in the transition areas, a set of improved 27-refinement templates was proposed and the refinement modes of these templates were given in details. A new set of effective 8-refinement templates was developed to ensure the hexahedral mesh transition gradually and conformably. Adjustment rules were built for conversion of every element in the refinement to a corresponding 8-refinment template. The corresponding date structure and the procedures for realization of the algorithm were presented. In order to resolve the propagation problems of meshes, a buffer layer was inserted on the transition refinement domains that contain concave geometric features. Since one important requirement of mesh generation algorithm is that finite element meshes should give good description of the geometry features of a solid model, therefore, this paper summarized and gave six different types of free element facet configurations for matching the surface of the hexahedral element meshes to the surface of the solid model. A precise matching of the hexahedral element meshes to the boundaries of the solid model was realized by using the above methods and according to the relative position of boundary elements and the characteristic boundaries of the solid model.Automatic mesh generation and regeneration 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 regeneration was studied. The judgment criteria, i.e. the conditions under which mesh regeneration should be done, were given. Aiming at the problem of finite element mesh distortion, the degeneracy problem and the overlapping problem of the distorted elements in the process of dividing a quadrilateral free face into two triangles were studied and the corresponding treating method were given. To reduce the impact of geometrical interference between workpiece and die, the workpiece's triangle facets in the contact region were substituted by the die's triangle facets. Based on the posteriori error estimates of finite element and the adaptive hexahedral mesh generation technique, the new mesh generation was discussed. In order to continue the simulation with a new mesh system, state variables such as effective strain, damage and temperature calculated in the old mesh system must be accurately transferred to the new mesh system. Therefore, the data transfer process was given in this dissertation.The mesh quality directly impacts on the effectiveness and accuracy of the results of numerical simulations. In the dissertation, the quality metric and improvement technique for three-dimensional hexahedral element mesh were studied. By using the Scaled Jacobian and the Condition Number of Jacobian matrix as mesh quality evaluation criterion, the quality metrics of hexahedral element mesh were constructed. The metrics quantified the quality of hexahedral element mesh and make sure that the quality of all the hexahedral elements after improvement were in the acceptable range of finite element analysis. 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 four new element point inserting modes and five new element edge inserting modes are suitable for hexahedral elements on the convex characteristic edges. The proposed four element collapsing modes are suitable for hexahedral elements on the straight or small curvature concave characteristic edges. Three new element inserting combined with element collapsing modes suitable for hexahedral elements on the concave characteristic edges of large curvature are proposed. To improve the quality of the surface meshes and the interior elements, an optimization approach is proposed by using mesh quality metric as the objective function. By combining the Laplacian smoothing method with the optimization approach, the mesh quality is improved significantly. For the surface meshes, the Condition Number of a set of Jacobian metric associated with the quadrilateral elements is taken as the optimization objective function. For the interior elements, the Condition Number metric associated with the hexahedral elements is employed as the optimization objective function. The combination of Laplacian smoothing with low computational cost and the Condition Number based optimization approach used only for the poor quality elements can effectively improve the overall mesh quality and overcome the drawbacks they both have. The whole mesh quality can effectively preserve the geometrical characters and satisfy the requirement of three-dimensional finite element numerical simulation. A quality optimization program for three-dimensional hexahedral element mesh was compiled. 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 framework and function of the self-developed software AUTOMESH-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 DEFORM-3D, etc. 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 AUTOMESH-3D was developed. It could be a current platform for three-dimensional mesh model constructions of the researches in science and engineering fields.