Research On Key Technology For Hexahedral Mesh Generation Of3D Solid And Software Development

With the development of three-dimensional modeling technology and numerical method, thefinite element technology for three-dimensional entities has been used more widly in engineering. Thesolid mesh generation is an important premise of three-dimensional finite element analysis, and thehexahedral mesh is becoming the main element in finite element analysis for its superiority incalculation accuracy, element number and other aspect compared with the tetrahedral mesh. Now,automatic hexahedral mesh generation for arbitrary three-dimensional volumes is still not trulyresolved. In this thesis, the key techniques in automatic hexahedral mesh generation, such as solidmodel expression, volume decomposition, swept volume hexahedral mesh generation, hexahedralmesh quality optimization, etc are deeply studied, and a mesh generation software forthree-dimensional volumes has been developed. The research achievements are as follows:(1) A local rigid and global linear-elastic reverse deformation finite element method basedsurfaces parameterization method has been proposed, whcih overcomes the shortcomings that thecomposite surfaces are difficult to parameterize. Base on the local to global methodology, the localrigid transformation can be taken by analyzing the Jacobian of affine transformation of each triangleand adjusting the corresponding singular values, and then the final parameterization result can beobtained by linear-elastic finite element method globally.(2) A three-dimensional volume decomposition method based on swept volume recognition ispresented. Firstly, all boundary edges are classified and all composite surfaces are extracted bywidth-first searching algorithm; Then, the constraint faces and linking faces corresponding to thesource face are determined by depth-first searching algorithm. Finally, the cutting surfaces can begenerated for different type of constraint faces, and the entire geometric models can be decomposedinto the combination of multiple swpet volumes. The divided meshable pieces can generatehexahedral mesh by applying mapping or sweeping method directly.(3) A surface mesh projection algorithm based on intrinsic characteristics and energyconstraints is presented. The source surface mesh and the target base mesh are flattened by meshparameterization method; A quadratic energy equation based on scaled intrinsic characteristics ofplanar mesh, mesh deformation energy and boundary constraints is established, then a least-squaremethod is used to minimize this energy function to morph the planar source mesh onto the planartarget base mesh; The target surface mesh is then obtained by mapping the plane source mesh onto the target base mesh. Mesh projection between multi surfaces can be implemented by using this method,which ensures that the target mesh is homeomorphism to source mesh.(4) A double octahedron based local transformation and global linear-elastic finite elementmethod hexahedral mesh quality optimization method is presented. A double octahedron based localtransformation method is used to regularize a hexahedron locally, and regular hexahedral elements areobtained for every single mesh. Locally by analyzing the displacement of hexahedral element nodesbetween pre and post regularization, and the residual internal force can be calculated by linear elasticfinite element method. Globally by treating the surface features as constraints, the hexahedral meshquality optimization result can be obtained by loading the unbalanced residual internal force into itscorresponding node. After the optimization, the hexahedral mesh could preserve the geometricalfeatures of original model, and the hexahedral mesh quality is highly improved.On the basis of deep study of these methods, and with the Open CASCADE geometric modelingplatform, a multi-functional three-dimensional solid mesh generation software is developed, includingstandard geometric and finite element data exchange interface, automatic hexahedral mesh generationand hexahedral mesh quality measurement and so on. By utilizing soft plug-in technology, thefunction extended interface is implemented to provide convenience for user extensions. The practicalhexahedral mesh generation examples of aeronautical blade and other complex parts show that thedeveloped software has higher mesh generation efficiency and can generate good quality hexahedralmesh, which meets the requirements of three-dimensional finite element numerical simulation.