三维有限元网格先进编辑技术研究

发布时间：2018-06-20 13:25

本文选题：体网格编辑 + 体网格重生成　；参考：《浙江大学》2014年博士论文

【摘要】：在使用有限元分析进行产品设计验证的过程中,需要将产品的几何模型离散为相应的有限元网格模型以支持分析求解,并且为了达到设计目标,设计和分析通常是一个反复迭代的过程,其中的再分析特别是网格重生成非常耗时。因此,为了提高产品设计开发的效率,必须提高有限元网格的重新生成效率。网格编辑正是一种高效的网格重新生成技术,其通过重用原有的有限元网格,能够快速得到用于再分析的新网格模型,并有助于加强产品设计模型与有限元网格模型之间的关联互动。为此,以提高有限元网格重生成的效率和质量为目标,本文对三维有限元网格编辑技术展开研究。论文的主要工作包括以下几个方面：提出一种CAD模型变动驱动的四面体网格编辑方法首先根据CAD模型的变动,依据网格划分的逼近度要求,以及变动区域附近网格单元密度函数的变化,确定原始网格中的可重用单元；然后提取保留单元与被移除单元之间的边界网格面和边界网格边,并将其用于构建需要进行网格重生成的变动区域；最后使用Delaunay方法生成新的网格单元。该方法能够提高网格的重新生成效率,并在网格编辑的过程中保证单元的几何密度自适应性。提出一种基于对偶操作和直接编辑操作的六面体网格编辑方法通过对其几何模型进行直接编辑,实现对六面体网格模型的有效变形。为了优化变形后的网格模型,首先高效地将网格模型转换为表面体网格单元质量较好的元网格；然后使用较为整体的对偶操作进行粗略的密度控制；最后根据提出的单元形变度概念,通过使用易于局部化的对偶操作,对需精化区域进行精化。该方法能够提高变形后网格的单元质量,保证单元密度自适应性,并加强几何模型与网格模型之间的关联互动。提出一种基于实体切割操作的六面体网格编辑方法首先识别网格元素与实体模型几何元素之间的相交关系,以高效生成由于网格被实体模型切割而新增到网格模型中的几何元素；然后通过使用启发式的A*最短路径算法和波前推进法,将网格元素匹配到新增几何元素以分离需要被切割的网格单元；最后通过插入fundamental sheet对切割后的表面单元进行质量优化。该方法能够支持使用复杂的实体模型进行六面体网格切割,以及允许切割实体与网格模型存在复杂交互的情况,并且能够提高网格切割后的表面边界准确性。开发三维有限元网格编辑原型系统FEAMeshLab在该系统中集成了上述网格编辑功能,设计了可扩展的CAD/FEA集成模型,并利用该系统对本文所提出的方法进行了验证。
[Abstract]:In the process of using finite element analysis to verify the product design, it is necessary to discretize the geometric model of the product into the corresponding finite element mesh model to support the analysis and solution, and in order to achieve the design goal, Design and analysis is usually an iterative process in which reanalysis, especially grid regeneration, is time-consuming. Therefore, in order to improve the efficiency of product design and development, it is necessary to improve the efficiency of finite element mesh generation. Grid editing is an efficient mesh generation technique. By reusing the original finite element mesh, a new mesh model for reanalysis can be obtained quickly. It also helps to strengthen the interaction between the product design model and the finite element mesh model. In order to improve the efficiency and quality of finite element mesh generation, this paper studies the three dimensional finite element mesh editing technology. The main work of this paper includes the following aspects: a new method of tetrahedron mesh editing driven by variation of CAD model is proposed. Firstly, according to the change of CAD model and the requirement of approximation degree of mesh division, And the change of the density function of the grid cell near the variable region to determine the reusable element in the original grid; then the boundary mesh surface and the boundary grid edge between the retention unit and the removed element are extracted. It is used to construct the variable region which needs to be reborn into grid. Finally, the new grid unit is generated by Delaunay method. This method can improve the efficiency of mesh generation and ensure the self-adaptability of geometric density in the process of grid editing. A hexahedron mesh editing method based on dual operation and direct editing operation is proposed. By editing the geometric model directly, the hexahedron mesh model can be deformed effectively. In order to optimize the deformed mesh model, the mesh model is firstly converted into a metamere with good quality of surface mesh elements, and then the rough density control is carried out by using a more general dual operation. Finally, according to the concept of element deformability, the region in need of refinement is refined by using dual operation which is easy to localize. This method can improve the cell quality of the deformed mesh, ensure the self-adaptation of the cell density, and enhance the correlation and interaction between the geometric model and the mesh model. A hexahedron mesh editing method based on entity cutting operation is proposed to identify the intersecting relationship between the mesh elements and the geometric elements of the solid model. The geometric elements added to the mesh model due to the mesh being cut by the solid model are generated efficiently, and then the heuristic A * shortest path algorithm and the wave-front propulsion method are used to generate the geometric elements that are added to the mesh model. The mesh elements are matched to the new geometric elements to separate the mesh elements that need to be cut. Finally, the quality of the surface elements after cutting is optimized by inserting fundamental sheet. This method can support the hexahedron mesh cutting using complex solid model, and allow the complex interaction between the cutting entity and the mesh model, and can improve the accuracy of the surface boundary after mesh cutting. A 3D finite element mesh editing prototype system, FEA MeshLab, is developed in which the above grid editing functions are integrated, and an extensible CAD / FEA integration model is designed, and the proposed method is verified by the system.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TP391.72;TB472

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