【作者】 张洪梅；

【导师】 赵国群；

【作者基本信息】 山东大学 ， 材料加工工程， 2007， 博士

【摘要】 随着计算机技术和数值方法的发展,有限元法、有限体积法和有限差分法等数值方法已成为计算科学与工程问题的重要方法,其数学基础是变分原理,基本思想是离散化和分片插值,即用网格去逼近所分析物体的空间。数值分析或模拟的主要步骤包括几何建模、模型离散、求解、后处理等过程,其中首要任务是模型离散,其依赖于有限元网格生成技术的发展。据调查统计,模型离散(即网榷格划分)通常占整个项目完成时间和费用的80%左右,而且网格的质量直接影响数值分析结果的精度和效率。在三维分析问题中,有四面体和六面体及二者混合单元,目前四面体网格的划分方法和有关商业化软件已渐成熟,而六面体网格由于其复杂的拓扑关系和与物体表面边界的一致性等方面的限制,现有六面体网格划分方法中都存在各自的优缺点。但六面体网格在计算精度、划分数量、抗畸变程度及重划分次数等方面比四面体网格具有明显优势,因此根据三维实体模型几何形状的复杂性,研究在任意三维空间内自动生成过渡均匀、协调、自适应的六面体网格,建立可靠、高效的六面体网格离散算法,可以为金属成形、岩土工程、流体力学、生物医学工程等领域分析大型复杂科学与工程问题建立三维模型离散平台,直接推动工程分析软件的商品化进程。本文以基于栅格法六面体网格生成方法作为基础方法,开展了基于实体模型几何形状的六面体网格自适应生成方法的研究。建立了基于STL文件进行三维实体模型几何特征自动识别的关键技术;提出了基于实体模型几何形状的六面体网格单元密度信息场的生成方法、加密准则和加密模板,将基于实体模型几何形状的网格自适应生成技术直接应用于栅格法六面体初始网格的生成;在六面体初始网格自适应生成方法研究的基础上,研究了六面体网格再生成过程的关键技术;建立了三维六面体网格质量评价准则,研究给出了提高网格单元质量的优化方法,主要包括网格质量评价模型的建立、网格单元拓扑关系优化、网格单元形状质量优化等;研究了三维网格显示消隐技术、三维剖切面算法等关键技术,应用计算机图形学知识开发了三维六面体网格自适应生成软件AUTOMESH-3D。首先,从力学角度和计算角度并以金属体积成形为例论述了三维有限元分析中六面体单元的优越性。对典型的六面体网格生成方法进行了总结对比,得出基于栅格法六面体网格生成方法具有高度自动化和易于网格局部加密的优点,适合于六面体网格自适应生成和再生成。在此基础上,本文选择基于栅格法的六面体网格自适应生成方法作为深入研究的方法。采用CAD造型软件生成的STL文件传递实体模型的表面几何形状信息,并建立了新的具有拓扑关系的STL数据文件,通过计算实体模型表面三角形面片的曲率,实现了几何特征的精确识别,为获得能够全面反映实体模型几何特征的六面体网格奠定了基础;提出了基于实体模型的几何特征建立单元密度信息场技术,给出了基于实体模型表面曲率和局部厚度建立加密源点信息场和单元密度信息场的具体方法和步骤;为保证生成过渡均匀的协调六面体网格,提出了一套六面体网格加密过渡模板。与Schneiders等人提出的加密模板相比较,本文改进了面加密模板和点加密模板,减少了一次加密后网格单元和节点的数目,并增加了两个拐角模板,有效地控制了加密区域的蔓延现象。将几何自适应技术与基于栅格法六面体网格生成方法相结合,提出了基于实体模型几何特征的栅格法六面体网格自适应生成方法。主要研究了从外向内栅格法六面体网格生成方法和从内向外栅格法六面体网格生成方法的基本算法和关键技术。鉴于目前常用的“最近距离反复搜索法”不能满足复杂网格模型的边界拟合,本文提出了穿插法边界拟合方法,并建立了相应的拟合规则。研究给出了基于表面四边形单元的六面体单元空隙填充法,提出了基于雅可比矩阵的最优边界拟合方法,基于网格边界单元与实体模型特征边界的相对位置关系,实现了从内向外栅格法六面体网格与实体模型边界的精确拟合,达到了因地制宜的拟合效果。网格再划分是金属体积成形等大变形模拟中不可缺少的过程,本文在研究六面体初始网格自适应生成的基础上,深入研究了六面体网格再划分技术。主要包括六面体网格再划分的两个主要标准;工件与模具几何离散造成的干涉和工件网格单元的变形,并给出了两个标准的建议值;提出并建立了新旧网格之间包容测试和方程迭代求解物理量传递的具体算法,经汽车转向节锻压成形过程等工程实例计算表明,该算法具有计算速度快、物理量传递准确的特点。网格的质量直接影响着数值模拟结果的精度和效率,本文针对三维六面体网格质量评价准则和优化技术进行了研究。建立了基于六面体单元雅可比矩阵行列式的值和条件数的网格质量评价准则。单元的雅可比矩阵能够全面地反映网格的质量,包括角度、面积、长度等网格质量指标。评价准则量化了六面体网格质量,使网格质量的检测更加简便和精确,确保获得符合有限元数值分析要求的六面体网格单元;研究分析了基于栅格法生成六面体网格的拓扑关系,提出了插入新单元技术和单元退化技术,显著改善了网格单元间的拓扑关系,为网格形状质量优化奠定了基础。提出了六种插入新单元模式和三种单元退化模式,分别适合于六面体网格凸特征边界和凹特征边界单元拓扑关系的调整;研究提出了基于曲率拉普拉斯边界优化方法,该方法不仅能够实现网格边界质量的优化,而且保证了优化后网格边界单元很好地描述实体模型的边界几何特征;提出了基于单位化雅可比矩阵条件数为目标函数的六面体网格表面和内部节点优化方法,建立了基于四边形单元的雅可比矩阵条件数的目标函数,实现了网格表面节点质量的优化,优化后网格保留了原网格的表面几何特征,确保获得的六面体网格符合有限元数值模拟计算的要求;建立了通用的三维六面体网格质量评价准则,并将其与网格质量优化技术相结合,采用C++语言编写了三维六面体网格质量优化程序,将其应用于基于栅格法自适应生成的六面体网格实例中,验证了本文提出算法的有效性和开发的六面体网格优化程序的准确性。深入研究了计算机图形学基础及OpenGL技术和可视化技术的基本原理,并给出了自主研发的六面体网格自适应生成软件AUTOMESH-3D的结构及其功能特点。主要通过设计合理的输入输出数据接口,实现了与三维CAD造型软件和DEFORM-3D等数值模拟软件的数据衔接;针对基于三维六面体网格的消隐技术、三维剖切算法进行了研究,实现了任意剖切面上物理量的可视化,方便了用户的操作;通过网格质量检测模块对所生成网格进行跟踪检查,实现了及时检查网格质量,确保获得满足有限元数值模拟计算要求的六面体网格;将OpenGL技术和计算机图形学理论引入到三维六面体网格自动生成软件的开发,自主开发了三维六面体网格自适应生成软件AUTOMESH-3D,可为科学与工程问题数值计算的三维六面体网格模型建立通用平台。更多还原

【Abstract】 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.更多还原