自由形态空间网格结构的网格设计方法研究与实现

发布时间：2018-06-26 20:30

  本文选题：空间网格结构 + 自由形态　； 参考：《浙江大学》2014年博士论文

【摘要】：自由形态空间网格结构的网格设计是一项十分复杂的工作,而目前大部分网格设计的研究都是针对某个具体工程,无法直接应用到或指导其他结构的网格设计。针对此问题,本文深入研究自由形态空间网格结构的网格设计,提出一种面向自由曲面的网格设计新方法,发展了已有的网格生成方法和网格优化技术,实现了自由形态点云的网格设计。 本文结合已有研究,给出了自由形态空间网格结构的定义,回顾了自由形态空间网格结构的的应用现状,阐述了网格设计的内涵,总结了网格生成方法和网格优化方法的研究现状。 当前的自由曲面造型技术以B样条方法为基础,本文阐述了B样条、B样条曲线曲面以及非均匀有理B样条(NURBS)的定义和重要性质；介绍了B样条曲线曲面的正向计算和反向映射的计算方法；解析了CAD/CAM/CAE领域普遍应用的IGES接口文件的数据格式,以获取各类建模软件中构造的自由曲面信息,用于网格设计。 基于空间网格结构对网格的要求,提出了一种自由曲面网格生成的新方法—等参线分割法。该方法的基本原理是利用B样条曲面的张量积特性,通过提取等参线,将二维的曲面网格划分问题,降为一维的曲线分割问题。为实现等参线分割,建立了等参线等弦长分割算法。 基于等参线分割法分别对简单自由曲面和复杂边界自由曲面进行网格生成。依据边界轮廓形状,将简单自由曲面归纳为四边形边界曲面、三角形边界曲面和圆形边界曲面三类,针对每种曲面设计不同形式的网格,发展了相应网格形式的生成算法。介绍了复杂边界自由曲面的生成途径,以及与之相关的重要定义；建立了曲面边界线的分类准则、提出了分类方法,结合物理空间与参数域内边界线之间的关系,提出了复杂边界曲面网格生成的基本方法,并探讨了网格的细部优化方法,完善了网格生成算法流程。 发展了面向3D扫描点云的网格生成方法,在点云上直接剖分网格。基于有限元中广泛应用的波前推进法(AFT),针对点云的数据特点,引入搜索盒数据结构以建立起离散数据点之间的拓扑关系,提出了点云初始边界的搜索方法,完善了前沿推进过程中生成新节点的算法,形成了应用于点云的网格生成方法。在此基础上,进一步研究了网格的优化调整方法。提出了包括Delaunay优化和Laplacian优化两个步骤的优化流程,并通过对Laplacian优化方法的改进,克服传统Laplacian优化网格收缩的缺陷。提出了针对线约束和点约束的网格调整方法。采用两种不同工艺制作实物模型,展示了基于3D扫描的自由形态空间网格结构几何设计全过程。 根据上述理论与方法编制了自由形态空间网格结构网格设计程序FreeMesh。该系统包括前处理模块,网格设计模块和后处理模块。其中,网格设计模块是程序的主体,完成了自由曲面的网格设计和自由形态点云的网格设计两大功能。 通过理论推导、数值模拟以及程序系统的编制,证明了本文所提出的自由形态空间网格结构网格设计方法是可行且有效的,能为实际工程应用提供技术支持。最后,论文提出并讨论了今后有待解决的若干问题。
[Abstract]:The grid design of free form space grid structure is a very complicated work. At present, most of the research of grid design is aimed at a specific project and can not directly apply or guide the grid design of other structures. In this paper, the grid design of free form space grid structure is deeply studied, and a kind of surface is proposed. The new method of grid design for freeform surface has developed the existing grid generation method and grid optimization technology, and realized the grid design of free form point cloud.
In this paper, the definition of free form space grid structure is given in this paper. The application status of free form space grid structure is reviewed, the connotation of grid design is expounded, and the research status of grid generation method and grid optimization method is summarized.
The current free form surface modeling technology is based on the B spline method. This paper describes the definition and important properties of B spline, B spline curve and surface and non-uniform rational B spline (NURBS), introduces the forward calculation and reverse mapping calculation method of B spline curve and surface, and analyzes the IGES interface file which is widely used in the CAD/CAM/CAE field. Data format is used to obtain freeform information in various modeling software for grid design.
Based on the requirement of space grid structure to the grid, a new method of generating free surface mesh - isoparametric line segmentation is proposed. The basic principle of this method is to use the tensor product characteristics of B spline surface and extract isoparametric lines to divide the two-dimensional surface mesh into one dimension curve segmentation problem, and to realize isoparametric segmentation. A string length segmentation algorithm, such as isoparametric line, is established.
Based on the isoparametric line segmentation, the simple free-form surface and the complex boundary free-form surface are generated. According to the shape of the boundary contour, the simple free-form surface is divided into three kinds of quadrilateral boundary surface, triangular boundary surface and circular boundary surface, and different forms of grid are designed for each surface, and the corresponding grid forms are developed. The generation method and the important definition related to the complex boundary free-form surface are introduced, the classification criterion of the surface boundary line is established, the classification method is put forward, and the basic method of generating the complex boundary surface mesh is put forward by combining the relationship between the physical space and the boundary line in the parameter domain, and the fine grid is discussed. The optimization method of the Department has improved the grid generation algorithm flow.
The grid generation method for 3D scanning point cloud is developed, and the grid is directly dissecting on the point cloud. Based on the wave front propulsion method (AFT) widely used in the finite element, the search box data structure is introduced to establish the topological relation between the discrete data points, and the search method of the initial boundary of the point cloud is proposed. The algorithm of generating new nodes in the process has formed a grid generation method applied to point cloud. On this basis, the optimization and adjustment method of grid is further studied. The optimization process of two steps including Delaunay optimization and Laplacian optimization is put forward, and the traditional Laplacian optimization grid is overcome by improving the Laplacian optimization method. A mesh adjustment method for line constraints and point constraints is proposed. Two different processes are used to make the physical model, and the whole process of geometric design of free form space grid structure based on 3D scanning is presented.
According to the theory and method mentioned above, a free form space grid structure grid design program FreeMesh. is developed. The system includes the pre processing module, the grid design module and the post-processing module. Among them, the grid design module is the main body of the program. It completes the two functions of the grid design of free surface and the grid design from the form point cloud.
Through theoretical deduction, numerical simulation and programming system, it is proved that the free form space grid structure grid design method proposed in this paper is feasible and effective, and can provide technical support for practical engineering applications. Finally, the paper puts forward and discusses some problems to be solved in the future.
【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】：TU399

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