【作者】 但文蛟；

【导师】 胡树根； 王耘；

【作者基本信息】 浙江大学 ， 机械设计及理论， 2004， 硕士

【摘要】 近十几年来，随着计算机技术的飞速发展，数值模拟技术在理论和应用上都取得了巨大的成功。数值模拟技术作为工程领域复杂问题求解不可或缺强有力手段，已得到工程人员足够高重视，成为推动工程技术发展重要工具。网格划分是数值模拟技术关键技术之一，在CAE分析之前，网格划分需要花费大量时间。同时，数值模拟技术准确性和分析速度都直接受到网格质量影响。所以研究快速生成高质量网格，对数值模拟技术而言，具有不可替代的意义。 铺路法作为四边形网格经典算法之一，已得到广泛应用。但是由于铺路法存在网格生成过程操作复杂而且生成的网格均匀性较低的缺陷，本文提出了分层发散网格划分法。为有效保证所生成的四边形网格的质量，在三角不等式的基础上，推导出一种新的网格质量评价因子。在对网格平滑过程中，结合被搜索节点周围网格形成区域的凹凸性，对等参Laplacian网格平滑法进行了修正。 本文围绕以上几个目标开展了如下的工作： 文章介绍了网格生成的国内外研究状况，在四边形网格生成的背景以及研究意义的基础上，提出了论文研究的主要内容。 在铺路法的思想基础上，提出的一种基于分层发散思想的有限元网格生成方法。详细地介绍了这种分层发散网格生成过程中的初始条件确定、布点、点的存贮等网格划分预处理的关键内容，最后给出了布点生成实例。 在分层发散网格划分法产生的节点基础上进行网格生成，研制并实现了基于分层发散网格生成法的四边形网格生成器，给出了网格生成流程图和大量网格生成实例，最后对分层发散算法进行了分析。 为保证所生成网格合理性，在三角不等式的基础上，推导了一种四边形网格质量判断因子。然后在经典Laplacian平滑法和等参Laplacian平滑法的基础上，结合被搜索节点邻近的网格的凹凸性，对等参Laplacian平滑法进行了修正。 对分层发散的四边形网格划分方法在空间曲面上进行推广，讨论了空间曲面的连续区域和非连续区域布点，空间曲面网格生成等内容。更多还原

【Abstract】 In the past few years, with the development of computer technology, the method of the numerical simulation has received great success both in theory and in practice. It has powerful means to complicated problems in engineering community. The mesh generation, which is a key technology for numerical simulation, is very complicated and easily be mistaken. It takes up a major part of the total time of the numerical simulation. At the same time, the quality of a mesh directly affects both the reliability of finite element and the time that the analysis process cost. As a result, how to generate high quality mesh rapidly is extremely valuable for the numerical simulation.Paving method has received wide acceptance, which generates all-quadrilateral meshes in an arbitrary 2D region. However, it has several defects, such as the complexity of making program and irregular mesh. In order to avoid those defects of the paving, a new algorithm, named delamination & divergence algorithm, has been brought forward. Base on the triangle inequality, a new judgment parameter for mesh quality has been advanced to guarantee the mesh quality. Based on the irregular mesh around a node, a modification is made to the IsoLaplacian smooth method in the mesh smoothing.In this dissertation, research work related to the content that discusses above has been introduced.Firstly, the dissertation expatiates the status about mesh generation research. After analyse the significances of researching quadrilateral meshes, the structure of the dissertation details is presented.Secondly, Based on the thought of the delamination & divergence, the dissertation expatiates the pre-dispose of the FEM method. It introduces how to prepare for the pre-condition of mesh generation and how to distribute and store the points by which the mesh is generated.Thirdly, the dissertation introduces the details of how to generate the meshbased on the thought of the delamination & divergence. FreeDraw software, which generates quadrilateral meshesbased on the delamination &’ divergence, mesh generation algorithm, has been developed.Fourthly, Base on the triangle inequality, a new judgment parameter of meshquality has been advanced to protect the mesh quality. Based on the irregular mesh around a node, a modification to the IsoLaplacian smooth method is presented.Fifthly, the delamination & divergence mesh generation algorithm extends to the space facet. It expatiates how to generate node in space facet and how to mesh space facet.更多还原