有限元网格生成方法发展综述

在参阅和分析大量有关文献的基础上，对现有的各种有限元网格生成方法进行了总结，特别是对当前广泛使用的Ｄｅｌａｕｎａｙ三角化，推进波前法和八叉树方法等，从理论到具体的算法程序实现等各个方面都作了详尽的剖析，分析了各种方法的优缺点。为深入研究开发全自动、自适应有限元网格生成软件提供了有益的参考。     

三维有限元网格自动剖分中对边界的处理方法:单元提取算法

在用八叉树法进行三维有限元网格的自动剖分算法中，对边界的处理是算法中的难点。本文叙述了边界处理方法之一：单元提取算法的理论和实现。由于本文在单元提取算法中加入了单元形状测试算子，使得形成的四面体单元在形状质量上有所保证，在一定程度上避免了狭长单元的产生     

三维有限元网络自动剖分中对边处理方法：单元提…

在用八叉树法进行三维有限元网格的自动剖分算法中，对边界的处理是算法中的难点。本文全叙述了边界处理方法之一：单元提取算法的和理论和实现。     

从表面重构的体数据实现三维网格剖分

针对有限元分析中网格最优化问题,本文提出一种改进的生成四面体网格的自组织算法。该算法首先应用几何方法将三角形表面模型重新构造成规定大小的分类体数据,同时由该表面模型建立平衡八叉树,计算用以控制网格尺寸的三维数组;然后将体数据转换成邻域内不同等值面的形态一致的边界指示数组;结合改进的自组织算法和相关三维数据的插值函数,达到生成四面体网格的目的。实验对比表明,该方法能够生成更高比例的优质四面体,同时很好地保证了边界的一致。在对封闭的三维表面网格进行有限元建模时,本文算法为其提供了一种有效、可靠的途径。     

扫掠法有限元网格生成方法

为了提高有限元网格的生成质量,扫掠法生成六面体网格过程中内部节点定位成为关键一步,在研究复杂扫掠体六面体有限元网格生成算法过程中,提出了一种基于扫掠法的六面体网格生成算法,算法利用源曲面已经划分好的网格和连接曲面的结构化网格,用仿射映射逐层投影,生成目标曲面,提出基于Roca算法的内部节点定位的新算法,运用由外向内推进的波前法思想,生成全部的六面体网格。通过实例表明,该算法快速,稳定,可靠,可处理大量复杂2.5维实体六面体网格生成问题。     

支持裂纹扩展的三维有限元网格生成算法

描述了任意形状三维区域的非结构四面体网格生成算法,该算法对不含裂纹的区域、含单裂纹或多裂纹的区域都适用。算法首先使用八叉树来确定网格单元大小,然后采用前沿推进技术来生成网格。在前沿推进过程中,采用基于几何形状和基于拓扑结构的两个步骤来保证前沿向前移动过程中发生问题时仍能进行正确执行,并且使用了一种局部网格优化方法来提高网格划分的质量。最后,将算法运用到带有裂纹的复杂实体模型,实验结果表明该算法具有较强的适用性和较高的性能。     

改进波前法初始布点的高质量CVT网格生成

利用改进波前法(AFT)生成网格初始布点和Voronoi质心块(CVT)网格优化技术,在任意平面域获得了几乎是等边三角形的高质量非结构化网格.该算法在边界网格的基础上将离散边界作为初始波前,通过规范边长将网格单元分为合格与不合格单元,在不合格单元侧根据网格尺寸函数的要求构造新的最优点集,并过滤后进行Delaunay插入.利用CVT技术进一步调整网格节点位置,结合局部边交换,获得了网格几何平均质量在0.985以上的几乎是等边三角形的高质量网格.     

基于黎曼度量的复杂参数曲面有限元网格生成方法

给出了三维空间的黎曼度量和曲面自身的黎曼度量相结合的三维复杂参数曲面自适应网格生成的改进波前推进算法.详细阐述了曲面参数域上任意一点的黎曼度量的计算和插值方法;采用可细化的栅格作为背景网格,在降低了程序实现的难度的同时提高了网格生成的速度;提出按层推进和按最短边推进相结合的方法,在保证边界网格质量的同时,提高曲面内部网格的质量.三维自适应黎曼度量的引入,提高了算法剖分复杂曲面的自适应性.算例表明,该算法对复杂曲面能够生成高质量的网格,而且整个算法具有很好的时间特性和可靠性.     

基于八叉树的三维地质剖面生成算法

针对目前构建三维地质剖面算法复杂度高、效率低的问题,提出一种基于八叉树的三维地质剖面生成算法。利用八叉树算法对传统的地质剖面生成算法进行改进,使算法在搜索过程中的时间复杂度降低至O(log8(n/M)),在算法中加入轮廓边约束,对搜索到的边进行预处理,以保证边的正确性和有序性。采用八叉树为复杂三维地质体网格模型内的三角形创建空间索引,通过八叉树快速查找出经过剖面的三角形,计算交点并追踪出轮廓边界,通过画廊看守算法对追踪出的边界三角化并构建三维剖面。实验结果表明,该算法具有复杂度低、鲁棒性强的特点,与传统的地质剖面生成算法相比,时间复杂度由O(n2)降低到O(nlbn)。     

基于STEP的三维表面有限元网格生成技术的研究*

研究了三维表面有限元网格自动生成的技术,利用映射法实现了模型表面的三角网格剖分。基于STEP文件格式的模型的导入和重建,将模型的每个表面映射至参数空间,利用推进波前法生成参数面网格,然后映射回三维表面。研制了一套网格剖分策略,运用该策略对多种类型表面进行了分析求解。     

二维有限元网格自动自适应生成

为使有限元法能更有效地应用于日益复杂的科学和工程计算,提出一种自动自适应网格生成方法．该方法在结合推进波前法和法向偏移法的优势的基础上产生,改进了节点的生成方式,融入了简单灵活的密度控制方式和合理准确的边界离散方式．剖分实例显示,该方法能有效地生成高质量网格,自动化程度高,适应能力强;它已成功地应用于复杂海域下波浪与结构物相互作用的有限元计算,并取得了很好的效果．     

一个高效可靠的三维AFT四面体网格生成算法

针对三维推进波前算法(AFT-Advancing Front Technique)存在的效率与收敛性问题,文中提出了一整套改进方案,给出了基于拓扑连接的网格数据结构和基于Hash表的网格元素的插入、查找、删除算法,提高了整个算法的效率.通过在网格生成过程中动态维护前沿的尺寸信息,提高四面体单元的整体质量.在内核回退求解时通过引入前沿优先因子,改变前沿推进的路径,大大增加了回退求解的成功概率;对于极少数不能回退求解的内核采用基于线性规划的插点方法加以解决,这样就基本保证了整个算法的收敛.在网格生成以后,通过删除不必要的内部节点、合并相关四面体单元以及对所有内部节点进行基于角度的优化,从而进一步有效提高了网格质量.数值算例表明,文中提出的改进算法具有接近线性的时间复杂度,生成网格质量好.该算法已经得到工程应用.     

Reliable Whisker Weaving via Curve Contraction

Whisker Weaving is an advancing front algorithm for all-hexahedral mesh generation. It uses global information derived from grouping the mesh dual into surfaces, the STC, to construct the connectivity of the mesh, then positions the nodes afterwards. Currently, we are able to reliably generate hexahedral meshes for complicated geometries and surface meshes. However, the surface mesh must be modified locally. Also, in large, highly-unstructured meshes, there are usually isolated regions where hex quality is poor. Reliability has been achieved by using new, provable curvecontraction algorithms to sequence the advancing front process. We have also demonstrated that sheet moving can remove certain types of invalid connectivity.     

Anisotropic quadrilateral mesh generation: An indirect approach

In this paper a new indirect approach is presented for anisotropic quadrilateral mesh generation based on discrete surfaces. The ability to generate grids automatically had a pervasive influence on many application areas in particularly in the field of Computational Fluid Dynamics. In spite of considerable advances in automatic grid generation there is still potential for better performance and higher element quality. The aim is to generate meshes with less elements which fit some anisotropy criterion to satisfy numerical accuracy while reducing processing times remarkably. The generation of high quality volume meshes using an advancing front algorithm relies heavily on a well designed surface mesh. For this reason this paper presents a new technique for the generation of high quality surface meshes containing a significantly reduced number of elements. This is achieved by creating quadrilateral meshes that include anisotropic elements along a source of anisotropy.     

All-hexahedral mesh generation via inside-out advancing front based on harmonic fields

The generation of hexahedral meshes is an open problem that has undergone significant research. This paper deals with a novel inside-out advancing front method to generate unstructured all-hexahedral meshes for given volumes. Two orthogonal harmonic fields, principal and radial harmonic fields, are generated to guide the inside-out advancing front process based on a few user interactions. Starting from an initial hexahedral mesh inside the given volume, we advance the boundary quadrilateral mesh along the streamlines of radial field and construct layers of hexahedral elements. To ensure high quality and uniform size of the hexahedral mesh, quadrilateral elements are decomposed in such a way that no non-hexahedral element is produced. For complex volume with branch structures, we segment the complex volume into simple sub-volumes that are suitable for our method. Experimental results show that our method generates high quality all-hexahedral meshes for the given volumes.     

An Algorithm for Three-Dimensional Mesh Generation for Arbitrary Regions with Cracks

An algorithm for generating unstructured tetrahedral meshes of arbitrarily shaped three-dimensional regions is described. The algorithm works for regions without cracks, as well as for regions with one or multiple cracks. The algorithm incorporates aspects of well known meshing procedures, but includes some original steps. It uses an advancing front technique, along with an octree to develop local guidelines for the size of generated elements. The advancing front technique is based on a standard procedure found in the literature, with two additional steps to ensure valid volume mesh generation for virtually any domain. The first additional step is related to the generation of elements only considering the topology of the current front, and the second additional step is a back-tracking procedure with face deletion, to ensure that a mesh can be generated even when problems happen during the advance of the front. To improve mesh quality (as far as element shape is concerned), an a posteriori local mesh improvement procedure is used. The performance of the algorithm is evaluated by application to a number of realistically complex, cracked geometries.     

Automatic generation of tetrahedral meshes from medical images

A new tetrahedral meshing algorithm from the series of medical images is proposed. Sectional contours are extracted from medical images, and by the use of correspondence, tiling, and branching process, the side surfaces between sections are triangulated in addition to the triangulation on each section. As for the mesh generation for an object between two sections, an advancing front algorithm is employed to generate tetrahedral elements by using basic operators. Sample meshes are constructed from medical images for finite element analysis of biomechanical models.     

A modified advancing layers mesh generation for thin three-dimensional objects with variable thickness

A method of generating modified advancing layers mesh is proposed. In this paper the mesh generation process of semi-unstructured prismatic/tetrahedral mesh is presented for relatively thin three-dimensional geometries with variable thickness, as in the case of injection molding analysis. Prismatic meshes are generated by offsetting initial surface triangular meshes. During the mesh generation process, mesh quality is efficiently improved with the use of a new node relocation method. Finally, tetrahedral meshes are automatically generated in the rest of the domain. The mesh generating capability of the proposed algorithm is demonstrated with the several practical test cases.