有限元网格划分及发展趋势

总结近十年有限元网格划分技术发展状况。首先,研究和分析有限元网格划分的基本原则;其次,对当前典型网格划分方法进行科学地分类,结合实例,系统地分析各种网格划分方法的机理、特点及其适用范围,如映射法、基于栅格法、节点连元法、拓扑分解法、几何分解法和扫描法等;再次,阐述当前网格划分的研究热点,综述六面体网格和曲面网格划分技术;最后,展望有限元网格划分的发展趋势。     

全四边形有限元网格的拓扑优化策略

基于有限元网格的局部拓扑结构,给出一些非结构化全四边形有限元网格的拓扑优化策略,这些策略被组织成"型-操作"的形式.型是指一类满足一定约束条件的局部区域网格,而操作则是指与特定型相对应的拓扑变换,它能优化局部网格中节点的度值,从而优化局部网格质量.这些策略可分成针对网格内部单元和针对网格边界单元2类.实验结果表明,这些策略能较好地改善四边形网格的质量.     

一种新的六面体有限元网格算法

在有限元网格产生过程中，吸取弦须编织法中的STC概念，将六面体以节点剖分为基础的思想转变为以单元点为基础，建立了以单元生长为核心的剖分算法，以期解决节点拓扑结构在三维情况下的控制问题，对进一步实现稳定、全自动的六面体剖分具有很大的帮助。     

基于简化和细分技术的三角形网格拓扑优化方法

由于采用自动生成技术得到的网格往往不能满足数值模拟和仿真的要求,为此基于网格简化和细分技术,提出一种简单、高效的三角形网格拓扑优化方法.首先根据边折叠简化算法对三角形网格进行简化,得到具有较好拓扑连接关系的粗网格;然后对简化后的粗网格进行细分,引入具有良好节点度的新节点;最后再进行简化,直到网格的节点数达到给定的阈值.实验结果表明,该方法可以很好地改善网格的拓扑连接关系,与网格修匀技术结合能够大幅度提高网格的质量.     

适应于体绘制技术的三维有限元网格剖分

有限元分析结果的体绘制为有限元分析提供了直观、有效的方法，但有限元网格在几何上的复杂性以及拓扑上的非结构化给值接利用传统的绘制技术带来困难，这篇文章首先给出了将三维有限元网格剖分成四面体网格的方法，然后，为了便于体绘制，将网格进一步剖分成不包含空洞的凸网的集合，剖分过程用ＢＳＰ树表示，以便实现任意有限元网格的深度排序，而ＢＳＰ树的结点数不超过网格相邻边界面之间二面角小于１８０℃的角的总数，同时给出     

分段光滑曲面重构的面片图稀疏优化方法

针对离散点云拓扑关系恢复及特征提取困难的问题,提出了一种健壮有效的分段光滑曲面重构方法。获得由基函数集定义的局部曲面面片图,建立尖锐特征节点的拓扑连接,通过求解一个稀疏优化问题,获得每个节点基函数的最优系数,并输出清洁的流形网格曲面。实例证明,该算法实用性好,对分段光滑曲面重构效果理想。     

平面任意区域四边形网格自动生成的一种方法

在改进节点连接法的基础上，提出了一种平面任意区域的有限元网格全自动剖分方法，既能快速生成四边形单元网格，也能生成三角形单元网格；     

纯虚拓扑理论与建模方法

为了将复杂的B-rep模型有效地转换成可供有限元分析的壳网格,提出一种基于纯虚拓扑的建模方法.首先使用合并、分割、插入和收缩4种基本算子将B-rep模型转换成纯虚拓扑模型;之后利用基于约束列表的网格优化算法将纯虚拓扑模型自动划分成较为均匀的网格.实验结果表明,该方法可以快速、鲁棒地生成实际复杂模型的壳网格,网格质量均匀、有效,从而为后续有限元求解分析提供了良好的基础.     

基于剪挖操作的三角形网格自动生成

本文在系统比较了现有的几种主要有限元网格自动生成算法，即映射法、Ｄｅｌａｕｎａｙ方法、推进网阵法的基础上，给出了基于剪挖操作的直接网格自动生成算法。此算法具有全自动生成的特点，无需象Ｄｅｌａｕｎａｙ方法那样先配置内部节点，也无需象映射法那样经过复杂的数学变换。灵活性与可靠性都明显优于它们。剪挖顺序基于优先级，本文还给出了具体的基于权平均的优先级函数。本网格自动生成方法是我们注塑成型ＣＡＥ／ＣＡＤ软件ＷＰ－Ｆｌｏｗ的一部分，它同推进网阵方法组成了ＷＰ－Ｆｌｏｗ的两种主要网格自动生成算法。     

二阶多面体网格中关键特征控制的表面重建技术

针对基于二阶多节点多面体网格的表面重建过程中存在的准确拓扑及绘制、传输代价等问题,提出了一种基于关键特征控制的表面重建技术.研究并分析了二阶多节点多面体单元等参插值函数的性质特征,在网格单元棱边插值计算曲面轮廓点,在网格表面及体内提取曲面的几何特征关键点;根据3类插值关键点间的逻辑关系制定了令拓扑准确唯一的面片三角化规则及修复策略,设计了基于关键点的三角面片压缩索引结构.实验结果表明,该方法可准确计算并描述基于二阶多节点多面体网格单元的曲面几何拓扑结构,反映网格单元内部面片的真实凹凸性质,克服了拓扑二义性,具备对不同精度要求的适应性,并有效降低了绘制与传输代价.     

A new scheme for mesh generation and mesh refinement using graph theory

There are an extensive number of algorithms available from graph theory, some of which, for problems with geometric content, make graphs an attractive framework in which to model an object from its geometry to its discretization into a finite element mesh. This paper presents a new scheme for finite element mesh generation and mesh refinement using concepts from graph theory. This new technique, which is suitable for an interactive graphical environment, can also be used efficiently for fully automatic remeshing in association with self-adaptive schemes. Problems of mesh refinement around holes and local mesh refinement are treated. The suitability of the algorithms presented in this paper is demonstrated by some examples.     

三维实体仿真建模的网格自动生成方法

有限元网格模型的生成与几何拓扑特征和力学特性有直接关系。建立网格模型时，为了更真实地反映原几何形体的特征，在小特征尺寸或曲率较大等局部区域网格应加密剖分；为提高有限元分析精度和效率，在待分析的开口、裂纹、几何突变、外载、约束等具有应力集中力学特性的局部区域，网格应加密剖分。为此，该文提出了基于几何特征和物理特性相结合的网格自动生成方法。该方法既能有效地描述几何形体，又能实现应力集中区域的网格局部加密及粗细网格的均匀过渡。实例表明本方法实用性强、效果良好。     

改进遗传算法的ERT有限元网格节点编号优化

在电阻层析成像中,有限元网格节点编号对整体刚度矩阵的带宽具有重要决定性的作用,而整体刚度矩阵的带宽直接决定了数据的存储量以及求解方程组的计算量。为了提高电阻层析成像中有限元的计算效率,减少数据存储量,利用改进遗传算法,对电阻层析成像中两种典型拓扑结构的有限元模型节点编号进行优化。实验结果表明,与常用节点编号规则相比,利用改进遗传算法可得到更优的带宽值,从而节省了计算机的内存空间,提高了计算效率。     

Topological improvement procedures for quadrilateral finite element meshes

This paper presents a set of procedures for improving the topology of unstructured quadrilateral finite element meshes. These procedures are based on the topology of the finite element mesh, and all operations act only on local regions of the mesh. The goal is to optimize the topology such that the smoothing process can produce the best possible element quality. Topological improvement procedures are presented both for elements that are interior to the mesh and for elements connected to the boundary. Also presented is a discussion of efficiency and optimal ordering of the procedures. Several example meshes are included to show the effectiveness of the current approach in improving element qualities in a finite element mesh.     

Massively parallel adaptive mesh refinement and coarsening for dynamic fracture simulations

We use the graphical processing unit (GPU) to perform dynamic fracture simulation using adaptively refined and coarsened finite elements and the inter-element cohesive zone model. Due to the limited memory available on the GPU, we created a specialized data structure for efficient representation of the evolving mesh given. To achieve maximum efficiency, we perform finite element calculation on a nodal basis (i.e., by launching one thread per node and collecting contributions from neighboring elements) rather than by launching threads per element, which requires expensive graph coloring schemes to avoid concurrency issues. These developments made possible the parallel adaptive mesh refinement and coarsening schemes to systematically change the topology of the mesh. We investigate aspects of the parallel implementation through microbranching examples, which has been explored experimentally and numerically in the literature. First, we use a reduced-scale version of the experimental specimen to demonstrate the impact of variation in floating point operations on the final fracture pattern. Interestingly, the parallel approach adds some randomness into the finite element simulation on the structured mesh in a similar way as would be expected from a random mesh. Next, we take advantage of the speedup of the implementation over a similar serial implementation to simulate a specimen whose size matches that of the actual experiment. At this scale, we are able to make more direct comparisons to the original experiment and find excellent agreement with those results.     

Automating the Finite Element Method

The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations. However, the generality of the framework provided by the finite element method is seldom reflected in implementations (realizations), which are often specialized and can handle only a small set of variational problems and finite elements (but are typically parametrized over the choice of mesh). This paper reviews ongoing research in the direction of a complete automation of the finite element method. In particular, this work discusses algorithms for the efficient and automatic computation of a system of discrete equations from a given variational problem, finite element and mesh. It is demonstrated that by automatically generating and compiling efficient low-level code, it is possible to parametrize a finite element code over variational problem and finite element in addition to the mesh.     

Finite element simulation of stretch forging using a mesh condensation method

In order to reduce the computation time of finite element simulations of stretch forging process,a mesh condensation method is presented and applied to a three-dimensional rigid-viscoplastic finite element program.In this method,a conventional mesh for the whole zone of a workpiece is condensed to a computational mesh for the active deformation zone.Two vital problems are solved,which are automatic construction of the computational mesh and treatment of interfaces between the deformation zone and the rigid ...     

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。     

Automatic Delaunay mesh generation method and physically-based mesh optimization method on two-dimensional regions

Delaunay mesh generation method is a common method for unstructured mesh (or unstructured grid) generation. Delaunay mesh generation method can conveniently add new points to the existing mesh without remeshing the whole domain. However, the quality of the generated mesh is not high enough if compared with some mesh generation methods. To obtain high-quality mesh, this paper developed an automatic Delaunay mesh generation method and a physically-based mesh optimization method on two-dimensional regions. For the Delaunay mesh generation method, boundary-conforming problem was ensured by create nodes at centroid of mesh elements. The definition of node bubbles and element bubbles was provided to control local mesh coarseness and fineness automatically. For the physically-based mesh optimization method, the positions of boundary node bubbles are predefined, the positions of interior node bubbles are adjusted according to interbubble forces. Size of interior node bubbles is further adjusted according to the size of adjacent node bubbles. Several examples show that high-quality meshes are obtained after mesh optimization.