边界面法数值结果的云图表征

边界面法继承了传统边界元法的优点,并将几何实体的边界曲面离散为参数空间里的曲面单元,在处理一些特殊问题如移动边界、高梯度、大变形等方面显示出特殊的优越性。但是也使得计算结果的后处理遇到困难。提出了一种基于黎曼度量推进波前法生成三角背景网格的实用边界面法计算结果后处理方法。该法对求解域剖分成三角背景网格然后将计算结果映射到网格节点上,通过区域填充获得计算结果的云图。温度场的数值算例表明该方法可靠实用。     

三角网格模型上的四边形曲线网生成新方法

四边形网格划分是组合曲面建模技术的首要条件。针对海量流形三角网格数据,提出了基于网格简化技术与调和映射算法的四边形网格生成新方法--映射法。该方法采用基于顶点删除的网格简化技术对三角网格模型进行简化,进而借助调和映射算法将简化网格映射到二维平面上进行四边形划分,并将所获得的平面四边形节点数据逆映射回物理域,采用短程线边界形式最终得到适于组合曲面建模的空间四边形拓扑。该方法简单、实用,运行速度较快,实际的算例也验证了方法的有效性与可行性。     

NURBS曲面的四边形网格的分割与逼近

介绍了一个用于对NURBS曲面进行四边形网格的分割与逼近的算法。该算法采用二叉树递归分割的方法分割和逼近曲面，所分割的四边形除了在高度方向和曲面边界处满足给定精度外，同时在四边形四条边界满足给定的切矢精度。实例测试结果表明，用本文所述算法生成的四边形网格具有网格逼近原曲面、网格四边形接近于规则四边形等特点。     

两自由度空间机器人运动规划方法

采用微分几何中的活动标架方法,对空间机器人进行了建模分析,提出了以黎曼曲面上的测地线为依据进行操作臂与安装基座耦合状态下的空间机器人运动规划的方法。以空间机器人末端运动轨迹弧长作为黎曼度量,并融合系统动量守恒约束条件,建立了具有此种黎曼度量的黎曼曲面上的测地线微分方程,并对微分方程的初始条件进行了分析计算。最后以测地线作为空间机器人轨迹规划的方法,对2自由度机器人的运动规划进行了计算机仿真研究。     

基于三角网格的ternary插值细分法

本文针对规则三角网格,首先提出了一种基于插值√3细分法的ternary插值曲面细分法,极限曲面可达C1连续.为使得细分法生成的曲面形状可调,本文进而研究了带参数的ternary插值曲面细分法的构造问题,分析了细分法的连续性.     

基于三角网格的ternary插值细分法

本文针对规则三角网格,首先提出了一种基于插值3~(1/3)细分法的ternary插值曲面细分法,极限曲面可达C1连续。为使得细分法生成的曲面形状可调,本文进而研究了带参数的ternary插值曲面细分法的构造问题,分析了细分法的连续性。     

任意平面区域的变密度四边形网格生成方法

：基于三角形网格的合并方法,首先生成光滑过渡的变密度三角形网格,然后进行三角形的合并,接着将合并后残留的三角形细分成三个较小的四边形,相应把合并生成的四边形进一步细分成四个较小的四边形,最终生成了光滑过渡的四边形网格。     

多裁剪曲面的三角划分算法

提出一种新的多裁剪曲面三角划分的方法。把裁剪曲面展开,得到曲面的平面展开图。在平面展开图内进行三角划分,把三角形上点的拓扑关系映射到裁剪曲面,生成三角网格。由于平面展开图上两点的欧氏距离接近这两点在裁剪曲面上的测地距离,所以生成的三角网格保持了平面展开图中三角形的形态,解决了在参数域内进行三角划分所产生的狭长三角形的问题。此外,还提出了一种对带孔的平面散乱点进行三角划分的办法,有效的防止了划分网格出现裂缝和覆盖等现象。     

船体曲面柔性敷设块的展开

以船体外表面敷设矩形柔性块的三维仿真设计为背景,在四边形网格等面积曲面展开法的基础上进行了扩充,修正了该算法展开轴对角线上存在的不合理拉伸和压缩变形,在MDT平台上研制出一套曲面展开系统。测试表明该系统可适用于可展和其他不可展复杂曲面,包括含有内轮廓的曲面,对可展曲面的展开与数学展开能保持一致,同时可进行曲面局部区域的展开,实现曲面与展开面上任意点之间的相互映射,能较好的应用于矩形块三维仿真设计。     

四边形网格生成的基区拼合法

提出了一种新的四边形有限元网格的生成方法——基区拼合法。在基区划分的基础上,先进行基区内部的网格生成,然后把各个基区缝合起来,形成完整的有限元网格。该方法简单且行之有效,特别适用于解决轮廓形状不太复杂的二维问题。     

An extended advancing front technique for closed surfaces mesh generation

An extended advancing front technique (AFT) with shift operations and Riemann metric named as shifting‐AFT is presented for finite element mesh generation on 3D surfaces, especially 3D closed surfaces. Riemann metric is used to govern the size and shape of the triangles in the parametric space. The shift operators are employed to insert a floating space between real space and parametric space during the 2D parametric space mesh generation. In the previous work of closed surface mesh generation, the virtual boundaries are adopted when mapping the closed surfaces into 2D open parametric domains. However, it may cause the mesh quality‐worsening problem. In order to overcome this problem, the AFT kernel is combined with the shift operator in this paper. The shifting‐AFT can generate high‐quality meshes and guarantee convergence in both open and closed surfaces. For the shifting‐AFT, it is not necessary to introduce virtual boundaries while meshing a closed surface; hence, the boundary discretization procedure is largely simplified, and moreover, better‐shaped triangles will be generated because there are no additional interior constraints yielded by virtual boundaries. Comparing with direct methods, the shifting‐AFT avoids costly and unstable 3D geometrical computations in the real space. Some examples presented in this paper have demonstrated the advantages of shift‐AFT in 3D surface mesh generation, especially for the closed surfaces. Copyright © 2007 John Wiley & Sons, Ltd.     

Automatic generation of anisotropic quadrilateral meshes on three‐dimensional surfaces using metric specifications

A new algorithm for constructing full quadrilateral anisotropic meshes on 3D surfaces is proposed in this paper. The proposed method is based on the advancing front and the systemic merging techniques. Full quadrilateral meshes are constructed by systemically converting triangular elements in the background meshes into quadrilateral elements.By using the metric specifications to describe the element characteristics, the proposed algorithm is applicable to convert both isotropic and anisotropic triangular meshes into full quadrilateral meshes. Special techniques for generating anisotropic quadrilaterals such as new selection criteria of base segment for merging, new approaches for the modifications of the background mesh and construction of quadrilateral elements, are investigated and proposed in this study. Since the final quadrilateral mesh is constructed from a background triangular mesh and the merging procedure is carried out in the parametric space, the mesh generator is robust and no expensive geometrical computation that is commonly associated with direct quadrilateral mesh generation schemes is needed. Copyright © 2002 John Wiley & Sons, Ltd.     

A new finite point generation scheme using metric specifications

A new approach to generate finite point meshes on 2D flat surface and any bi‐variate parametric surfaces is suggested. It can be used to generate boundary‐conforming anisotropic point meshes with node spacing compatible with the metric specifications defined in a background point mesh. In contrast to many automatic mesh generation schemes, the advancing front concept is abandoned in the present method. A few simple basic operations including boundary offsetting, node insertion and node deletion are used instead. The point mesh generation schemeis initialized by a boundary offsetting procedure. The point mesh quality is then improved by node insertion and deletion such that optimally spaced nodes will fill up the entire problem domain. In addition to the point mesh generation scheme, a new way to define the connectivity of a point mesh is also suggested. Furthermore, based on the connectivity information, a new scheme to perform smoothing for a point mesh is proposed toimprove the node spacing quality of the mesh. Timing shows thatdue to the simple node insertion and deletion operations, the generation speed of the new scheme is nearly 10 times faster than a similar advancing front mesh generator. Copyright © 2000 John Wiley & Sons, Ltd.     

An element implementation of the boundary face method for 3D potential problems

This work presents a new implementation of the boundary face method (BFM) with shape functions from surface elements on the geometry directly like the boundary element method (BEM). The conventional BEM uses the standard elements for boundary integration and approximation of the geometry, and thus introduces errors in geometry. In this paper, the BFM is implemented directly based on the boundary representation data structure (B-rep) that is used in most CAD packages for geometry modeling. Each bounding surface of geometry model is represented as parametric form by the geometric map between the parametric space and the physical space. Both boundary integration and variable approximation are performed in the parametric space. The integrand quantities are calculated directly from the faces rather than from elements, and thus no geometric error will be introduced. The approximation scheme in the parametric space based on the surface element is discussed. In order to deal with thin and slender structures, an adaptive integration scheme has been developed. An adaptive method for generating surface elements has also been developed. We have developed an interface between BFM and UG-NX(R). Numerical examples involving complicated geometries have demonstrated that the integration of BFM and UG-NX(R) is successful. Some examples have also revealed that the BFM possesses higher accuracy and is less sensitive to the coarseness of the mesh than the BEM.     

A universal measure of the conformity of a mesh with respect to an anisotropic metric field

In this paper, a method is presented to measure the non‐conformity of a mesh with respect to a size specification map given in the form of a Riemannian metric. The measure evaluates the difference between the metric tensor of a simplex of the mesh and the metric tensor specified on the size specification map. This measure is universal because it is a unique, dimensionless number which characterizes either a single simplex of a mesh or a whole mesh, both in size and in shape, be it isotropic or anisotropic, coarse or fine, in a small or a big domain, in two or three dimensions. This measure is important because it can compare any two meshes in order to determine unequivocally which of them is better. Analytical and numerical examples illustrate the behaviour of this measure. Copyright © 2004 John Wiley & Sons, Ltd.     

Adaptive triangular–quadrilateral mesh generation

In this paper, we begin by recalling an adaptive mesh generation method governed by isotropic and anisotropic discrete metric maps, by means of the generation of a unit mesh with respect to a Riemannian structure. We propose then an automatic triangular to quadrilateral mesh conversion scheme, which generalizes the standard case to the anisotropic context. In addition, we introduce an optimal vertex smoothing procedure. Application test examples, in particular a CFD test, are given to demonstrate the efficiency of the proposed method. © 1998 John Wiley & Sons, Ltd.     

Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 2: Mesh generation algorithm and examples

In this paper, a new metric advancing front surface mesh generation scheme is suggested. This new surface mesh generator is based on a new geometrical model employing the interpolating subdivision surface concept. The target surfaces to be meshed are represented implicitly by interpolating subdivision surfaces which allow the presence of various sharp and discontinuous features in the underlying geometrical model. While the main generation steps of the new generator are based on a robust metric surface triangulation kernel developed previously, a number of specially designed algorithms are developed in order to combine the existing metric advancing front algorithm with the new geometrical model. As a result, the application areas of the new mesh generator are largely extended and can be used to handle problems involving extensive changes in domain geometry. Numerical experience indicates that, by using the proposed mesh generation scheme, high quality surface meshes with rapid varying element size and anisotropic characteristics can be generated in a short time by using a low‐end PC. Finally, by using the pseudo‐curvature element‐size controlling metric to impose the curvature element‐size requirement in an implicit manner, the new mesh generation procedure can also generate finite element meshes with high fidelity to approximate the target surfaces accurately. Copyright © 2003 John Wiley & Sons, Ltd.     

On curvature element‐size control in metric surface mesh generation

A new procedure is suggested for controlling the element‐size distribution of surface meshes during automatic adaptive surface mesh generation. In order to ensure that the geometry of the surface can be accurately captured, the curvature properties of the surface are first analysed. Based on the principal curvatures and principal directions of the surface, the curvature element‐size requirement is defined in the form of a metric tensor field. This element‐size controlling metric tensor field, which can either be isotopic or anisotopic depending on the user requirement, is then employed to control the element size distribution during mesh generation. The suggested procedure is local, adaptive and can be easily used with many parametric surface mesh generators. As the proposed scheme defines the curvature element‐size requirement in an implicit manner, it can be combined with any other user defined element size specification using the standard metric intersection procedure. This eventually leads to a simple implementation procedure and a high computational efficiency. Numerical examples indicate that the new procedure can effectively control the element size of surfacemeshes in the cost of very little additional computational effort. Copyright © 2001 John Wiley & Sons, Ltd.     

基于参变量变分原理的三维Cosserat体模型弹塑性分析与应变局部化模拟

基于参变量变分原理,该文发展了三维Cosserat连续体模型弹塑性有限元分析的二次规划算法。由于Cosserat连续体模型的本构方程中存在材料内尺度参数,该模型可以解决经典连续介质理论在分析应变软化问题时病态的有限元网格依赖性问题。数值结果表明所发展的三维Cosserat连续介质弹塑性有限元模型可以有效的模拟应变局部化现象并且该算法具有很好的数值稳定性,同时获得的数值结果具有良好的非网格依赖性。