面向四面体网格生成的曲面Delaunay三角化算法

提出了一种曲面域Delaunay三角网格的直接构造算法。该算法在曲面网格剖分的边界递归算法和限定Delaunay四面体化算法的基础上,利用曲面采样点集的空间Delaunay四面体网格来辅助曲面三角网格的生成,曲面上的三角网格根据最小空球最小准则由辅助四面体网格中选取,每个三角形都满足三维Delaunay空球准则,网格质量有保证,并且极大的方便了进一步的曲面边界限定下的Delaunay四面体化的进行。     

基于球面三角网格逼近的等距曲面逼近算法

给出了一种基于球面三角网格逼近的等距曲面逼近新算法。利用三角网格逼近基球面,然后计算此三角网格按中心沿在曲面扫凉而成空间区域的边界作为等距曲面的逼近。该算法计算简单,方便地解决了整体误差问题,而且所得到的逼近曲面是与原曲面同次数的NURBS曲面。     

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。     

一种新型球面等积六边形网格系统生成算法

分析了构建球面等积网格系统的基本原理和常用剖分方法的特点,提出了在二十面体展开图上对顶点和面统一编码的研究思路,将两个相邻三角面合并为一个四边形并建立坐标系描述孔径为4的新型递归剖分网格,最后借助施奈德等积多面体投影将平面网格映射到球面,得到了将孔径为4的等积六边形剖分产生的球面网格系统ISEA4H-3.实验结果表明,用这种算法生成的ISEA4H-3网格的几何属性优于现有球面六边形网格,更适用于海量空间信息管理,具有较强的应用价值.     

裁剪曲面的三角化及图形显示

结合自主版权的超人ＣＡＤ／ＣＡＭ系统的开发，本文提出了一种适合于裁剪曲面图形显示的曲面三角化算法，该算法将曲面的三角化转化为曲面参数域的三角化，并将二维图形的集合运算与Ｄｅｌａｕｎａｙ三角剖分应有和于曲面参数域边界的处理，从而使裁剪曲面在边界上的三角形分布均匀。     

正交平面织物球面成型渔网模型的几何分析

为了从理论上表征平面正交织物球面成型后的几何特征, 提出基于坐标变换求解渔网模型的新方法, 确定单层正交平面织物在球面上铺覆成型后的网格位置、 织物剪切变形和纱线弯曲变形。依据弧长不变条件确定方形织物完全包覆球面后的对称面上的网格位置和局部坐标系下中间网格的位置, 利用坐标变换获得中间网格在整体坐标系成型球面上的坐标位置; 根据变形前后的网格形状确定织物面内剪切变形和两个方向纱线的弯曲曲率, 为织物的球面成型性评价提供几何参数。通过实例证明了当网格尺寸远小于球体半径时铺覆变形程度与网格 尺寸无关, 也与球体半径无关。铺覆后织物的剪切变形和纱线弯曲变形分布只与织物在球面上的球坐标位置有关。     

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。     

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。     

基于局部三维Delaunay的插值网格边界增量构造算法

网格构造的质量和效率是插值于大规模测量点三角网格构造算法的关键,但在算法中既保证插值网格的三维Delaunay性质又实现网格的线性构造仍存在困难。笔者针对此问题,提出了基于局部三维Delaunay的插值网格边界增量构造算法,利用网格的局部Delaunay构造及其边界的循环膨胀、分裂及自裁减操作实现整个模型的自动构造。应用实例表明,算法在保证构造网格满足三维Delaunay性质的同时,线性构造任意拓扑结构的三角网格模型。     

颗粒流体系统Euler/Lagrange模型中自适应三角网格的生成

针对二维颗粒流体系统Euler／Lagrange模型的有限元模拟,建立了三角网格生成的自适应算法。该算法能够根据颗粒分布与颗粒大小自适应地调整网格的疏密程度,使其网格密度在系统边界附近及颗粒边缘附近较大,而在其它地方较小。与此同时,网格的光滑化也提高了网格质量, 从而为颗粒流体系统介观尺度的有限元模拟奠定了基础。     

Analyzing static three-dimensional elastic domains with a new infinite boundary element formulation

A new two-dimensionally mapped infinite boundary element (IBE) is presented. The formulation is based on a triangular boundary element (BE) with linear shape functions instead of the quadrilateral IBEs usually found in the literature. The infinite solids analyzed are assumed to be three-dimensional, linear-elastic and isotropic, and Kelvin fundamental solutions are employed. One advantage of the proposed formulation over quadratic or higher order elements is that no additional degrees of freedom are added to the original BE mesh by the presence of the IBEs. Thus, the IBEs allow the mesh to be reduced without compromising the accuracy of the result. Two examples are presented, in which the numerical results show good agreement with authors using quadrilateral IBEs and analytical solutions.     

‘Ultimate’ robustness in meshing an arbitrary polyhedron

Given a boundary surface mesh (a set of triangular facets) of a polyhedron, the problem of deciding whether or not a triangulation exists is reported to be NP‐hard. In this paper, an algorithm to triangulate a general polyhedron is presented which makes use of a classical Delaunay triangulation algorithm, a phase for recovering the missing boundary facets by means of facet partitioning, and a final phase that makes it possible to remove the additional points defined in the previous step. Following this phase, the resulting mesh conforms to the given boundary surface mesh. The proposed method results in a discussion of theoretical interest about existence and complexity issues. In practice, however, the method should provide what we call ‘ultimate’ robustness in mesh generation methods. Copyright © 2003 John Wiley & Sons, Ltd.     

Automatic merging of tetrahedral meshes

A generic algorithm is proposed to merge arbitrary solid tetrahedral meshes automatically into one single valid finite element mesh. The intersection segments in the form of distinct nonoverlapping loops between the boundary surfaces of the given solid objects are determined by the robust neighbor tracing technique. Each intersected triangle on the boundary surface will be triangulated to incorporate the intersection segments onto the boundary surface of the objects. The tetrahedra on the boundary surface associated with the intersected triangular facets are each divided into as many tetrahedra as the number of subtriangles on the triangulated facet. There is a natural partition of the boundary surfaces of the solid objects by the intersection loops into a number of zones. Volumes of intersection can now be identified by collected bounding surfaces from the surface patches of the partition. Whereas mesh compatibility has already been established on the boundary of the solid objects, mesh compatibility has yet to be restored on the bounding surfaces of the regions of intersection. Tetrahedra intersected by the cut surfaces are removed, and new tetrahedra can be generated to fill the volumes bounded by the cut surfaces and the portion of cavity boundary connected to the cut surfaces to restore mesh compatibility at the cut surfaces. Upon restoring compatibility on the bounding surfaces of the regions of intersection, the objects are ready to be merged together as all regions of intersection can be detached freely from the objects. All operations, besides the determination of intersections structurally in the form of loops, are virtually topological, and no parameter and tolerance is needed in the entire merging process. Examples are presented to show the steps and the details of the mesh merging procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

The elastostatic axisymmetric problem of a sphere containing a penny-shaped crack in a nonequatorial plane

The axisymmetric problem of a sphere containing a penny-shaped crack in a nonequitorial plane is solved with the use of Bousinesq stress functions. Two coordinate systems—oblate spheroidal for representing the crack surface and spherical polars for the spherical surface, translated along the z-axis with respect to each other—are used to satisfy boundary conditions. Integral representations and transformations of harmonic functions are used to relate stress functions in the two coordinate systems. This procedure-leads to a system of algebraic equations which is solved, for axisymmetric tractions on both the surfaces. Graphical results are presented for a specific loading case.     

Three-dimensional nonplanar fracture model using the surface integral method

A computer code based on the use of the surface integral method, which represents a crack as a distribution of force dipoles, has been developed for modeling 3D nonplanar fractures. The nonplanar geometry was approximated as piecewise linear by subdividing the fracture surface into triangular elements that assume constant crack opening in the interior, and a p ^1/2 variation of opening along the crack front. The resulting singular integral equations were integrated using a combination of numerical and analytical techniques.Convergence studies using the surface integral formulation have yielded accurate stress intensity factors and crack opening displacements for both planar and nonplanar cracks under a variety of mixed mode loading conditions. Elliptical meshes were mapped on to cylindrical and spherical surfaces to model nonplanar fractures that could be compared to published results. Also, a high aspect ratio rectangular mesh was used to model a nonplanar kinked crack under plane strain conditions.     

A new infinite boundary element formulation combined to an alternative multi-region technique

The main objective of this work is to obtain an efficient three-dimensional boundary element (BE) formulation for the simulation of layered solids. This formulation is obtained by combining an alternative multi-region technique with an infinite boundary element (IBE) formulation. It is demonstrated that such a combination is straightforward and can be easily programmed. Kelvin fundamental solutions are employed, considering the static analysis of isotropic and linear-elastic domains. Establishing relations between the displacement fundamental solutions of the different domains, the alternative technique used in this paper allows analyzing all domains as a single solid, not requiring equilibrium or compatibility equations. It was shown in a previous paper that this approach leads to a smaller system of equations when compared to the usual multi-region technique and the results obtained are more accurate. The two-dimensionally mapped infinite boundary element (IBE) formulation here used is based on a triangular BE with linear shape functions. One advantage of this formulation over quadratic or higher order elements is that no additional degrees of freedom are added to the original BE mesh by the presence of the IBEs. Thus, the IBEs allow the mesh to be reduced without compromising the accuracy of the result. The use of IBEs improves the advantages of the alternative multi-region technique, contributing for the low computational cost and allowing a considerable mesh reduction. Furthermore, the results show good agreement with the ones given in other works, confirming the accuracy of the presented formulation.     

三角网格曲面纹理合成技术研究

纹理合成是真实感图形绘制中重要的技术。对由三角网格组成的曲面模型,提出了一种基于表面三角块矢量场的纹理合成方法。首先用矢量加平滑方法来计算曲面上每个三角块上的纹理方向矢量,并根据这些纹理方向来合成纹理;然后在样本纹理空间按扫描线顺序搜索样本纹理空间,找出最匹配的纹理坐标;算法用队列作为存取结构,并且结果保存在队列中,达到了实时绘制效果。实验结果与理论分析表明,算法纹理合成质量较高,运行结果较好。