三维弹性问题高次有限元方程的代数多层网格法

有限元法是数值求解三维弹性问题的一类重要的离散化方法,高次有限元又是其中的一类常用有限元。由于高次元对问题具有更好的逼近效果及具有某些特殊的优点,如能解决弹性问题的闭锁现象(Poisson’s ratio locking),使得它们在实际计算中被广泛使用。但与线性元相比,它具有更高的计算复杂性。通过分析高次有限元空间与线性有限元空间之间的关系,提出了一种求解三维弹性问题高次有限元方程的两水平方法,然后,通过调用现有的代数多层网格法求解粗水平方程,建立了求解高次有限元方程的AMG法。数值实验表明,本文设计的AMG法对求解三维弹性问题高次有限元方程具有很好的计算效率和鲁棒性。     

约束数据域Delaunay四面体网格生成算法

提出了一种快速Delaunay四面体网格生成的分治算法,将给定约束数据域边界进行Delaunay三角剖分,然后从边界三角形开始递归生成四面体网格．该算法在约束数据域内部生成Delaunay四面体,边界三角形都将成为内部四面体的面,不需要进行边界一致性检查,可避免四面体穿过边界和狭长四面体的产生,而且算法容易理解方便编程．     

Zwei Kennzeichnungen der Hillschen Tetraeder

For a geometric approach to volume such d-simplices are of special interest which are equidissctable with a d-cube. Hill-simplices are in this sense rectifiable. Two new characterizations of Hill-simplices are given in three-dimensional case, using a canonical dissection of simplices and an equidissection of prisms. Received 16 August 1999; revised 10 August 2000.     

三维问题的一类对称有限体格式的构造

针对三维Poison问题,在四面体网格剖分下,利用线性有限元空间,并选取“vertex—centred”型控制体,从而构造了一类保对称的有限体格式,数值实验表明其误差的模达到了饱和阶,同时也表明了该格式对非一致网格有好的收敛精度和稳定性,由于格式对称,相应离散系统可采用PCG等方法快速求解,从而提高了运算效率。     

Crystal Structure and Antitumor Activity of Tri[2- [N-(4''''-methyl-benzylsulfonyl)amino]ethyl]-amine

1 INTRODUCTION The supramolecular architectures of tripodal ligands with special cavities have attracted much attention of chemists and biochemists because of their interesting structures and possible properties such as ion and molecular recognition, selective inclusion and important biological function[1～5]. However, their potential applications in supra- molecular and biological chemistry for constructing various complexes have not been clearly realized until recent years. Few crystal…     

Electric Field Induced Changes of Spin Lattice Relaxation Time T1 in Polar Liquids

T ₁ was found to change linearly with applied electric field for the liquids nitrobenzene, chlorobenzene, ether and dioxane: no change was observed in hexane and cyclohexane. These substantial reductions in T ₁ are explained in terms of quasi-crystalline structures in the liquid.     

二元碱金属硅酸盐精细结构和拉曼光谱的从头计算研究

应用量子化学从头计算方法研究了二元碱金属硅酸盐的精细结构,对典型的系列二元碱金属硅酸盐离子簇模型采用6-31G(d)基组和闭壳层Hartree-Fock(RHF)方法优化构型,并计算了二元碱金属硅酸盐的拉曼光谱,采用硅氧四面体应力指数这一精细结构参数分析和讨论了计算得到的非桥氧高频区对称伸缩振动频率和其拉曼光学活性,以及不同阳离子对该拉曼光学活性的影响。研究表明,二元碱金属硅酸盐非桥氧高频区对称伸缩振动频率与其精细结构密切相关,而且与Q₃相连的Q₄会对该Q₃的拉曼光学活性表现出增强作用。这说明二元碱金属硅酸盐的拉曼散射等性质主要依赖于其精细结构而非其初级结构单元-硅氧四面体。研究还表明,半径较大的阳离子有利于增强离子簇的拉曼光学活性,但对于小的离子簇,过多的电荷迁移反而会起到抑制作用。     

一类由正四面体和正八面体组成的共轭套中心构型

A new case configuration in R3,the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed.If the configuration is a central configuration,then all masses of outside layer are equivalent,the masses of inside layer are also equivalent.At the same time the following relation between p(r=√3/3ρ is the radius ratio of the sizes)and mass ratio r=～m/m must be satisfied r=-m/m=ρ(ρ+3)(3+2ρ+ρ2)-3/2+ρ(-ρ+3)(3-2ρ+ρ2)-3/2-4.2-3/2ρ-2-4-1ρ-2/2(1+ρ)(3+2ρ+ρ2)-3/2+2(ρ-1)(3-2ρ+ρ2)-3/2-4(2√2)-3ρ,and for any mass ratio T,when mass ratio T is in the open interval(0,0.03871633950…),there exist three central configuration solutions(the initial configuration conditions who imply hamagraphic solutions)corresponding radius ratios are r1,r2,and r3,two of them in the interval(2.639300779…,+∞)and one is in the interval(0.7379549890…,1.490942703…).when mass ratio T is in the open interval(130.8164950…,+∞),in the same way there have three corresponding radius ratios,two of them in the interval(0,0.4211584789…)and one is in the interval(0.7379549890…,1.490942703…).When mass ratio T is in the open interval(0.03871633950…,130.8164950…),there has only one solution T in the interval (0.7379549890…,1.490942703…).     

用逐点插入法生成Delaunay四面体自适应网格

介绍一种基于Delaunay算法的四面体自适应网格的自动划分方法。该方法用单元尺度场控制生成网格的疏密分布,在不满足尺度场要求的单元面形心处插入新节点,同时计算新节点单元尺寸参数,实现三维实体的Delaunay四面体自动划分。此方法具有几个特点:一是表面网格与体内网格同步划分,无需区分两者;二是结点与单元同时生成;三是生成网格自适应性好,疏密分布任意。另外,还介绍了三维网格划分中两个相关算法:一个是约束面恢复算法,该算法基于约束面不允许有单元边与之相交的性质而提出的;另一个是将二维射线法推广至三维空间,判断一个点是否在一多面体内,实现了凹多面体的划分。最后通过算例对单元质量进行了评价。本文所述方法是一种有效的四面体自适应单元生成算法。     

四面体的十二点二次曲面

垂心四面体中四条高的垂足,四个面的重心及从各顶点与四面体的垂心连线的三等分点,共十二个点共球.试图把垂心改为四面体内的任意点,相应地把四条高线改换为过该点与每个顶点连线的共点直线组时,则将把垂心四面体的十二点球有趣地推广为四面体的十二点二次曲面.