椭圆环壳在一般荷载下的轴对称问题

本文给出了在任意分布荷载下轴对称椭圓环壳的简化复变量方程。该方程准确度在薄壳理论误差范围内,并消除了全部经线极值奇点。得到了问题的等价的积分方程组,用数值积分方法给出了数值解。计算了膨胀节、液压圆环壳和半椭圆形密封环的算例,与准确解和实验结果作了比较。     

旋转壳的一般轴对称问题及积分方程分析*

本文得到了旋转弹性薄壳在一般荷载下轴对称问题的一种简化形式的复变量方程,该方程准确度在薄壳理论误差范围,并消除了经线极值奇点;给出了问题的Voltera积分方程表述及其数值解.     

变壁厚轴对称圆环壳的复变量方程及其一般解

本文导出了变壁厚轴对称圆环壳的复变量方程,并给出了它的一般解.     

一般旋转壳在轴对称变形下的复变量方程

本文在Love-Kirchhoff的假定下,求得了一般旋转壳在轴对称变形下的复变量方程.当旋转壳是圆截面环壳时,这些方程简化为F.Tölke(1938)[3],R.A.Clark(1950)和B.B.Новожилов(1951)[3]的方程.当平均半径R比环截面半径a大得很多时,求得了细环壳的复变量方程,当这个细环壳的截面是圆形时,简化作为作者(1979)[6]的圆截面的细环壳复变量方程,我们列出了椭圆截面的细环壳复变量方程.当椭圆截面近似于圆截面时,该方程在形式上和圆细环壳方程基本相同.     

正交异性悬臂柱壳轴对称问题的弱形式解

导出层合柱壳轴对称问题的平衡方程和边界条件的弱形式,提供了方程和边界条件放在一起的算子形式,建立了悬臂柱壳轴对称问题的热应力混合方程,给出了正交异性层合悬臂柱壳在热荷载和机械荷载作用下的弱形式解。本文提出的方法弱化了求解方程和边界条件,化解了问题,具有一般性并便于推广。     

轴对称圆环壳的一般解

本文是前文[1]的推广,它不限于细环壳a=a/R<<1的假定,其中a为环壳的截面半径,R为环壳的总体半径.提出了轴对称圆环壳在0≤a<1范围内的一般解,本文的解可以用来解决波纹壳、热膨胀器、高压容器的过渡部分和波登管等实用问题.本文的结果是前人从未求得的圆环壳的一般解.     

摄动有限元法解一般轴对称壳几何非线性问题

本文在处理几何非线性问题时,利用在变分方程中引入振动过程,得到各级变分摄动方程,并通过有限元法求解.由于有限元法能成功地处理各种复杂边界条件、几何形状的力学问题,摄动法又可将非线性问题转化为线性问题求解.若结合这两种方法的优点,将能够解决大量复杂的非线性力学问题.并能够消除单独使用有限元法或摄动法求解复杂非线性问题所出现的困难. 本文应用摄动有限元法求解了一般轴对称壳的几何非线性问题.     

圆柱壳的轴对称平面应变弹性动力学解

给出一种圆柱壳的轴对称平面应变弹性动力学问题的解析方法。首先通过引入一特定函数将非齐次边界条件化为齐次边界条件,然后利用分离变量法将位移减去特定函数的量展开为关于贝塞尔函数和时间函数乘积的级数,并由贝塞尔函数的正交性,导出时间函数的方程,容易求得此方程的解。将两者叠加可得弹性动力学问题的位移解。运用此方法,可以避免积分变换,并适宜于各种载荷。文中给出了各向同性和柱面各向同性圆柱壳内表面和实心圆柱外表面受冲击荷载作用以及内表面固定的柱面各向同性圆柱壳外表面受冲击荷载作用的数值结果。     

中心集中载荷作用下圆底扁球壳的轴对称非线性弯曲和稳定性

本文研究圆底扁薄球壳在中心集中载荷作用下的轴对称非线性弯曲和稳定性,利用Newton-样条函数方法(简称NS方法)求解了圆底扁球壳非线性方程,获得了问题的屈曲前和屈曲后解答,并将所得结果与前人的理论和实验结果进行了比较。     

U型波纹壳轴对称大挠度非线性变形问题(Ⅰ)——计及圆环壳的非线性变形、压缩角

本文是文献[1、2]工作的继续,在以下方面作了发展:考虑了内、外圆环壳中面法线的中小转动变形(转角的平方与应变是同阶小量);计及了压缩角.计算结果与实验符合良好.本文方法对波纹壳的设计计算有实用价值,有关压缩角对特征关系影响的讨论有助于工程设计.     

球壳中球形夹杂对SH波的三维散射与动应力集中

研究了一般情况下球壳中球形夹杂（包括孔洞）引起的SH波三维散射与动应力集中现象.根据球壳与夹杂的几何特点,分别以球壳和夹杂中心建立球坐标,用于描述球壳中的入射波、散射波和夹杂中的驻波势函数,并采用球波函数的加法公式,实现了不同坐标下球波函数的变换,推导出位移、应力分量的解析解.结合球壳的边界条件和夹杂界面的连续条件,求解了不同材料属性夹杂,以及空洞情况下弹性波的散射和动应力集中因子分布情况,并分析了频率以及夹杂中心位置对动应力集中因子的影响.文中的研究为球壳结构的力学性能分析以及无损检测提供了理论支持.     

The one-sided kissing number in four dimensions

Summary Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"10"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"11"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"12"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"13"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>H$ be a closed half-space of $n$-dimensional Euclidean space. Suppose $S$ is a unit sphere in $H$ that touches the supporting hyperplane of $H$. The one-sided kissing number $B(n)$ is the maximal number of unit nonoverlapping spheres in $H$ that can touch $S$. Clearly, $B(2)=4$. It was proved that $B(3)=9$. Recently, K. Bezdek proved that $B(4)=18$ or 19, and conjectured that $B(4)=18$. We present a proof of this conjecture.     

圆底扁球壳非线性稳定问题的自由参数摄动法解

用自由参数摄动法求解了圆底扁球壳在均布载荷作用下的非线性稳定问题．作为一种改进的正则摄动方法,使研究者可以不确定摄动参数具体意义而直接求得问题的全部特征方程．通过算例研究了扁球壳在失稳过程中变形和应力的变化特点,并与其他研究者的结果进行了比较．     

Über Die Enge Von Kugelpackungen und Dicke Von Punktsystemen im Sphärischen Raum

It is given a lower bound for the closeness of packings of balls (Theorem 1) and an upper bound for thickness of point sets (Theorem 2) in d-dimensional spherical space. The bounds are improved for d = 2 (Theorem 3, 4).     

扁球壳和扁锥壳的轴对称非线性热弹耦合振动

假设温度场与应变场相互耦合,研究了旋转扁薄球壳和锥壳的轴对称非线性热弹振动问题．基于von Krmn理论和热弹性理论,导出了本问题的全部控制方程及其简化形式．应用Galerkin技术进行时空变量分离后,得到了一个关于时间的非线性常微分方程组．根据方程的特点,分别用多尺度法和正则摄动法求得了壳体振动的频率与振幅间特征关系和振幅衰减规律的一次近似解析解,并讨论了壳体几何参数、热弹耦合参数以及边界条件等因素对其非线性热弹耦合振动特性的影响．     

Extremal Polygons with Minimal Perimeter

In this paper we will investigate an isoperimetric type problem in lattices. If K is a bounded O-symmetric (centrally symmetric with respect to the origin) convex body in En of volume v(K) = 2n det L which does not contain non-zero lattice points in its interior, we say that K is extremal with respect to the given lattice L. There are two variations of the isoperimetric problem for this class of polyhedra. The first one is: Which bodies have minimal surface area in the class of extremal bodies for a fixed n-dimensional lattice? And the second one is: Which bodies have minimal surface area in the class of extremal bodies with volume 1 of dimension n? We characterize the solutions of these two problems in the plane. There is a consequence of these results, the solutions of the above problems in the plane give the solution of the lattice-like covering problem: Determine those centrally symmetric convex bodies whose translated copies (with respect to a fixed lattice L) cover the space and have minimal surface area.

     

Polynomial interpolation on the unit sphere II

The problem of interpolation at (n+1)² points on the unit sphere by spherical polynomials of degree at most n is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials. Dedicated to Mariano Gasca on the occasion of his 60th birthday The second author was supported by the Graduate Program Applied Algorithmic Mathematics of the Munich University of Technology. The work of the third author was supported in part by the National Science Foundation under Grant DMS-0201669.     

Universally optimal distribution of points on spheres

We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are distances between distinct points in it and it is a spherical -design. We prove that every sharp configuration minimizes potential energy for all completely monotonic potential functions. Examples include the minimal vectors of the and Leech lattices. We also prove the same result for the vertices of the -cell, which do not form a sharp configuration. For most known cases, we prove that they are the unique global minima for energy, as long as the potential function is strictly completely monotonic. For certain potential functions, some of these configurations were previously analyzed by Yudin, Kolushov, and Andreev; we build on their techniques. We also generalize our results to other compact two-point homogeneous spaces, and we conclude with an extension to Euclidean space.

     

应用虚拟功的互等定理求解均载悬臂厚矩形板的弯曲

悬臂矩形板的弯曲问题一直是平板经典理论中的著名难题,利用中厚板虚拟功的互等定理,借助付宝连提出的角点静力边界条件,得到了均布载荷作用下悬臂厚矩形板弯曲的封闭解析解,并采用现代数值方法和计算软件对所得解析解进行了数值计算.结果表明功的互等法是求解中厚板弯曲问题的一个简明有效的方法.