An Extension of the Two-Dimensional JKR Theory to the Case with a Large Contact Width

In the Hertz and JKR theories, parabolic assumptions for the rounded profiles of the sphere or cylinder are adopted under the condition that the contact radius （width） should be very small compared to the radius of the sphere or
cylinder. However, a large contact radius （width） is often found in experiments even under a zero external loading. We aim at extending the plane strain JKR theory to the case with a large contact width. The relation between the external loading and the contact width is given. Solutions for the Hertz, JKR and rounded-profile cases are compared and analyzed. It is found that when the ratio of a/R is approximately larger than about 0.4, the parabolic assumptions in the Hertz and JKR theories are no longer valid and the exact rounded profile function should be used.     

从高分子运动的温度依赖关系看高分子运动特点

高分子的运动是高分子科学中最为基本、最为重要的问题之一,也是教学的重点之一,它是联系高分子微观结构与高聚物宏观性能之间的桥梁,本文就高分子运动的特点尤其是高分子运动的温度依赖关系进行了讨论,进而从本质上理解高聚物结构与性能之间的关系.     

FATIGUE GROWTH MODELING OF MIXED-MODE CRACK IN PLANE ELASTIC MEDIA

This paper presents an extension of a displacement discontinuity method with cracktip elements （a boundary element method） proposed by the author for fatigue crack growth analysis in plane elastic media under mixed-mode conditions. The boundary element method consists of the non-singular displacement discontinuity elements presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or right crack-tip element is placed locally at the corresponding left or right crack tip on top of the non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the maximum circumferential stress criterion. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the numerical approach. Crack growth is modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characteristics of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the fatigue growth process of cracks emanating from a circular hole in a plane elastic plate is simulated using the numerical simulation approach.     

求解变系数线性对流扩散方程的AGE方法

1、引言 对流扩散方程是描述粘性流体运动的非线性方程的线性化模型方程,而且它本身也描述了许多自然现象,例如在水中或大气中污染物质浓度的扩散,沿海盐度,温度扩散等等．因此求解对流扩散方程的计算方法特别是并行解法引起了充分的重视。     

用矩阵的秩判断两空间直线及直线与平面的位置关系

空间两直线的位置关系可分为两大类:异面、共面;在同一平面内又分为:平行、相交和重合;直线与平面相对位置可分为:平面与直线平行、直线与平面相交、直线在平面上。这里介绍用矩阵的秩来判断两空间直线及直线与平面的位置关系。引理1非齐次线性方程组a11x1+a12x2+…+a1nxn=b1,a21x1+a22x2+…+a2nxn=b2,………………am1x1+am2x2+…+amnxn=bm,有解的充要条件是:系数矩阵A与增广矩阵B的秩RA=RB;且RA=RB=n时有唯一解。引理2设向量βi=(Ai,Bi,Ci)(i=1,2,3),则(β1×β2)·β3=A1B1C1A2B2C2A3B3C3=0三向量共面。定理1设两空间直线L1∶A1…     

利用特征根研究二次曲面的切平面问题

利用特征根研究二次曲面的切平面问题,给出了平面为二次曲面的切平面的充要条件.     

双目遥感凝视系统中运动小目标的快速自动检测

从双目遥感凝视系统的视场重叠区进入系统的信息量大于通过非重叠区的信息量,根据这一特征建立了一种新的运动小目标双目并行快速实时自动检测算法。首先采用差分向量无穷范数算法对原始图像序列做预处理,去掉大量低频噪音和背景,然后采用光流场法对运动小目标进行分割,最后用所提出的空间时间并行快速判定算法对分割的可疑运动小目标进行判定。实验结果表明:由于识别判定算法的空间时间是并行处理的,所以识别判定的平均速度比单目视觉系统提高了50%;在图像信噪比不小于5dB的情况下,准确判定识别的概率为97%。     

地球表面水平运动物体偏转推演及判断

本依据科氏力原理,利用数学矢量公式推断地球表面水平运动物体的偏转方向,并依据其对地球表面出现的系列现象给予物理意义上的解释,使得传统的地表水平运动物体偏转方向的判断进一步规范化。     

求空间点到直线距离的一种方法--谈平面束的应用

根据点到直线的距离即为点到过直线的平面束距离的最大值,将空间点线距离转化为点面距离,然后求其最大值。     

矩量法研究平面波导点缺陷引起的散射损耗

对平面波导工艺过程里出现的点缺陷,如气泡、灰尘颗粒等对平面波导内光场造成的散射提供了一种简单而又实用的计算方法。计算基于格林函数方法,并利用矩量法求解积分方程,采用分块矩阵优化算法,使得算法的计算时间直接与点缺陷大小相关,提高了效率。证明了一定大小的点缺陷在特定的波长处会产生很大的散射损耗,证明点缺陷的散射损耗依赖于缺陷大小和光学性质而与其在波导中的位置无直接关系。以二氧化硅平面波导为例,分析了对中心波长1．55μm的入射光场,分别存在气泡和灰尘颗粒两种点缺陷时,散射损耗随点缺陷大小的关系特性,指出工艺过程特别应该避免某些孔径的点缺陷。