非均匀双周期裂纹场的反平面问题

本文从虎克定律与平衡方程出发,利用复变函数映象的理论.将裂纹发生的矩形区域保角变换到ζ平面的上半平面去.再根据H.И.穆斯黑里什维利[1]的理论,对非均匀双周期裂纹场的反平面问题,我们求得闭合解,并推出了应力强度因子.     

非均匀半平面问题的弹性力学解

本文使用非均匀平面弹性力学的基本方程,通过富氏积分变换,求得了应力函数通解。在此基础上对弹性模量E(x)=E_oexp[βx]为指数型的非均匀半平面问题,具体求得了当边界上受任意载荷作用的精确解。最后经退化处理,还得到了有名的Boussnesq解,这说明本文的方法是成功的。     

平面各向异性弹性介质的周期裂纹问题

§1 导引 关于平面各向异性介质的非周期裂纹问题,H. Lieabwitz, G. C. Sih等曾经有过研究,以及W. T. Koiter,路见可等曾研究过平面各向高性介质的周期裂纹问题。本文,旨在讨论平面各向异性介质在平面对称载荷情况下的周期裂纹问题,此时平面各向异性介质被无限个同在一直线上按周期分布的裂纹所削弱,如图1所示。我们得到了封闭形式的解答     

非均匀调和函数的两类边值问题与积分表达式

本文给出非均匀指数函数的定义及性质,并且进一步引入了非均匀三角函数、非均匀双曲函数和非均匀对数函数.最后利用非均匀指数函数表达形式和非均匀解析函数的Cauchy积分理论,建立了非均匀泊松积分公式和非均匀施瓦茨积分公式,获得了非均匀调和函数在两类特殊边界上的狄利克雷问题和诺伊曼问题解的显示表达式.     

不均匀等分平面坐标系

<正>在学习函数时,首先要学到自变量和函数用平面坐标系表示,一般平面直角坐标系横坐标轴为x轴,纵坐标轴为y轴.平面直角坐标系的坐标轴上均匀等分单位为1.平面极坐标系中极轴和极角都均匀等分,极轴均匀等分单位长度为1,极角均匀等分单位角度为1°.坐标轴上数值均匀等分特点是能够准确表达两个     

一维六方准晶非周期平面内中心开口裂纹的平面热弹性问题

考虑裂纹内部介质的热传导率,研究了一维六方准晶非周期平面内含中心开口裂纹的平面热弹性问题.利用Fourier积分变换技术,得到了热应力、裂纹尖端处的热应力强度因子和应变能密度因子的封闭解.数值结果讨论了裂纹内部介质的热传导率、外载荷及声子场-相位子场耦合系数对热应力强度因子和应变能密度因子的影响.结果表明,声子场-相位子场耦合系数对裂纹扩展影响较大.当声子场载荷较小或热流密度较大时,裂纹不易扩展,热流密度在裂纹尖端处会出现集中热效应.随着裂纹内部介质热传导率的增大,热流密度逐渐增加而热应力强度因子逐渐减小.该文所得结果为准晶热力学性质的实际应用提供了理论依据,进而可用于优化准晶元器件的设计和制备.     

关于带缺陷和裂纹的半无限平面加筋结构的应力强度因子的计算

本文研究两种不同材料、不同厚度、各带裂纹和椭圆孔的半无限平面加筋结构受均匀拉伸的问题.采用复变函数、振动法以幂级数形式给出裂纹尖端应力强度因子的计算公式.本文的实际计算扩充了“应力强度因子手册”中的结果,本文的特例,计算结果与[1]、[3]一致.     

平面应力裂纹问题的高阶渐近场

本文对平面应力I型裂纹问题高阶渐近场,进行了严格的数学分析.证实了二阶渐近场不是含有独立常数的高阶本征场,而必须与一阶渐近场的弹性应变项相匹配.二阶渐近场对裂纹前方的应力场的影响很小.裂纹前方应力场由HRR奇性场表征,因而J积分单参数准则可以作为平面应力问题的起裂准则.     

非均匀网格定位模型

在正方形网格钻井布局模型的基础上 ,讨论了非均匀网格定位模型 .一般情形可用穷举法求解最优化问题来解决定位问题 .本文给出了一种更为有效的定位方法     

穿越各向同性不均匀等离子体层的电磁波的传播

本文以飞行器再入大气层后的通信障碍为背景,考虑了两个问题:一、平面波入射到非均匀等离子体平面层上时的反射系数与传输系数,其中等离子体层的电子密度分布取非对称的双指数分布与正态分布;二、圆柱飞行器上开槽天线辐射的电磁波穿越径向非均匀等离子体鞘的远场方向图.文中给出了反射系数及传输系数的显式表示及若干以图或表格表示的数值结果.     

On Inhomogeneous GBBM Equations

In this paper we consider the Cauchy problem and the initial boundary value (IBV) problem for the inhomogeneous GBBM equations. For any bounded or unbounded smooth domain, the existence and uniqueness of global strong solution for the Cauchy problem and IBV problem for the inhomogeneous GBBM equations in W^{2,p}(Ω) are established by using Banach fixed point theorem and some a priori estimates. These results have improved the known results even in the case of GBBM equation. Meanwhile, we also discuss the regularity of the Strong solution and the system of inhomogeneous GBBM equations.     

Inhomogeneous Cauchy-Riemann equation in Octonion space

The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representationAs an application, the Cousin problem analogue of Mittag-Laffler problem is discussed.     

Scattering by an Inhomogeneous Medium

A method is given for constructing the total field resultingfrom a plane wave scattered by an inhomogeneous medium withcompact support. The problem is reformulated as a Fredholm integralequation of the second kind, whose solutions may be representedas a convergent Neumann series, for small values of the wavenumber. A truncation error estimate of this series is given.To illustrate the method, examples of both a sphere and a prolatespheroid filled with an inhomogeneous medium are considered.In both cases the scattering amplitude is investigated as afunction of the wave number. A comparison is made between themethod presented here for finding the total field and Rorres'method (1970).     

Inhomogeneous diophantine approximation with prime constraints

We study the problem of inhomogeneous diophantine approximation under certain primality restrictions.     

On Finite Element Methods for Inhomogeneous Dielectric Waveguides

We investigate the problem of computing electromagnetic guided waves in a closed,inhomogeneous, pillared three-dimensional waveguide at a given frequency. The problem is formulated as a generalized eigenvalue problem. By modifying the sesquilinear form associated with the eigenvalue problem, we provide a new convergence analysis for the finite element approximations. Numerical results are reported to illustrate the performance of the method.     

Many-Dimensional Zaremba Problem for an Inhomogeneous p-Laplace Equation

Doklady Mathematics - Higher integrability of the gradient of the solution to the Zaremba problem in a bounded Lipschitz many-dimensional domain for an inhomogeneous p-Laplace equation is proved.     

一类具有非齐次项对称双曲系统整体弱解的存在性

研究一类具有非齐次项的对称双曲系统Cauchy问题,用补偿紧性方法和最大值原理,得到其有界弱解的整体存在性结果.这一结果推广文献[7]中对称双曲系统到非齐次对称双曲系统.这样一类问题产生于弹性理论、磁流体动力学和石油再开采领域中,具有一定理论和应用价值.     

Equilibrium State of Inhomogeneous Plasma

We consider the problem of a self-consistent determination of an essentially inhomogeneous equilibrium state of classical plasma. The solutions of the stationary Vlasov–Poisson equations are constructed in the form of a localized transition layer that separates the domains of homogeneous plasmas with different equilibrium parameters. The layer can also transform into a local perturbation inside a homogeneous plasma. In both cases, the solution contains neither mass currents nor electric currents, and all electrodynamic and hydrodynamic quantities and their derivatives are continuous. The parameters of the adjacent domains uniquely determine the transition layer structure.     

Path Collapse for an Inhomogeneous Random Walk

On an open interval we follow the paths of a Brownian motion which returns to a fixed point as soon as it reaches the boundary and restarts afresh indefinitely. We determine that two paths starting at different points either cannot collapse or they do so almost surely. The problem can be modelled as a spatially inhomogeneous random walk on a group and contrasts sharply with the higher dimensional case in that if two paths may collapse they do so almost surely.     

对波动方程初边值问题边界条件齐次化函数的一个注解

基于传统的齐次化边界条件方法,采用傅里叶级数法讨论了波动方程初边值问题第一类非齐次边界条件齐次化函数问题,分析表明:对同一定解问题,在不同齐次化函数下的解在适定意义下是等价的.