具有抛物线边界的各向异性体的二维变形问题

文章通过Lekhnitskii方法及映射函数法系统地研究了具有抛物线边界的各向异性体的二维变形问题,并利用所获得的结果研究了一种特殊的结构--半无限裂纹问题,求得了裂纹尖端的应力奇异场及应力强度因子。     

各向异性板半无限裂纹平面问题的保角变换解法

本文给出了各向异性板半无限裂纹平面问题的保角变换解.首先,简单介绍了各向异性板平面问题的基本理论.随后采用复变函数的方法,通过引用适当的保角映射研究了各向异性板半无限裂纹平面弹性问题,得到了各向异性板中半无限裂纹在任意面内集中载荷作用下的裂纹尖端的应力强度因子的解析解.最后,作为特例得到了当集中力作用在裂纹表面时的应力强度因子的解析解,依此验证了结果的正确性.结果表明该方法简单实用.     

半无限及含孔无限平面在各种边界条件下的复位势基本解*

运用Riemann-Schwarz对称原理和线弹性力学解的叠加原理建立了半无限平面及含孔无限平面在各种边界条件下基本解的一般求解方法,并分别导出边界上受不同荷载以及边界固定等各种边界条件下的复位势基本解。     

点群6一维六方准晶椭圆孔口与半无限裂纹反平面弹性问题的解析解

导出了点群6-维六方准晶反平面弹性问题的控制方程.利用复变方法,给出了点群6-维六方准晶在周期平面内的反平面弹性问题的应力分量以及边界条件的复变表示,通过引入适当的保角变换,研究了点群6-维六方准晶中带有椭圆孔口与半无限裂纹的反平面弹性问题,得到了椭圆孔口问题应力场的解析解,给出了半无限裂纹问题在裂纹尖端处的应力强度因子的解析解.在极限情形下,椭圆孔口转化为Griffith裂纹,并得到该裂纹在裂尖处的应力强度因子的解析解.当点群6-维六方准晶体的对称性增加时,其椭圆孔口与半无限裂纹的反平面弹性问题的解退化为点群6mm-维六方准晶带有椭圆孔口与半无限裂纹的反平面弹性问题的解。     

单裂纹问题的虚边界无网格伽辽金法分析

使用含裂纹复变基本解,虚边界无网格伽辽金法被进一步推广应用于弹性材料的单裂纹问题求解.为了清晰地说明单裂纹问题的虚边界元法实现过程,单裂纹问题的虚边界元法示意图、复变坐标平面下含裂纹问题的复变位移和复变面力基本解示意图被展示.含裂纹复变基本解,因自动满足裂纹处边界条件,故使用虚边界无网格伽辽金法计算单裂纹问题,无需在裂纹处布置节点或单元.给出含裂纹复变基本解中的Φ'(x)的详细表达式、裂纹左右裂尖应力强度因子的虚边界无网格离散公式,方便了其他学者使用本方法计算裂纹问题.数值计算两端受拉长方形钢板中心含有裂纹的应力强度因子的算例,计算结果证明了本方法的精确性与稳定性.     

用“调和函数”表示的压电介质平面问题的通解

本文首先从压电介质平面问题基本方程出发，引入一个位移函数，导出其通解，然后利用推广的Almansi定理，将通解化为简单形式，即通过三个“调和函数”来表示所有的物理量，其次，推导了楔形体顶端受集中力和点电荷作用时有限形式的解，退化可得半无限平面直线边界受集中力和点电荷的解。     

裂纹问题的非局部弹性力学分析

求解并给出非局部弹性力学平面问题的单位集中不连续位移基本解,基于这些基本解和经典弹性力学中的不连续位移边界积分方程＿边界元方法,提出了一种非局部弹性力学平面问题的一般解法·利用该解法,研究分析了Ｇｒｉｆｉｔｈ裂纹、边缘裂纹等断裂力学中基本的但又很重要的问题·结果表明,裂纹前沿的应力集中系数与裂纹长度有关,给出了裂纹长度对断裂韧性ＫⅠｃ的影响·所得结果与已有实验结果一致·     

具有两种流体的轴对称渗流的一个自由边界问题

本文处理带有两种流体的轴对称的一个自由边界问题，其中在渗流区域的上部都是油，下部是水，这是同时取油注水的一个数学模型。下面，我们将用复分析方法求出此自由边界问题的一个解，并证明其解的唯一性。     

一维正方准晶中半无限裂纹问题的解析解

运用广义复变函数方法,通过构造适当的广义保角映射,研究了含有沿准周期方向穿透的半无限裂纹的一维正方准晶的反平面弹性问题,给出了在部分裂纹面上受均匀面外剪切时应力场和裂纹尖端应力强度因子的解析解.将此方法进一步推广到半无限裂纹垂直于一维正方准晶的准周期方向穿透的情形中,得到了相应的平面弹性问题的解析解.当准晶体的对称性增加时,还可以得出一维四方准晶相应问题的解析解.     

含椭圆孔或裂纹压电介质平面问题的基本解

应用复变函数的方法，并基于精确的电边界条件，导出了含一椭圆孔或裂纹的横观各向同性压电体在任意集中力和集中电荷作用下的复变函数解，即Ｃｒｅｎ函数解·叠加该解，得到了裂纹表面作用任意集中载荷或分布载荷时的一般解·这些解不但澄清了从前文献中一些不合理的结果，同时也为应用边界元法求解更复杂的压电介质断裂力学问题提供了基本解·     

Boundary collocation method for a cracked rectangular plate with double external tension

In this article, the boundary collocation method is employed to investigate the problems of a central crack in a rectangular plate which applied double external tension on the outer boundary under the assumption that the dimensions of the plate are much larger than that of the crack. A set of stress functions has also been proposed based on the theoretical analysis which satisfies the condition that there is no external force on the crack surfaces. It is only necessary to consider the condition on the external boundary. Using boundary collocation method, the linear algebra equations at collocation points are obtained. The least squares method is used to obtain the solution of the equations, so that the unknown coefficients can be obtained. According to the expression of the stress intensity factor at crack tip, we can obtain the numerical results of stress intensity factor. Numerical experiments show that the results coincide with the exact solution of the infinite plate. In particular, this case of the double external tension applied on the outer boundary is seldom studied by boundary collocation method.     

Stressed State of a Magnetically Soft Ferromagnetic Material with a Parabolic Crack Acted on by a Uniform Magnetic Field

The stressed-deformed state of an unbounded isotropic body consisting of a magnetically soft ferromagnetic material and containing a parabolic crack is examined. It is assumed that the body is acted on by an external magnetic field perpendicular to the plane of the crack. The major characteristics of the stressed-deformed state and the induced magnetic field are determined and their features near the parabolic crack are studied. Formulas are given for determining the stress intensity factors for the mechanical force and magnetic fields at the crack vertex.     

集中力作用下的半平面边缘裂纹问题

讨论了半平面中的倾斜裂纹问题。集中力作用于裂纹表面上,或作用于开裂半平面的边界上。利用有理保角映像函数方法求解这个问题,同时得到了闭合形式的解。最后,给出了二个数值例子和计算结果。     

Stress intensity factors for a finite plate with an inclined crack by boundary collocation

In this paper, we combine the Muskhelishvili＇s complex variable method and boundary collocation method, and choose a set of new stress function based on the stress boundary condition of crack surface, the higher precision and less computation are reached. This method is applied to calculating the stress intensity factor for a finite plate with an inclined crack. The influence of θ （the obliquity of crack） on the stress intensity factors, as well as the number of summation terms on the stress intensity factor are studied and graphically represented.     

Semilinear parabolic problems in thin domains with a highly oscillatory boundary

In this paper, we study the behavior of the solutions of nonlinear parabolic problems posed in a domain that degenerates into a line segment (thin domain) which has an oscillating boundary. We combine methods from linear homogenization theory for reticulated structures and from the theory on nonlinear dynamics of dissipative systems to obtain the limit problem for the elliptic and parabolic problems and analyze the convergence properties of the solutions and attractors of the evolutionary equations.     

Spannungsfeld der auf den Rand einer elastisch anisotropen Halbebene wirkenden Tangentialkraft

Summary The stress distribution obtained by solving the two-dimensional problem in an anisotropic medium, with boundary conditions of a concentrated tangential load acting on the boundary of a semi-infinite plate, is purely radial. The solution is given in closed form and is combined with the solution for a concentrated normal load to solve the problem of an inclined force acting on the boundary.     

关于非局部场论的几个新观点及其在断裂力学中的应用(Ⅰ)──基本理论部分

在线性非局部弹性理论中,具有均匀常应力边界的裂纹混合边界值问题的解是不存在的.本文从非局部场论的基本理论出发针对这一问题进行了研究.内容包括:对非局部能量守恒定律的客观性的考察,非局部热弹性体本构方程的推导,非局部体力的确定以及线性化理论,得到了一些新结果.其中,在线性化理论中所推出的应力边界条件不仅解决了本摘要开头所提到的问题,而且自然地包括了Barenblatt裂纹尖端的分子内聚力模型.     

An inverse problem for a parabolic equation in a free-boundary domain degenerating at the initial time moment

We consider an inverse problem for a one-dimensional parabolic equation with unknown time-dependent major coefficient in a domain whose unknown boundary weakly degenerates at the initial time moment. The conditions for existence and uniqueness of the classical solution of the problem are established.