关于任意边界缺口或裂纹群的一类解法——(Ⅳ)深度缺口或裂纹群的计算*

本文是欧阳鬯所作文[1]研究任意边界缺口或裂纹群问题的一类解法的继续(亦见[2]、[3])。这里我们利用该文作出的基本方法,进一步发展了关于边界深度裂纹或缺陷群问题的计算方法。数值计算实例表明,本文所给出的方法是行之有效的。本文结果拓充了“应力强度因子手册”的工作。     

关于任意边界缺口或裂纹群问题的一类解法——(Ⅲ)边界裂纹群的计算*

本文是文献[1]、[2]关于任意边界缺口或裂纹群问题的一类解法研究的继续。这里我们利用和发展了文献[1]、[2]所提出的理论和计算公式,对边界裂纹群问题进行了实际计算.数值计算实例表明:本文所给出的方法在特征参数适当的范围内是行之有效的.本文的结果扩充了“应力强度因子手册”中的工作.     

关于任意边界缺口或裂纹群问题的一类解法——(Ⅱ)缺口群的计算

本文是欧阳鬯所作文“关于任意边界缺口或裂纹群问题的一类解法(I)解析方法”的继续。这里我们利用该文提出的理论和公式对缺口群问题进行了实际计算。在计算中对该文陈述的参数平面上边界条件计算方法作了改动。数值计算实例表明:在所研究的特征参数,例如本文中的L,的适当范围内,所叙述的方法是行之有效的。     

弹性波在平面多连通域中的绕射与动应力集中

本文用复变函数论方法研究了弹性波在平面多连通域中的绕射问题,给出了这一问题解的完备逼近序列及边备条件的一般表示。问题归结为无穷代数方程组的求解,使用电子计算机可直接求得解答。特别是,对弱耦合问题,本文提出了渐近求解方法并且使用这个方法详细地讨论了P波对圆孔群的绕射问题。基于绕射波场的解,文中给出了任意形状空腔动应力集中系数的一般算式。     

具有周期直线裂纹的无限各向异性弹性平面的平衡问题

对于被周期直线裂纹所削弱,且裂纹上所承受的载荷关于裂纹对称或斜对称的无限各向异性平面的弹性平衡问题,在蔡海涛的文[1][2]中已得到了封闭形式的解答。本文讨论裂纹上具有任意载荷的一般情况,也得到了封闭形式的解答,并指出[1][2]的结果是本文的特例。     

任意形状孔口单边裂纹问题的边界配位解法

本文提出了一组复应力函数,采用边界配位方法对不同形状孔口(包括圆、椭圆、矩形及菱形孔口)的单边裂纹平板的应力强度因子进行了计算.计算结果表明,对长度和宽度远大于孔口和裂纹几何尺寸的试件,配位法与用其他方法所得的无限大板含圆或椭圆孔边裂纹问题的解符合得很好.同时,对其他孔口问题,特别是有限大板情形,本文给出了一系列计算结果.本文所提出的函数及计算过程可以应用于任意形状孔口单边裂纹平板的计算.     

椭圆孔边裂纹对SH波的散射及其动应力强度因子

采用复变函数和Green函数方法求解具有任意有限长度的椭圆孔边上的径向裂纹对SH波的散射和裂纹尖端处的动应力强度因子．取含有半椭圆缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时的位移解作为Green函数,采用裂纹“切割”方法,并根据连续条件建立起问题的定解积分方程,得到动应力强度因子的封闭解答．讨论了孔洞的存在对动应力强度因子的影响．     

含曲线裂纹复合圆柱体的扭转断裂分析

研究含任意曲线裂纹的复合圆柱体的Saint-Venant扭转,将内外材料的交界面视为一边界,将问题划归为内、外边界和裂纹上的积分方程的求解.提出了新的边界元数值方法,分别对含有直线裂纹和曲折裂纹的典型问题进行了数值计算,并与文献中数据结果进行了比较,证明了该文方法的正确性和有效性.     

无限大板包含任意排列多个椭圆孔洞的应力集中和多裂纹的应力强度因子计算

对于无限平面上任意排列的多个椭圆孔的应力集中,采用复变函数方法,直接构造能够反映各孔相互影响的应力函数,通过依次映射方法来满足各孔的边界条件,再利用围线积分方法化为线性代数方程求解.对于裂纹情况,将裂纹化为相应的椭圆,通过应力集中系数近似求得应力强度因子值.文中给出若干计算结果.     

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·     

Crack plane identification in anisotropic linear elastic material using the reciprocity principle

Nondestructive test methods are important for examination of elastic devices regarding existence, position and size of cracks. In the case of hidden cracks (which do not touch the boundary), a simple visual control is not sufficient. The basic idea of this paper is to examine appropriate boundary measurements under certain loads. We focus on a method presented by ANDRIEUX, BEN ABDA and BUI [1] for isotropic linear elasticity, and generalize the crack plane detection to anisotropic linear elastic material. The main idea is the use of the reciprocity principle in order to connect data from the outer boundary with the unknown crack properties. Some 2D numerical examples demonstrate, that the method is working with simulated data. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of the Factorization Method to Recover Cuts with Oblique Derivative Boundary Condition

Direct and inverse problems for the scattering of cracks with mixed oblique derivative boundary conditions from the incident plane wave are considered, which describe the scattering phenomenons such as the scattering of tidal waves by spits or reefs. The solvability of the direct scattering problem is proven by using the boundary integral equation method. In order to show the equivalent boundary integral system is Fredholm of index zero, some relationships concerning the tangential potential operator is used. Due to the mixed oblique derivative boundary conditions, we cannot employ the factorization method in a usual manner to reconstruct the cracks. An alternative technique is used in the theoretical analysis such that the far field operator can be factorized in an appropriate form and fulfills the range identity theorem. Finally, we present some numerical examples to demonstrate the feasibility and effectiveness of the factorization method.     

含曲线裂纹圆柱扭转问题的新边界元法

研究含曲线裂纹圆柱的Saint-Venant扭转,将问题化归为裂纹上边界积分方程的求解．利用裂纹尖端的奇异元和线性元插值模型,给出了扭转刚度和应力强度因子的边界元计算公式．对圆弧裂纹、曲折裂纹以及直线裂纹的典型问题进行了数值计算,并与用Gauss-Chebyshev求积法计算的直裂纹情形结果进行了比较,证明了方法的有效性和正确性．     

On inverse crack problems in elastostatics

In solid mechanics, nondestructive testing has been an important technique in gathering information about unknown cracks, or defects in material. From a mathematical point of view, this is described as an inverse problem of partial differential equations, that is, the problem is to extract information about the location and shape of an unknown crack from the surface displacement field and traction on the boundary of the elastic material. By using the enclosure method introduced by Prof. Ikehata we can derive the extraction formula of an unknown linear crack from a single set of measured boundary data. Then, we need to have precise properties of a solution of the corresponding boundary value problem; for instance, an expansion formula around the crack tip. In this paper we consider the inverse problem concentrating on this point. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gradient type noises II - Systems of stochastic partial differential equations

The present paper is the second and main part of a study of partial differential equations under the influence of noisy perturbations. Existence and uniqueness of function solutions in the mild sense are obtained for a class of deterministic linear and semilinear parabolic boundary initial value problems. If the noise data are random, the results may be seen as a pathwise approach to SPDE's. For typical examples, such as spatially one-dimensional stochastic heat equations with additive or multiplicative perturbations of fractional Brownian type, we recover and extend known results. In addition, we propose to consider partial noises of low order.     

A BALANCED OVERSAMPLING FINITE ELEMENT METHOD FOR ELLIPTIC PROBLEMS WITH OBSERVATIONAL BOUNDARY DATA

In this paper we propose a finite element method for solving elliptic equations with observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier and requires balanced oversampling of the measurements of the boundary data to control the random noises. We show the convergence of the random finite element error in expectation and, when the noise is sub-Gaussian, in the Orlicz $\psi_2$-norm which implies the probability that the finite element error estimates are violated decays exponentially. Numerical examples are included.     

On the determination of stress concentration in a stretched plate with two holes

We present a short survey of studies of the elastic interaction of two holes in a stretched plate. Special attention is paid to the study of the concentration of stresses on the contours of closely positioned holes. For two identical elliptic holes, numerical results are obtained by the method of singular integral equations. With the help of the limit transition, we determined the stress intensity factors at the vertices of semi-infinite parabolic notches. A comparison of the numerical data with known analytic solutions for two circular holes and collinear cracks is performed.     

Reconstruction of cracks of different types from far‐field measurements

In this paper, we deal with the acoustic inverse scattering problem for reconstructing cracks of possibly different types from the far‐field map. The scattering problem models the diffraction of waves by thin two‐sided cylindrical screens. The cracks are characterized by their shapes, the type of boundary conditions and the boundary coefficients (surface impedance). We give explicit formulas of the indicator function of the probe method, which can be used to reconstruct the shape of the cracks, distinguish their types of boundary conditions, the two faces of each of them and reconstruct the possible material coefficients on them by using the far‐field map. To test the validity of these formulas, we present some numerical implementations for a single crack, which show the efficiency of the proposed method for suitably distributed surface impedances. The difficulties for numerically recovering the properties of the crack in the concave side as well as near the tips are presented and some explanations are given. Copyright © 2009 John Wiley & Sons, Ltd.