带裂纹组合柱的扭转

本文联合使用组合柱体扭转的单层势函数解及均质柱体扭转的单裂纹解,对带有裂纹的组合柱体的扭转作了讨论,最后将问题归结为解一组混合型积分方程,并为其建立了数值方法,对于裂纹与材料分界面接触的情形,本文通过积分方程组的主部分析,精确地求得了奇性指数的特征方程。文中对组合柱的抗扭刚度和裂纱端点的应力强度因子作了数值计算,与文献上已有的结果符合很好。     

含径向裂纹系的圆柱的弯曲与扭转

圆柱中任意径向裂纹系的Saint-Venant弯曲与扭转,还无一般的解析解法,本文采用裂纹面二侧应力差和位移差的混合边界条件提法,在求解了一组三节积分方程和一个Neumann问题后,精确地求得到了单裂纹基本解,利用此解给出了解决这类问题的一般方法。文中对二条非共线的等长边界裂纹的应力强度因子和柱的扭转刚度作了数值计算,扭转刚度的结果与L.A.Wigglesworth的完全一致。     

夹杂和裂纹相互影响时的界面应力分析

本文结合无限域上单根夹杂和单根裂纹的基本解,将裂纹与夹杂相互作用的问题归结为解一组柯西型奇异积分的积分方程组,使问题得到解决。本文还使用夹杂两侧的未知界面应力差,进一步推导了夹杂两侧的界面应力,并做了数值计算。有关这方面的计算可以作为研究与设计纤维与基体的联结强度的工程参考。     

带裂纹圆柱体的Saint-Venant扭转

横截面上带有任意径向裂纹系的圆柱体的Saint-Venant扭转,还无一般的解析解法。本文采用裂纹二侧应力差和位移差的混合边界条件提法,通过Mellin变换,在求解了一组三节积分方程和一个Neumann问题后,精确地求得了单裂纹基本解,利用此解给出了解决这类问题的一般方法。文中还使用奇异积分方程的数值理论,对二条非共线的等长径向裂纹的应力强度因子和抗扭刚度作了数值计算。     

用样条边界元与奇异积分方程法联合求解多裂纹柱体的扭转

通过间解的分离，本文将径向多裂纹柱体的导曲函两个调和函数表示，使问题归为解一组混混合型积分方程。针对方程的特点，本文联合使用三次样条边界法与奇异积分方程的数值方法对所得方程建立了数值法，并对裂纹相交情形作了特殊处理。最后对工程中感兴趣的一些典型的多裂纹柱体的扭转作了例题计算，结果表明，本文方法具有收敛快，精度高的特点。     

线夹杂的力学模型及其界面应力分析

采用材料力学的直杆和梁的变形假定，对平面线夹杂问题提出了一种能同时考虑夹杂两侧法向应力和剪应力间断的新的力学模型，然后通过集中力作用的Ｋｅｌｖｉｎ解答，求得了单夹杂问题的基本解。文中还导出了夹杂两侧的界面应力公式。最后对夹杂端点的应力强度因子及界面应力作了计算，结果令人满意     

弹性功能梯度材料板条中周期裂纹的反平面问题

讨论了弹性功能梯度材料板条中裂纹的反平面问题. 用Fourier 变换方法得到了一个基本解. 这个基本解表示了实轴上一点作用有点位错时引起的影响. 利 用此基本解可得单裂纹和周期裂纹问题的奇异积分方程. 在周期裂纹求解时, 远处裂纹对于中央裂纹的影响作了有效的近似处理. 最后, 给出了数值结果, 它表示了材料性质对于裂纹端应力强度因子的影响.     

线夹杂和线夹杂的相互作用

以短纤维复合材料为工程背景，本文利用线夹杂的工程计算模型以及无限平面中单夹杂的基本解，导出了线夹杂和线夹杂相互作用的平面问题的奇异积分方程。给出了夹杂端点的应力强度因子和夹杂界面应力的表达式，并作了具体的数值计算。     

有限圆板上的径向裂纹系分析

本文在工作和■的复函数法的基础上,对有限圆板上的径向裂纹系作了讨论,得到了单裂纹的基本解,并利用此解给出了解决这类问题的一般方法.为了说明方法的应用,这里使用奇异积分方程的数值解法和Gauss-Chebyshev 求积公式作了例题计算,数值结果绘制了函数图,它们指出了应力强度因子随裂纹几何和作用力变化的关系,这可供工程应用.     

半平面多边缘裂纹反平面问题的奇异积分方程

利用复变函数和奇异积分方程方法,求解弹性范围内半平面多边缘裂纹的反平面问题．提出了满足半平面边界自由的由分布位错密度表示的单边缘裂纹的基本解,此基本解由主要部分和辅助部分组成．将半平面多边缘裂纹问题看作是许多单边缘裂纹问题的叠加,建立了一组Cauchy型奇异积分方程．然后,利用半开型积分法则求解该奇异积分方程,得到了裂纹端处的应力强度因子．最后,给出了几个数值算例．     

SAINT-VENANT’S TORSION PROBLEM FOR A COMPOSITE CIRCULAR CYLINDER WITH ANINTERNAL EDGE CRACK

In this paper the writer uses Muskhelishvili single-layer potential function solutionand single crack solution for the torsion problem of a circular cylinder to discuss thetorsion problem of a composite cylinder with an internal crack,and the problem isreduced to a set of mixed-type integral equation with generalized Cauchy-kernel.Then,by using the integration formula of Gauss-Jacobi.the numerical method isestablished and several numerical examples are calculated.The torsional rigidity andthe stress intensity factors are obtained.The results of these examples fit the resultsobtained by the previous papers better.     

METHOD OF STRONGLY SINGULAR INTEGRAL EQUATION FOR THE TORSION OF CYLINDER WITH EDGE CRACK

From the dislocation type solution of the torsion of single crack,by using the concept of finite part integrals,we reduce the torsion problem of cylinder with a single crack into an integral equation with strong singularity.The numerical method is also obtained and several numerical examples are calculated successfully at the end of this paper.     

Method of strongly singular integral equation for the torision of cylinder with edge crack

From the dislocation type solution of the torsion of single crack, by using the concept of finite part integrals, we reduce the torsion problem of cylinder with a single crack into an integral equation with strong singularity. The numerical method is also obtained and several numerical examples are calculated successfully at the end of this paper. Project supported by P. H. D. Foundation of the State Education Commission of China     

Method to Calculate Bending Center and Stress Intensity Factors of Cracked Cylinder Under Saint-Venant Bending

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Boundary element method to solve torsion problem of cracked cylinder

Separating the discontinuous solution by use of the single crack solution, together with the regular solution of harmonic function, the torsion problem of a cracked cylinder is reduced to solving a set of mixed-type integral equations and its numerical technique is then proposed by combining the numerical method of singular integral equation with the boundary element method. Several numerical examples are calculated which will be useful to engineering practice. The method proposed is characterized by its fine accuracy and convenience for using, which can be extended to the cases of multiple crack.The project supported by National Natural Science Foundation of China.     

Stress intensity factors of the eccentric and edge cracked cylinders

Using the single crack solution and the regular solution of harmonic function,thetorsion problem of a cracked cylinder is reduced to solving a set of mixed-type integralequations which can be solved by combining the numerical method of singular integralequation with the boundary element method.Several numerical examples arecalculated and the stress intensity factors are obtained.     

含圆形嵌体弹性平面中径向裂纹问题的超奇异积分方程方法

根据含圆形嵌体平面问题在极坐标下的弹性力学基本解,使用Betti互换定理,在有限部积分意义下将问题归结为两个以裂纹岸位移间断为基本未知量、对于Ⅰ型和Ⅱ型问题相互独立的超奇异积分方程,对含圆形嵌体弹性平面中的径向裂纹问题进行了研究.根据有限部积分原理,建立了问题的数值算法.计算结果表明,嵌体半径、裂纹位置及材料剪切弹性模量等都对裂纹应力强度因子具有较为明显的影响.     

The Crack-Inclusion Interaction and the Analysis of Singularity for the Horizontal Contact

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Penny-shaped crack in a fiber-reinforced matrix

Using the slender inclusion model developed earlier the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles the problem is reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given and distribution of the stress intensity factor along the crack border is obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.     

Fundamental formulation for transformation toughening

In this paper, the transformation toughening problem is addressed in the framework of plane strain. The fundamental solution for a transformed strain nucleus located in an infinite plane is derived first. With this solution, the transformed inclusion problems are formulated by a Green’s function method, and the interaction of a crack tip with a single transformation source is found. On the basis of this solution, the fundamental formulations for toughening arising from martensitic and ferroelastic transformation are formulated also using the Green’s function method. Finally, some examples are provided to demonstrate the validity and relevance of the fundamental formulations proposed in the paper.