层状介质中多个非共面Griffith裂纹的弹性波散射问题研究

本文利用积分变换的方法,研究了层状介质中多个非共面Griffith裂纹的弹性波散射问题,导出了当入射波分别为P(SV)波及SH波时的散射对偶积分方程,并以双覆盖层半空间中的双裂纹为例,对反平面剪切波的散射场进行了求解和较为详尽的分析。最后通过数值计算,得到了许多有关的动力学特性曲线,从而揭示了层状介质中多裂纹弹性波散射问题中的某些内在规律。     

层状介质中双硬币形裂纹对扭转波的散射──远场解

本文在[1]的基础上,研究了多层介质中由于双硬币形裂纹引起的对弹性扭转波散射的远场特性.文中应用Hankel积分变换和Abel变换,将问题最后归结为求解一组第二类Fredholm积分方程,并导出了用积分形式给出的散射位移场表达式.最后运用围道积分技术和渐近分析的方法,对散射位移场在远离裂纹时的主要性态进行了分析讨论.     

加层半空间硬币形(Penny—Shaped)交界裂纹的弹性波散射——远场散射波导分析

本文研究了加层半空间硬币形交界裂纹的弹性波散射。文中采用Hankel积分变换,将散射问题转化为求解对偶积分方程,进而变换为奇异积分方程组.应用积分变换,围道积分技术和渐近分析方法,得到了弹性层中散射位移场的远场模式,理论分析表明弹性层中的散射位移场主要由RayLeigh-Like-Mode波组成,该波是弹性层中的散射波导.最后,给出两组弹性常数组合情形下的数值结果及讨论.     

应用力学学报 第8卷 总目次

固体力学非共面半椭圆形表面裂纹群问题的现代分析·········……法杨振国王允昌层状介质中的双cri[f」th交界裂纹的sH波散射(反平面运动)一近场解 ..…,.........................................·······……马兴瑞邹振祝黄文虎非完善板屈曲路径的有限元增量摄动法···········,一戴弘周祥玉吴连元考虑剪切变形的各项同性、正交各项异性矩形板的屈曲和后屈曲···……沈惠申非线性粘弹性拟静态问题与非线性弹性静力问题对应原理…胡强童忠钻集中载荷下含偏心裂纹椭圆盘的应力强度因子计劝-·········…     

三维空间中的周期裂纹阵对弹性波的散射

本文研究了三维空间中共面周期裂纹阵对正入射时间谐和平面弹性波的散射问题.散射波由无穷多个振型[M,N]~T和[M,N]~L,M,N=0,1,2……,迭加而成,但只有有限个振型是行波.当裂纹面为矩形时,在P波正入射的情况下进行了数值计算.数值计算的可靠性由能量平衡关系所证实.详细研究了[0,0]阶反射系数R_0~3与入射波的波数的关系.对细长的矩形裂纹,R_0~3趋于相应的二维问题的解.求出了沿裂纹周界的动态应力强度因子的分布,当波数趋于零时,其结果与相应的静态问题进行了比较,符合的程度是令人满意的.     

层状介质中的双Griffith交界裂纹的SH波散射(反平面运动)——近场解

本文研究层状介质中的双Griffith交界裂纹的SH波散射。文中采用积分变换法将双裂纹的弹性波散射化为对偶积分方程,进而将其转化为第一类奇异积分方程组,借助于第一类Chebyshev多项式,给出了奇异积分方程组的解答,并得到了双裂纹的动态应力强度因子的计算公式     

薄膜涂层材料中币形界面裂纹的弹性波散射

研究了薄膜涂层材料中币形界面裂纹的弹性波散射问题,建立了含有币形界面裂纹的覆层半空间模型,采用Hankel积分变换,将裂纹对弹性波散射的问题转化为求解矩阵形式的奇异积分方程。结合渐近分析和围道积分技术得到积分方程的解,进一步推导了散射波的应力场和位移场,以及动应力强度因子的理论计算公式。在数值算例中,分析了不同材料组合和裂纹尺寸情况下动应力强度因子与入射波频率的关系,并给出了裂纹张开位移的结果。为薄膜涂层材料的动态破坏分析提供了一定的理论基础。     

带单裂纹弹性半平面问题的几个解答

在论文[1]的基础上,文中提出了弹性半平面多裂纹问题的一个基本解。利用基本解和迭加原理,文中得出了弹性半平面多裂纹问题的Fredholm积分方程组。文中还给出了弹性半平面单裂纹问题的5个算例和解答。     

弹性波传播理论一些问题的研究现状和展望

本文简要地阐述了弹性波传播的一些基本理论,如位移势,表现定理及特征线理论等,并评述了两个领域内的问题。一为无限介质,半无限介质及层状介质中波的传播问题,重点在于地震波传播问题的解法。另一个领域为弹性波的绕射和散射。这一问题在动断裂、无损探伤及地震学中有重要的应用。评迷的重点是解题方法。 对本学科将来的发展也作了展望。认为反问题,随机波理论和在新技术领域中的应用是发展方向。在不少工程领域中的应用将越来越多地不能局限在弹性波范围内     

弹性波对多个椭圆孔的绕射问题

在弹性动力学问题中,弹性波对孔的绕射问题是一个重要课题.单个圆孔,椭圆孔为弹性波绕射问题早已解决,任意形孔为弹性波绕射问题也已基本解决.但是多连通问题,特别是多个非圆孔为弹性波绕射的问题,目前作者尚未见到比较好的处理办     

Two-dimensional thermal elasticity problem for a body weakened by a system of thermally insulated cracks

The thermally elastic state of a body in two dimensions with cracks has been investigated in a number of articles (see the survey in [1]). However, in the majority of cases problems have been investigated in which temperature stresses in a body are weakened by a single crack. The existing solutions of problems on the interaction between thermally insulated cracks in an elastic body have been confined to simple cases either with collinear [2, 3] or with arched cracks [4, 5]. Below the two-dimensional thermoelastic problem for an infinite body with arbitrarily positioned straight-lined thermally insulated cracks is studied by reducing it to a system of singular integral equations. An approximate solution is found for large distances between cracks. An exact solution is obtained in the case of a periodic system of collinear cracks.     

ON A CLASS OF METHOD FOR SOLVING PROBLEMS WITH RANDOM BOUNDARY NOTCHES AND/OR CRACKS—(Ⅲ) COMPUTATIONS FOR BOUNDARY CRACKS

This paper continues the discussions to a class of method for solving problems withrandom boundary notches and for cracks in refs.[1] and [2].Using the method developed in[1].[2]with important modifications about inclusion of singularities in the formulation. wearrive at a very effective computational process for problems with random boundarycracks. Actual computations for boundary cracks with or without apptied tractions in theirsurfaces. Show that the present method is quite workable for the problems consideredwithin proper range of characteristic parameters. The results obtained here extend thecontents of “Handbook of Stress Intensity Factors” given by G. C. Sih.     

Bending integral expressions of a cylinder with cracks

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小角裂纹应力强度因子的权函数解

本文把作者近年来发展的三维权函数法推广应用于平板角裂纹问题,计算了含小角裂纹的平板受远方拉伸及弯曲载荷下的应力强度因子,所提供的解答覆盖了疲劳断裂的研究及工程应用中所关心的小角裂纹的范围。本文的解与文献中的有限元结果进行了广泛的比较,两者之间有极好的一致性。     

Calculation of the scattering of elastic waves from a penny-shaped crack by the method of optimal truncation

The method of optimal truncation (MOOT) [1, 2], a least-squares boundary-residual method [3] for solving scattering problems, is applied to the plane circular crack. An equatorially cloven spherical inclusion is used to model the crack. Numerical advantages of this model are discussed and demonstrated. Results are given for cross sections for longitudinal waves incident on the crack at arbitrary angles. Both clear cracks and fluid-filled cracks are considered. A refinement of the method which would allow accurate calculation of dynamic stress-intensity factors is developed.     

Supplementary study on anisotropic plastic stress fields at a stationary plane-stress crack-tip

The results in Ref.[1]are not suitable for the cases of a≥2 .For this reason,we use the method in Ref.[1]to derive the general expressions of the anisotropic plastic stress fields at a stationary plane-stress crack-tip for both of the cases of a=2 and a>2 .As an example,we give the analytical expressions of the anisotropic plastic stress fields at the stationary tips of modeⅠand modeⅡplane-stress cracks for the case of a=2.     

On a class of method for solving problems with random boundary notches and/or cracks-(IV)

This paper continues the discussions to a class of method for solving problems with random boundary notches and/or cracks in references by C. Ouyang in [1] (See also [2] and [3]). Using the basic method given in this reference as well as some further developments. We develop here a new effective computational method for solving random deep boundary notches and/or cracks. The actual numerical computations given in this paper show that the present method is quite workable and the results obtained have enlarged the contents of Handbook of Stress Intensity Factors given by G. C. Sih.Project supported by the Science Funds of Chinese Academy of Sciences.     

Problem on circular-arc cracks between bonded dissimilar materials under concentrated force and moment

The method is very efficient by applying extended Schwarz principle integrated with the analysis of the singularity of complex stress functions to solve some plane-elastic problems under concentrated loads, in Ref.[1], this method is used to deal with the elastic problems of homogeneous plane. In this paper, it is extended to the case of dissimilar materials with co-circular cracks under concentrated force and moment. For several typical cases the solutions of complex stress function in closed form are built up and the stress intensity factors are given. From these solutions, we provide a series of particular results, in which two of them coincide with those in Refs. [1] and [6].     

Stress intensity factors for two offset parallel circular cracks: Part II — Semi-infinite solid

With the aid of the formulation in [1] (R. Muki, Progress in Solid Mechanics (North-Holland, 1961)) for general three-dimensional asymmetric problems and the superposition principle, Part II of this work makes use of the method in Part I (G.A.C. Graham and Q. Lan, J. Theor. Appl. Fract. Mech. 20, 207–225 (1994) [2]) to examine the interaction of arbitrarily located penny-shaped cracks in an infinite elastic solid to the case of a semi-infinite solid. As in Part I for the infinite body, the problem of a semi-infinite solid containing two penny-shaped cracks is reduced to a system of Fredholm integral equations of the second kind. These integral equations are then solved for some special cases when cracks are far apart and far away from the boundary. Some asymptotic solutions are presented and comparisons are made with the results for the special case where there is only one crack under axisymmetric loading.     

Bending of a circular cylinder containing a crack

The study of bending of cracked circular cylinders is of more significance. The bending of cylinders containing radical crack or cracks was discussed by refs. [1]–[4] and that of concentrically craked circular cylinders was studied by [5]. Continuing [6] and using complex variable methods in elasticity, this paper deals with the bending problems of a circular cylinder, containing an internal linear crack at any position under an acting force perpendicular to the crack. The general forms of displacements, stresses, and stressintensity factors, expressed in terms of series, are obtained and to this bending problems with small Ah are presented good approximate formulas for the stress-intensity factors whose variations with the center of the crack are analysed. Finally, the twist angle per unit length and the center of bending for the radically cracked circular cylinder, one of whose crack-tips is located at the origin, have been computed and the results are almost the same as that calculated in [1].