Cylindrical cavity with a circumferential edge crack subjected to a uniform shearing stress

This paper contains an analysis of the stress distribution in an elastic medium having cylindrical cavity with a circumferential edge crack when it is deformed by the application of uniform shearing stress. By making a suitable representation of the stress function for the problem, the problem is reduced to the solution of a pair of singular integral equations. This pair of singular integral equations is solved numerically, and the stress intensity factor due to the effect of the crack size is calculated. Also the crack opening displacements are displayed in graphical forms.     

Penny-shaped crack in a plate of finite thickness subjected to a uniform shearing stress

This paper contains an analysis of the stress distribution in a plate of finite thickness of an elastic material containing a penny-shaped crack when it is deformed by the application of a uniform shearing stress on the surface of the plate. The crack lies on the central plane of the plate with its surface parallel to those of the plate and is stress-free. By making a suitable representation of the stress function for the problem, the problem is reduced to the solution of a pair of Fredholm integral equations of the second kind. This pair of Fredholm integral equations of the second kind is solved numerically, and the increase in the stress intensity magnification factor due to the effect of the finite thickness of the plate is presented for various values of the thickness.     

压电压磁复合材料中界面裂纹对弹性波的散射

利用Schmidt方法分析了压电压磁复合材料中可导通界面裂纹对反平面简谐波的散射问题．经过富里叶变换得到了以裂纹面上的间断位移为未知变量的对偶积分方程A·D2在求解对偶积分方程的过程中,裂纹面上的间断位移被展开成雅可比多项式的形式．数值模拟分析了裂纹长度、波速和入射波频率对应力强度因子、电位移强度因子、磁通量强度因子的影响A·D2从结果中可以看出,压电压磁复合材料中可导通界面裂纹的反平面问题的应力奇异性形式与一般弹性材料中的反平面问题应力奇异性形式相同．     

中心裂纹夹紧矩形板的拉伸*

本文利用单裂纹基本解及无限板条的Fourier变换解,将含有中心裂纹的夹紧矩形板的拉伸问题,化归为解一组奇异积分方程,进而使用Gauss-Jacobi求积公式,计算了中心裂纹的应力强度因子及夹紧边的法向应力,在应力强度因子表中还作了数值结果比较.     

非对称载荷作用的外部圆形裂纹问题

使用边界积分方程方法,研究了三维无限弹性体中受非对称载荷作用的外部圆形裂纹问题。通过使用Fourier级数和超几何函数,将问题的二维边界奇异积分方程简化为Abel型方程,获得了一般非对称载荷作用的外部圆形裂纹问题的应力强度因子精确解,比用Hankel变换法得到的结果更为一般。结果表明:边界积分方程法在解析分析方面还有很大的潜力。     

压电压磁复合材料中一对平行裂纹对弹性波的散射

利用Schmidt方法对压电压磁复合材料中一对平行对称裂纹对反平面简谐波的散射问题进行了分析,借助富里叶变换得到了以裂纹面上的间断位移为未知变量的对偶积分方程．在求解对偶积分方程的过程中,裂纹面上的间断位移被展开成雅可比多项式的形式,最终获得了应力强度因子、电位移强度因子、磁通量强度因子三者之间的关系．结果表明,压电压磁复合材料中平行裂纹动态反平面断裂问题的应力奇异性与一般弹性材料中的动态反平面断裂问题的应力奇异性相同,同时讨论了裂纹间的屏蔽效应．     

Two problems with mixed boundary conditions for an elastic orthotropic strip

Two problems are considered for an elastic orthotropic strip: the contact problem and the crack problem. Both problems are reduced to integral equations of the first kind with different kernels, containing a singularity: logarithmic for the first problem and singular for the second problem. Regular and singular asymptotic methods are employed to construct approximate solutions of these integral equations. Numerical results are presented.     

条状功能梯度材料中偏心裂纹对反平面简谐波的散射问题

利用Schmidt方法研究了条状功能梯度材料中偏心裂纹对反平面简谐波的散射问题,裂纹垂直于条状功能梯度材料的边界．通过Fourier变换,问题可以转换为对一对未知变量是裂纹表面位移差的对偶积分方程求解．为了求解对偶积分方程,把裂纹表面的位移差展开为Jacobi多项式级数形式,进而得到了功能梯度参数、裂纹位置以及入射波频率对应力强度因子影响的规律．     

横观各向同性电磁弹性介质中裂纹对SH波的散射

研究横观各向同性电磁弹性介质中裂纹和反平面剪切波之间的相互作用．根据电磁弹性介质的平衡运动微分方程、电位移和磁感应强度微分方程,得到SH波传播的控制场方程．引入线性变换,将控制场方程简化为Helmholtz方程和两个Laplace方程A·D2通过Fourier变换,并采用非电磁渗透型裂面边界条件,得到了柯西奇异积分方程组．利用Chebyshev多项式求解积分方程,得到应力场、电场和磁场以及动应力强度因子的表达,并给出了数值算例．     

含圆形孔口和水平直裂纹的平面问题的应力分析

利用复变函数方法和积分方程理论研究了既含有圆形孔口又含有水平裂纹的无限大平面的平面弹性问题,将复杂的解析函数的边值问题化成了求解只在裂纹上的奇异积分方程的问题.此外,还给出了裂纹尖端附近的应力场和应力强度因子的公式.     

A study of the influence of the orientation of a planar surface crack in the shape of a limaçon of pascal on the stress concentration in a half-space

We study the stress state in the vicinity of a planar surface crack whose boundary is described by the limaçon of pascal. The problem is solved by a conformal mapping of the region occupied by the crack onto part of a disk in the plane. This makes it possible to apply a numerical-analytic method for solving systems of double singular integral equations of the mathematical theory of cracks. We present the graphs of the dependence of the stress intensity factor on the angular coordinate for cracks that are part of a limaçon of Pascal.     

Extension of a piezoceramic bimorph with a crack crossing the interface

We consider the boundary-value problem of electroelasticity for a composite plate weakened by a crack crossing the line joining the media. The initial boundary-value problem, is reduced to a mixed system of singular integral and algebraic equations. We present the calculation results characterizing the variation in the stress intensity factors as a function of the opening angle of a segmented crack for different types of loading.Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 482–488, July–August 1997.     

裂纹与线夹杂垂直接触问题的奇性分析

以短纤维复合等作为工程背景,采用现有文献中单裂纹和单夹杂的基本解,对于限平项（基体）上,裂纹和线夹杂的垂直接触问题从断理解力学的角度作了研究,得到了问题的积分方程,推出了接触点的性线指数,奇性应力及以此表示的接触点附近三个区域内的应力强度因子表达式,并给出一些数值结果,可供工程实际参考。     

Interaction of elastic waves with a curvilinear crack in a half-plane

We consider the problem of the interaction of monochromatic displacement waves with a curvilinear crack-cut in a half-plane. We find integral representations of the solution. The boundary-value problem is reduced to a system of singular integral equations. A parametric investigation is carried out for the effect of the form of the load, the fastening conditions on the boundary of the half-plane, and the curvature of the crack on the dynamic coefficients of the stress intensity.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 77–82, 1988.     

An interface crack moving between magnetoelectroelastic and functionally graded elastic layers

A constant crack moving along the interface of magnetoelectroelastic and functionally graded elastic layers under anti-plane shear and in-plane electric and magnetic loading is investigated by the integral transform method. Fourier transforms are applied to reduce the mixed boundary value problem of the crack to dual integral equations, which are expressed in terms of Fredholm integral equations of the second kind. The singular stress, electric displacement and magnetic induction near the crack tip are obtained asymptotically and the corresponding field intensity factors are defined. Numerical results show that the stress intensity factors are influenced by the crack moving velocity, the material properties, the functionally graded parameter and the geometric size ratios. The propagation of the moving crack may bring about crack kinking, depending on the crack moving velocity and the material properties across the interface.     

The solution of a problem in contact fracture mechanics on the nucleation and development of a bridged crack in the hub of a friction pair

The contact deformation of the hub of a plunger pair is considered. It is assumed that, during the repeated reciprocating motion of the plunger, a crack is initiated and fracture of the materials of the elements of the contact pair occurs. The problem of the equilibrium of the hub of a friction pair with a crack nucleus reduces to solving a system of non-linear singular integrodifferential equations with a Cauchy-type kernel. The normal and shear forces in the zone where the crack originates are found from the solution of this system of equations. The condition for the appearance of a crack is formulated, taking account of the criterion of the limit traction of the bonds in the material. A problem for the plunger of a friction pair as applied to a borehole sucker rod pump is considered as an example. In conclusion, the case when there are several arbitrarily distributed rectilinear bridged cracks, with bonds between the crack faces in the end zone, close to the contact surface of the hub is investigated.     

An axisymmetric problem of an embedded mixed-mode crack in a functionally graded magnetoelectroelastic infinite medium

This paper investigates the problem of an axisymmetric penny shaped crack embedded in an infinite functionally graded magneto electro elastic medium. The loading consists of magnetoelectromechanical loads applied on the crack surfaces assumed to be magneto electrically impermeable. The material’s gradient is parallel to the axisymmetric direction and is perpendicular to the crack plane. An anisotropic constitutive law is adopted to model the material behavior. The governing equations are converted analytically using Hankel transform into coupled singular integral equations, which are solved numerically to yield the crack tip stress, electric displacement and magnetic induction intensity factors. A similar problem but with a different crack morphology, that is a plane crack embedded in an infinite functionally graded magneto electro elastic medium, was considered by the authors in a previous work (Rekik et al., 2012) [25]. While the overall solution schemes look similar, the axisymmetric problem resulted in more mathematical complexities and let to different conclusions with respect to the influence of coupling between elastic, electric and magnetic effects. The main focus of this paper is to study the effect of material non-homogeneity on the fields’ intensity factors to understand further the behavior of graded magnetoelectroelastic materials containing penny shaped cracks and to inspect the effect of varying the crack geometry.     

Electro-mechanical sliding frictional contact of a piezoelectric half-plane under a rigid conducting punch

This paper investigates the two-dimensional sliding frictional contact of a piezoelectric half-plane in the plane strain state under the action of a rigid flat or a triangular punch. It is assumed that the punch is a perfect electrical conductor with a constant electric potential. By using the Fourier integral transform technique and the superposition theorem, the problem is reduced to a pair of coupled Cauchy singular integral equations and then is numerically solved to determine the unknown contact pressure and surface electric charge distribution. The effects of the friction coefficient and electro-mechanical loads on the normal contact stress, normal electric displacement, in-plane stress and in-plane electric displacement are discussed in detail. It is found that the friction coefficient has a significant effect on the electro-mechanical sliding frictional contact behaviors of the piezoelectric materials.