正交异性平面内的椭圆孔或裂纹系问题

应用Ｆａｂｅｒ级数展开和各向异性体平面问题复应力函数的方法，对于含有任意个椭圆孔或裂纹的正交异性平面，给出了孔周应力场解或孔附近裂纹应力强度因子解，其特例与前人结果一致．     

正交异性平面内的椭圆孔或裂纹系问题

应用Ｆａｂｅｒ级数展开和各向异性体平面问题复应力函数的方法，对于含有任意个椭圆或裂纹的正异性平面，给出了孔周应力场解或孔附近裂纹应力强度因子解，其特例与前人结果一致。     

平行于异材界面的三维椭圆平片裂纹分析

讨论了拉伸载荷作用下平行于两相材料界面的椭圆平片裂纹问题．首先,使用有限部积分概念和两相材料界面完全接合时的点力基本解导出了一组以裂纹表面位移差为未知函数的超奇异积分方程组．该组方程表明,此时三种裂纹模型同时存在;其次,在数值求解该组方程的过程中,未知函数裂纹表面位移差被近似为位移差的基本密度函数与多项式之积．基本密度函数反映了裂纹前沿应力奇性性态;最后,以拉伸载荷为例,讨论了椭圆平片裂纹与界面的距离、裂纹形状比和不同材料组合对应力强度因子的影响,并以图表形式给出。     

一维六方准晶中椭圆孔边裂纹的静态与动态分析

通过构造保角映射函数,借助复变函数方法,研究了一维六方准晶中椭圆孔边裂纹的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子的解析解.当椭圆的长、短半轴以及裂纹长度变化时,所得结果不仅可以还原为Griffith裂纹的情形,而且得到孔边裂纹问题、T型裂纹问题和半无限平面边界裂纹问题的应力强度因子的解析解.就声子场而言,这些解与经典弹性的结果完全一致.接着对椭圆孔边裂纹的动力学问题进行了研究,并得到了Ⅲ型动态应力强度因子的解析解.当裂纹速度V→0时,动力学解还原为静力学解.这些解在科学与工程断裂中有着潜在的应用价值.     

含椭圆孔或裂纹的等参数正交异性板平面问题基本解

应用Ｃａｕｃｈｙ积分的方法，分别给出了含椭圆孔或裂纹的等参数正交异性板在任意面内集中载荷作用下的复应力函数基本解或应力强度因子基本解，这些基本解对于应用边界元法求解此类正交异性板或各向同性板的某些弹性力学和断裂力学问题具有重要的意义。     

椭圆孔口端点和裂纹端点处的变动态应力分析

分析了椭圆孔口端点和裂纹端点处的变动态应力．在分析中,设带椭圆孔口的无限平板受远处应力作用,变动态应力分析指的是,令动点趋近于椭圆孔端点和椭圆孔变成裂纹这二个过程在各种相对关系下进行．在不同相对关系下,求出椭圆孔口或裂纹端点应力的极限值．分析表明,随着不同的变动状态,对于端点处的某些应力会得到不同的极限值．     

残余应力下厚壁筒表面裂纹的应力强度因子计算

本文首先介绍了边界元法计算裂纹尖端应力强度因子的基本理论,接着利用边界元法计算了在残余应力下不同厚壁筒内表面椭圆裂纹的应力强度因子,研究了其大不随椭圆裂纹不同而变化的规律,为厚壁筒结构的设计,制造以及疲劳寿命分析提供了许多有价值的参考资料。     

周期张开型平行裂纹问题研究

研究无限介质中周期平行裂纹问题，利用复应力函数在集中载荷作用点和裂纹尖端 的奇异性分析及双曲函数的周期性质，求得了问题在远场作用均匀载荷时裂纹尖端应力强度 因子的精确闭合形式解，并与已有的数值结果进行了比较. 其结果对于研究多裂纹的干 涉作用以及结构和材料的强度设计具有重要的实用价值.     

一维正方准晶椭圆孔口平面弹性问题的解析解

利用复变方法,引入广义保角映射,研究了一维正方准晶中具有椭圆孔口的平面弹性问题,给出了各应力分量的复变表示,并在特殊情况下转化为Griffith裂纹,得到该裂纹尖端处的应力强度因子的解析解.当准晶体的对称性增加时,正方准晶椭圆孔口平面弹性问题退化为一维四方准晶中具有椭圆孔口的平面弹性问题,同样在特殊情况下转化为Griffith裂纹,得到裂纹尖端处的应力强度因子的解析解.     

集中载荷下含偏心裂纹椭圆盘的应力强度因子计算

本文采用边界配置方法计算了受集中载荷作用时椭圆盘中偏心裂纹两端的应力强度因子,其中包括椭圆两半轴不同比值。不同裂纹长度和不同偏心程度的情况,在其特例椭圆盘中心裂纹情形,本文结果与Isida一致;在圆盘偏心裂纹情形,本文给出比Rooke等人更好的结果。     

Scattering of SH-wave by cracks originating at an elliptic hole and dynamic stress intensity factor

The method of complex function and the method of Green‘s function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamicstress intensity factor at the crack tip was given. A Green‘s function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.     

The mode III cracks emanating from an elliptical hole in the piezo-electro-magneto-elastic materials

The mode III crack problem in a medium possessing coupled electro-magneto-elastic is considered. Two asymmetrical edge cracks emanate from an elliptical hole. Combined stress, electric and magnetic loads are considered. The elliptical hole and cracks are assumed to be either magneto-electrically impermeable or permeable. The closed-form solution for stress, electric and magnetic intensity factors are derived explicitly. Also the solution for energy release rate is given in closed form. The solution is based on the complex variable method combined with the method of conformal mapping. Numerical computations are given to illustrate the effect of variable geometrical and material parameters on stress, electric and magnetic intensity factors and energy release rate.     

An exact and explicit treatment of an elliptic hole problem in thermopiezoelectric media

This paper presents an exact solution for the problem of an elliptic hole or a crack in a thermopiezoelectric solid. First, based on the extended version of Eshelby–Stroh's formulation, the generalized 2D problems of an elliptical hole in a thermopiezoelectric medium subject to uniform heat flow and mechanical–electrical loads at infinity are studied according to exact boundary conditions at the rim of the hole. The complex potentials in the medium and the electric field inside the hole are obtained in closed form, respectively. Then, when the hole degenerates into a crack, the explicit solutions for the field intensity factors near the crack tip and the electric field inside the crack are presented. It is shown that the singularities of all the field are dependent on the material constants, the applied heat load and mechanical loads at infinity, but not on the applied electric loads. It is also found that the electric field inside the crack is linearly variable, which is different from the result based on the impermeable crack model.     

Singular solutions for an anisotropic plate with an elliptical hole

A solution of the bending problem for a plate with an elliptical hole subjected to a point force (a singular solution) is obtained using the engineering theory of thin anisotropic plates and Lekhnitskiis complex potentials. The solution is constructed by conformal mapping of the exterior of the elliptical hole onto the exterior of a unit circle with evaluation of the Cauchy-type integrals over closed contours. Different versions of the boundary conditions on the holw contour are considered. In the limiting case where the ellipse becomes a slot, the solution describes the bending of a plate with a rectilinear crack or a rigid inclusion.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 144–152, January–February, 2005.     

Exact solutions for anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric material

Based on the complex variable method and the technique of conformal mapping, the anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric material is studied. The exact solutions of field intensity factors and energy release rate are presented in closed-form with the assumption that the surfaces of the cracks and the elliptical hole are electrically impermeable. With the variation of the hole-size and the crack length, the present results can be reduced to the cases of two symmetrical edge cracks and a single edge crack emanating from a circular hole given by Wang and Gao [Wang, Y.J., Gao, C.F., 2008. The mode III cracks originating from the edge of a circular hole in a piezoelectric solid. International Journal of Solids and Structures 45, 4590–4599]. Moreover, new models used for simulating more practical defects in a piezoelectric solid are obtained, such as two symmetrical edge cracks and a single edge crack emanating from an elliptical hole, two asymmetrical edge cracks emanating from a circular hole, T-shaped crack, cross-shaped crack and semi-infinite plane with an edge crack. Numerical examples are then conducted to reveal the effects of the hole-size and the crack length on the field intensity factors and the energy release rate.     

双压电材料内含椭圆孔孔边界面裂纹的反平面问题

利用复变函数方法,研究了横观各向同性压电双材料中椭圆孔孔边界面裂纹的反平面问题．首先,利用保角变换函数将椭圆孔保角变换到一直线裂纹;其次,基于孔边及裂纹表面均电不可穿透并且自由的假设,利用Stroh公式分别得到了本问题的复势函数、裂尖场集中系数的解析表达式;最后,在面内电载荷及面外机械载荷的作用下,分析了椭圆孔尺寸、裂纹长度和外载对裂尖场集中系数的影响,并得到了一个有意义的结论：椭圆孔一边裂纹长度的改变对另一边裂纹裂尖场的影响有限,然而一旦椭圆孔退化为竖直裂纹,该影响将变得非常显著．     

The solution of a crack emanating from an arbitrary hole by boundary collocation method

In this paper a group of stress functions has been proposed for the calculation of a crack emanating from a hole with different shape (including circular, elliptical, rectangular, or rhombic hole) by boundary collocation method. The calculation results show that they coincide very well with the existing solutions by other methods for a circular or elliptical hole with a crack in an infinite plate. At the smae time, a series of results for different holes in a finite plate has also been obtained in this paper. The proposed functions and calculation procedure can be used for a plate of a crack emanating from an arbitrary hole.     

A numerical analysis of cracks emanating from an elliptical hole in a 2-D elasticity plate

This paper is concerned with the stress intensity factors (SIFs) of cracks emanating from an elliptical hole in an infinite or a finite plate under biaxial loads by using a boundary element method, which consists of the non-singular displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. A few numerical examples are included to show that the present approach is very efficient and accurate for the calculating the SIFs of crack problems in an infinite or a finite plate. The present numerical results of cracks emanating from an elliptical hole under biaxial loads can reveal the effect of the elliptical aspect ratio and the transverse load on the SIFs.