带k条径向边裂纹的圆形孔口问题的应力分析

利用复变函数方法,通过构造保角映射研究了带k条径向边裂纹的圆形孔口的平面弹性问题,给出了裂纹尖端Ⅰ型与Ⅱ型问题应力强度因子的精确分析解.在极限情况下,不仅可以还原出星形裂纹,Griffith裂纹,十字裂纹等经典的裂纹问题的结果,而且当k取任意正整数值时,可以模拟出更多的、复杂的带裂纹的圆形孔口问题.     

带裂纹的弹性狭长体基本问题

利用复变方法和积分方程理论，讨论带任意裂纹的各向同性弹性狭长体的基本问题。通过适当的函数分解和积分变换，将问题简化为一正则型奇异积分方程。对方程解的情况和求解方法进行了研究，并导出裂纹尖端的应力强度因子。     

带任意裂纹的一维六方准晶弹性半平面第一基本问题

研究了周期平面内含任意裂纹的一维六方准晶的弹性半平面第一基本问题.首先借助保角变换将半平面第一基本问题转化为单位圆内带任意裂纹的第一基本问题;再利用复变函数方法将求有界域内的弹性平衡问题转化为奇异积分方程的求解,并证明方程是唯一可解的.该问题的求解为研究工程断裂问题提供了理论方法.     

裂纹面局部均布荷载下Ⅰ型裂纹有限宽板应力强度因子

采用应力强度因子的裂纹线求解方法,对裂纹面局部均布荷载作用下的Ⅰ型裂纹有限宽板应力强度因子进行了解析求解.其思路是:直接利用无限宽板裂纹问题应力场的解析解,求得应力分量在裂纹线上的形式,通过合理的修正,提出修正后的应力场在裂纹线应满足的条件;进而求解应力强度因子,得出了有限宽板对相应无限宽板的应力强度因子修正系数.当板宽趋于无限大时,得到的应力强度因子与相应的无限宽裂纹板的解答一致.     

圆形孔口裂纹的反平面剪切问题的解析解

利用复变函数方法,通过构造保角映射,研究了带裂纹的圆形孔口的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子.在极限情形下,求得Griffith裂纹在裂纹尖端处应力强度因子,这与已有的结果完全一致.最后数值算例给出了半经和裂纹长度对应力强度因子的影响.     

Ⅲ型裂纹弹塑性场在裂纹线附近匹配方程的一般形式

针对理想弹塑性Ⅲ型裂纹问题,对线场分析方法的步骤和匹配过程进行了凝练和归纳,给出了裂纹线附近塑性场、弹塑性边界、弹塑性匹配方程的一般形式及其一般求解步骤,将不同条件下的Ⅲ型裂纹问题归结为由4个匹配方程确定4个待定常数,并通过一个具体问题,验证了这一方法的正确性、简明性和通用性.     

一维六方准晶中带双裂纹的椭圆孔口问题的解析解

利用复变函数方法,通过构造保角映射,研究了一维六方准晶中带双裂纹的椭圆孔口的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子,在极限情形下,不仅可以还原为已有的结果,而且求得一维六方准晶中带双裂纹的圆形孔口问题、十字裂纹问题在裂纹尖端的应力强度因子．     

一维六方准晶中带三条不对称裂纹的圆形孔口问题的解析解

利用复变函数方法,通过构造保角映射,研究了一维六方准晶中带不对称三裂纹的圆形孔口的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子,在极限情形下,不仅可以还原为已有的结果,而且求得一维六方准晶中L裂纹问题在裂纹尖端的应力强度因子.     

边裂纹柱扭转的强奇性积分方程解法*

本文利用单裂纹扭转的位错型解答,使用有限部积分的概念和方法,最后将含有单根水平裂纹的柱体扭转问题归为解一个强奇性积分方程,并为其建立了数值求解方法,文末作了若干数值例子的计算,结果令人满意.     

利用Schmidt方法研究压电材料Ⅰ-型界面裂纹问题

在一定的假设条件下,即不考虑界面裂纹尖端处裂纹面的相互叠入现象,研究了压电材料Ⅰ-型界面裂纹问题．利用Fourier变换使问题的求解转换为求解两对对偶积分方程．进而把裂纹表面位移差展开成Jacobi多项式形式来求解对偶积分方程．结果表明裂纹尖端应力场和电位移场的奇异性与均匀材料裂纹问题的奇异性相同．当上下半平面材料相同时,解可以退化而得到其精确解．     

带裂纹圆柱体扭转的强奇性积分方程解法

本以裂纹的翘曲位移间断为基本未知函数，把带裂纹圆柱体的扭转问题化为求解一组强奇性积分方程，并利用数值法，对星形及其不同形状裂纹圆柱体的抗扭刚度和应力强度因子作了数值计算，计算结果令人满意。     

On the peculiarities of a crack growth path in anisotropic solid

One of the possibilities to increase the resistance of a structure to catastrophic fracture is to force a main line crack to deviate from its path. In this connection the influence of the elastic moduli of an anisotropic material on the possibilities of crack rotation are studied. In particular a linear elastic problem for a straight Mode I crack, located on a symmetry axis of an orthotropic plane is considered. The strength properties of the material are supposed to be isotropic. For studying a direction of a crack growth path several crack models are considered. It is shown that a thin elongated elliptical hole as a crack model leads to more plausible results concerning crack rotation conditions than an ideal cut model. The maximal tensile stresses are taken as a crack growth criterion. It is shown that for some class of orthotropic materials a crack deviates from the straight path just after it starts to grow even in the conditions of uniaxial normal tension. The problem of the stability of a straight crack path under Mode I loading is also considered. This problem is reduced to the problem of the fracture direction determination for thin elongated elliptical cavity slightly inclined to the initial direction. In the frame of the proposed approach the conditions of instability are obtained. It is shown that for some class of orthotropic materials a straight crack path is unstable in the conditions of uniaxial normal tension. This class of materials is wider than one for which a crack deviates from the straight crack path just after its start. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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．     

In-plane loading of a cracked elastic solid by a disc inclusion with a Mindlin-type constraint

The paper examines the problem related to the axisymmetric interaction between an external circular crack and a centrally placed penny-shaped rigid inclusion located in the plane of the crack. The interface between the inclusion and the elastic medium exhibits a Mindlin-type imperfect bi-lateral contact. Analytical results presented in the paper illustrate the manner in which the lateral translational stiffness of the inclusion and the stress intensity factor at the boundary of the external circular crack are influenced by the inclusion/crack radii ratio.     

On a finite crack partially penetrating two circular inhomogeneities and some related problems

We investigate a Mode-III finite slit crack partially penetrating two circular inhomogeneities embedded in an unbounded matrix. In order to obtain analytical solutions, it is assumed that the two circular inhomogeneity-matrix interfaces are Apollonius circles with respect to the two crack tips (or equivalently the two crack tips are just mutually image points with respect to each one of the two circular interfaces). Particularly closed-form expressions of the stress intensity factors at the two crack tips are obtained even though only series form solutions to the original boundary value problem can be derived. The loadings considered in this research include: (i) remote uniform anti-plane shearing; (ii) a straight screw dislocation at any position of the three-phase composite system; (iii) a Zener-Stroh crack. The results are verified by comparison with existing solutions. The related problem of a circular hole partially merged in two circular inhomogeneities is also addressed, with closed-form expressions of the stress concentration factors derived.     

泊松比对高速扩展平面应变裂纹尖端的理想塑性场的影响

在理想弹塑性材料中,高速扩展裂纹尖端的应力分量都只是θ的函数.利用这个条件以及定常运动方程,塑性应力应变关系和含有泊松比的Mises屈服条件,本文导出了高速扩展平面应变裂纹尖端的理想塑性场的一般表达式.将这些含有泊松比的一般表达式用于Ⅰ型裂纹,我们就得到高速扩展平面应变Ⅰ型裂纹尖端的理想塑性场.这个理想塑性场含有泊松比,所以,我们能知道泊松比对高速扩展平面应变Ⅰ型裂纹尖端的理想塑性场的影响.     

The equilibrium of an elastic space weakened by two spherical cavities and an external circular crack

Using the relationship between the basic solutions of Laplace's equation in toroidal and spherical coordinates, the Fourier method is employed to solve the problem of the equilibrium of an elastic space weakened by two spherical cavities and an external circular crack. The proposed approach leads to an infinite system of linear algebraic equations of the second kind with exponentially decaying matrix coefficients. A small-parameter expansion is used to obtain an asymptotic formula for the normal stress intensity factor.     

圆形弹性薄板非轴对称大挠度问题的一个解法

本文建议一个求解圆形弹性薄板非轴对称大挠度问题的方法.本文以周边固定受非轴对称载荷作用下圆形薄板的大挠度问题为例阐述所述方法的原理和解题步骤.文中所述方法可以用以求解其他边界及载荷作用下圆形薄板的非轴对称大挠度问题.     

Saint–Venant torsion of a circular bar with radial cracks incorporating surface elasticity

The Saint–Venant torsion problem of a circular cylinder containing a radial crack with surface elasticity is studied. The surface elasticity is incorporated into the crack faces by using the continuum-based surface/interface model of Gurtin and Murdoch. Both an internal crack and an edge crack are considered. By using the Green’s function method, the boundary value problem is reduced to a Cauchy singular integro-differential equation of the first order, which can be numerically solved by using the Gauss–Chebyshev integration formula, the Chebyshev polynomials and the collocation method. Due to the incorporation of surface elasticity, the stresses exhibit the logarithmic singularity at the crack tips. The torsion problem of a circular cylinder containing two symmetric collinear radial cracks of equal length with surface elasticity is also solved by using a similar method. The strengths of the logarithmic singularity and the size-dependent torsional rigidity are calculated.