Ⅲ型界面裂纹的非对称动态扩展问题

采用复变函数论的方法,对Ⅲ型界面裂纹的非对称动态扩展问题进行了研究．通过自相似函数的方法可以获得解析解的一般表达式．应用该法可以迅速地将所论问题转化为Riemann-Hilbert问题,并求得了非对称扩展裂纹分别在集中载荷、阶跃载荷作用下的解析解．利用这些解并采用叠加原理,就可以求得任意复杂问题的解．     

非对称Ⅲ型裂纹表面受运动载荷的动态扩展问题

通过复变函数论的方法,对非对称Ⅲ型裂纹表面受运动载荷的动态扩展问题进行了研究．采用自相似函数的方法可以获得解析解的一般表达式．应用该法可以迅速地将所讨论的问题转化为Riemann-Hilbert问题,并求得了非对称扩展裂纹表面分别受到常数运动载荷、阶跃运动载荷作用下的应力、位移和动态应力强度因子解析解．利用这些解并采用叠加原理,就可以求得任意复杂问题的解．     

各向异性板半无限裂纹平面问题的保角变换解法

本文给出了各向异性板半无限裂纹平面问题的保角变换解.首先,简单介绍了各向异性板平面问题的基本理论.随后采用复变函数的方法,通过引用适当的保角映射研究了各向异性板半无限裂纹平面弹性问题,得到了各向异性板中半无限裂纹在任意面内集中载荷作用下的裂纹尖端的应力强度因子的解析解.最后,作为特例得到了当集中力作用在裂纹表面时的应力强度因子的解析解,依此验证了结果的正确性.结果表明该方法简单实用.     

具水平直裂纹的弹性半平面运动载荷问题

利用平面弹性复变方法和积分方程理论，讨论具水平直裂纹的弹性半平面运动载荷问题，最后，得出应力函数封闭形式的解。     

带裂纹十次对称二维准晶平面弹性的无摩擦接触问题

借助经典平面弹性复变函数方法，研究了单个刚性凸基底压头作用下，带任意形状裂纹十次对称二维准晶半平面弹性的无摩擦接触问题.利用十次对称二维准晶位移、应力的复变函数表达式, 带任意形状裂纹的准晶半平面弹性无摩擦接触问题被转换为可解的解析函数复合边值问题，进而简化成一类可解的Riemann边值问题.通过求解Riemann边值问题，得到了应力函数的封闭解, 并给出了裂纹端点处应力强度因子和压头下方准晶体表面任意点处接触应力的显式表达式.从压头下方接触应力的表达式可以看出, 接触应力在压头边缘和裂纹端点处具有奇异性.当忽略相位子场影响时, 该文所得结论与弹性材料对应结果一致.数值算例分别给出了单个平底刚性压头无摩擦压入带单个垂直裂纹和水平裂纹的十次对称二维准晶下半平面的结果.该文所得结论为准晶材料的应用提供了理论参考.     

椭圆孔边裂纹对SH波的散射及其动应力强度因子

采用复变函数和Green函数方法求解具有任意有限长度的椭圆孔边上的径向裂纹对SH波的散射和裂纹尖端处的动应力强度因子．取含有半椭圆缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时的位移解作为Green函数,采用裂纹“切割”方法,并根据连续条件建立起问题的定解积分方程,得到动应力强度因子的封闭解答．讨论了孔洞的存在对动应力强度因子的影响．     

有限高狭长压电体中半无限反平面裂纹分析

利用保角变换和复变函数方法,研究了裂纹面上受反平面剪应力和面内电载荷共同作用下的有限高狭长压电体中半无限裂纹的断裂问题,给出了电不可通边界条件下裂纹尖端场强度因子和机械应变能释放率的解析解．当狭长体高度趋于无限大时,可得到无限大压电体中半无限裂纹的解析解．若不考虑电场作用,所得解可退化为纯弹性材料的已知结果．此外,通过数值算例,分析了裂纹面上受载长度、狭长体高度以及机电载荷对机械应变能释放率的影响规律．     

关于复合材料单层板裂纹尖端的J积分

该文采用复变函数方法,通过将裂纹尖端的应力和位移代入J积分的一般公式,推出了线弹性正交异性复合材料单层板受对称载荷作用的非弹性主方向的裂纹尖端犑积分的复形式－ 复变函数积分的实部,证明了该J积分的路径无关性,得到了它的具体计算公式     

含内裂纹的有限圆盘的平面问题

本文用弹性理论复变函数方法讨论了在内部任意位置含直线裂纹的有限圆盘在一般载荷作用下的平面问题,得到了复应力函数和应力强度因子用级数表示的一般表达式,并对此问题讨论了三种特殊情形,即裂纹受均布压应力,均布剪应力和圆盘匀速旋转的情形,其中还给出了计算应力强度因子的近似式.计算结果表明,对位于圆盘内部且不靠近外边界的中、小裂纹,这些近似式给出好的或较好的近似.     

纯扭正交异性复合材料板的断裂分析

对受纯扭载荷作用的线弹性正交异性复合材料板裂纹尖端附近的断裂性态进行探讨。利用复变函数方法，通过求解偏微分方程的边值问题，推出了裂纹尖端附近的弯矩、扭矩、应力和位移的表达式，最后给出了数值算例。     

Three dimensional axisymmetric problems in piezoelectric media: Revisited by a real fundamental solutions based new method

The purpose of the present work is to establish a set of real fundamental solutions for the differential governing equations of three dimensional axisymmetric problems in piezoelectric media. Firstly, conventional complex fundamental solutions are derived by analysis on the eigenvalue problem, and then, Euler’s formula is used to transform them into equivalent real fundamental solutions. As an example of application, the fracture problem of an axisymmetric penny-shaped crack in a piezoelectric layer is resolved by the real fundamental solutions based new method. Theoretical derivation and numerical computation are validated in the special case of a penny-shaped crack in an infinite piezoelectric body. Effects of geometrical parameters and electric-loading coefficient on energy release rates are surveyed and their agreement with the results of existing papers is also indicated. The advantage of such a real fundamental solutions based new method is that it can effectively help to avoid the difficult complex analysis in mixed boundary value problems.     

一维六方压电准晶中正六边形孔边裂纹的反平面问题

研究了一维六方压电准晶中正六边形孔边裂纹的反平面问题,利用复变函数中的Cauchy积分公式,通过构造保角映射函数,在电非渗透型的边界条件下得到了孔边裂纹尖端的应力分布以及场强度因子的解析解.通过数值算例,讨论了正六边形的边长和裂纹长度以及剪应力对场强度因子的影响.     

Analysis solution method for 3D planar crack problems of two-dimensional hexagonal quasicrystals with thermal effects

An analysis solution method (ASM) is proposed for analyzing arbitrarily shaped planar cracks in two-dimensional (2D) hexagonal quasicrystal (QC) media. The extended displacement discontinuity (EDD) boundary integral equations governing three-dimensional (3D) crack problems are transferred to simplified integral-differential forms by introducing some complex quantities. The proposed ASM is based on the analogy between these EDD boundary equations for 3D planar cracks problems of 2D hexagonal QCs and those in isotropic thermoelastic materials. Mixed model crack problems under combined normal, tangential and thermal loadings are considered in 2D hexagonal QC media. By virtue of ASM, the solutions to 3D planar crack problems under various types of loadings for 2D hexagonal QCs are formulated through comparison to the corresponding solutions of isotropic thermoelastic materials which have been studied intensively and extensively. As an application, analytical solutions of a penny-shaped crack subjected uniform distributed combined loadings are obtained. Especially, the analytical solutions to a penny-shaped crack subjected to the anti-symmetric uniform thermal loading are first derived for 2D hexagonal QCs. Numerical solutions obtained by EDD boundary element method provide a way to verify the validity of the presented formulation. The influences of phonon-phason coupling effect on fracture parameters of 2D hexagonal QCs are assessed.     

压电介质内裂纹问题的精确解

在压电介质断裂力学分析中,人们常假定裂纹面上的电位移法向分量为零,可是实验表明,这一假设将导致错误的结果。本文基于精确的电边界条件,并应用Stroh公式的方法,导出了含裂纹压电介质在无限远处均匀外载作用下二维问题的精确解。结果表明:(ⅰ)应力强度因子与各向同性材料相同,而电位移强度因子取决于材料常数和机械载荷,但与电载荷无关;(ⅱ)能量释放率大于纯弹性各向异性材料内的值,即总是正的,且与电载荷无关;(ⅲ)裂纹内所含空气的介电常数对介质内的场强无影响。     

二维各向异性压电介质机电耦合场的基本解

本文研究各向异性压电介质的机电耦台问题．应用平面波分解法和留数定理，首次得到了线力和线电荷作用下一般二维各向异性压电介质机电耦合场的基本解．本文的解适用于平面问题、反平面问题以及平面和反平面相互耦合问题．作为特例，文中给出了横观各向同性压电介质的基本解．     

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．     

Singularities at the tip of a crack on the interface of piezoelectric bodies

Singularities of elastic and electric fields are investigated at the tip of a crack on the interface of two anisotropic piezoelectric media under various boundary conditions on the crack surfaces. The singularity exponents form the spectrum of a certain polynomial pencil, and although explicit formulas are not available, this spectrum is described completely though. The mathematical results apply to problems in fracture mechanics. In this way the Griffith formulas are obtained for increments of energy functionals due to the growth of the crack, and the notion of energy release matrix is introduced. Normalization conditions for bases of singular solutions are proposed to adapt them to energy, stress, and deformation fracture criteria. Connections between these bases are determined, and additional properties of the deformation basis related to the notion of electric surface enthalpy are established. Bibliography: 44 titles. Dedicated to Vsevolod Alekseevich Solonnikov Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 362, 2008, pp. 241–271.     

Exact solution of four cracks originating from an elliptical hole in one-dimensional hexagonal quasicrystals

Based on the Stroh-type formalism for anti-plane deformation, the fracture mechanics of four cracks originating from an elliptical hole in a one-dimensional hexagonal quasicrystal are investigated under remotely uniform anti-plane shear loadings. The boundary value problem is reduced to Cauchy integral equations by a new mapping function, which is further solved analytically. The exact solutions in closed-form of the stress intensity factors for mode III crack problem are obtained. In the limiting cases, the well known results can be obtained from the present solutions. Moreover, new exact solutions for some complicated defects including three edge cracks originating from an elliptical hole, a half-plane with an edge crack originating from a half-elliptical hole, a half-plane with an edge crack originating from a half-circular hole are derived. In the absence of the phason field, the obtainable results in this paper match with the classical ones.     

双材料接合半无限体三维矩形界面裂纹应力强度因子分析

基于体积力法,研究了双材料接合半无限体三维矩形界面裂纹的应力强度因子问题．在数值计算中,未知的体积力密度采用基本密度函数和多项式乘积的形式来近似,其中基本密度函数是根据界面裂纹应力的振荡奇异性来选取的．计算结果表明,基于本算法得到的数值结果其收敛精度和计算误差都是令人满意的．算例中,给出了应力强度因子随矩形形状及双材料参数的变化规律．     

A subregion DRBEM formulation for the dynamic analysis of two-dimensional cracks

The dual reciprocity boundary element method employing the step by step time integration technique is developed to analyse two-dimensional dynamic crack problems. In this method the equation of motion is expressed in boundary integral form using elastostatic fundamental solutions. In order to transform the domain integral into an equivalent boundary integral, a general radial basis function is used for the derivation of the particular solutions. The dual reciprocity boundary element method is combined with an efficient subregion boundary element method to overcome the difficulty of a singular system of algebraic equations in crack problems. Dynamic stress intensity factors are calculated using the discontinuous quarter-point elements. Several examples are presented to show the formulation details and to demonstrate the computational efficiency of the method.