磁电热弹耦合材料三维多裂纹超奇异积分法

用超奇异积分方程法将多场耦合载荷作用下磁电热弹耦合材料内含任意形状和位置三维多裂纹问题转化为求解一以广义位移间断为未知函数的超奇异积分方程组问题,退化得到内含任意形状平行三维多裂纹问题的超奇异积分方程组;推导出平行三维多裂纹问题的裂纹前沿广义奇异应力场解析表达式、定义了广义(应力、应变能)强度因子和广义能量释放率;应用有限部积分概念及体积力法,为超奇异积分方程组建立了数值求解方法,编制了FORTRAN程序,以平行双裂纹为例,通过典型算例,研究了广义(应力、应变能)强度因子随裂纹位置、裂纹形状及材料参数变化规律,得到裂纹断裂评定准则. 最后,分析了裂纹间干扰、屏蔽作用及其在工程实际中的应用.      

垂直磁压电材料界面三维裂纹的超奇异积分法

应用有限部积分概念和广义位移基本解，垂直于磁压电双材料界面三维复合型裂纹问题被转 化为求解一组以裂纹表面广义位移间断为未知函数的超奇异积分方程问题. 进而，通过主部 分析法精确地求得裂纹尖端光滑点附近的奇性应力场解析表达式. 然后，通过将裂纹表面 位移间断未知函数表达为位移间断基本密度函数与多项式之积，使用有限部积分法对超奇异 积分方程组建立了数值方法. 最后，通过典型算例计算，讨论了广义应力强度因子的变化规 律.     

三维无限体中两平行平片裂纹相互干扰的超奇异积分方程解法

本文利用三维断裂力学的超奇异积分方程求解理论，对三维无限体中两平行平片裂纹在任意载荷作用下的相互干扰问题作了研究。首先导出了以裂纹面移间断（位借）为未知函数的超奇异积分方程组，然后为其建立了有限积分边界元法；在此基础上，讨论用了裂纹面位移间断计算应力强度因子的方法，最后用此计算了两平行平片裂纹的相对位置对裂前沿应力强度因子的影响，其数值结果令人满意。     

三维有限体中两平行裂纹干扰问题的有限部积分与边界元法

利用Ｓｏｍｉｇｌｉａｎａ公式及有限部积分的概念，导出含两平行平片裂纹三维有限体裂纹干扰问题的超奇异积分方程组，联合使用有限部积分与边界元法，建立了数值求解方法，为提高数值计算结果的精度，在裂纹前疝附近单元，采用平方根位移模型，并在此基础雌出直接计算应力强度因子的公式，最后计算若干典型例子裂纹前沿的应力强度因子。     

三维体内含垂直于双材料界面混合型裂纹的超奇异积分解法

利用双材料位移基本解和Somigliana公式,将三维体内含垂直于双材料界面混合型裂纹问题归结为求解一组超奇异积分方程。使用主部分析法,通过对裂纹前沿应力奇性的分析,得到用裂纹面位移间断表示的应力强度因子的计算公式,进而利用超奇异积分方程未知解的理论分析结果和有限部积分理论,给出了超奇异积分方程的数值求解方法。最后,对典型算例的应力强度因子做了计算,并讨论了应力强度因子数值结果的收敛性及其随各参数变化的规律。     

压电材料中三维I型断裂力学分析

讨论了不可导通情况下三维横观各向同性压电材料中受拉伸和电载荷作用的平片裂纹I型断裂力学问题. 使用有限部积分概念，从三维线性压电理论出发，严格得到了一组以裂纹面位移间断和电势间断为未知变量的超奇异积分方程组；应用二维超奇异积分的主部分析法，从理论上分析得到了裂纹前沿应力和电势奇性指数以及应力和电位移奇性场，从而找到了以裂纹面位移间断和电势间断表示的应力和电位移强度因子、能量释放率表达式；为所得到的超奇异积分方程组建立了数值法，并用此计算了若干典型的平片裂纹问题，数值结果令人满意.     

横观各向同性材料的三维断裂力学问题

从三维横观各向同性材料弹性力学理论出发, 使用Hadamard有限部积分概念, 导出了三维状态下单位位移间断(位错)集度的基 本解. 在此基础上, 进一步运用极限理论, 将任意载荷作用下, 三维无限大横观各向 同性材料弹性体中, 含有一个位于弹性对称面内的任意形状的片状裂纹问题, 归结为求 解一组超奇异积分方程的问题. 通过二维超奇异积分的主部分析方法, 精确地求得了裂纹前沿光滑点附近的应力奇异指数和奇异应力场, 从而找到了以裂纹表面位移间断表示的应力强度因子表达式及裂纹局部扩展所提供 的能量释放率. 作为以上理论的实际应用，最后给出了一个圆形片状裂纹问题 的精确解例和一个正方形片状裂纹问题的数值解例. 对受轴对称法向均布载荷作用下圆形片状裂纹问题, 讨论了超奇异积分方程的精确求解方法, 并获得了位移间断和应力强度因子的封闭解, 此结果与现有理论解完全一致.     

三维动态裂纹问题的超奇异积分方程法

基于弹性材料的动态基本方程，结合广义Betti-Rayleigh互易等式与时域下的边界积分方程，推导得到时域下的超奇异积分方程组。引入Laplace域下的动态基本解，将经过主部分析的积分核函数分解为静态和动态部分，其中动态积分核不具有奇异性。在裂纹前沿附近单元，采用与理论分析一致的平方根位移模型。结合Lubich时间卷积实现拉氏变换，采用配置点法计算超奇异积分，获得问题的数值解。并针对椭圆裂纹算例编写Fortran程序，得到冲击荷载作用下张开型裂纹的动态应力强度因子变化规律，数值结果稳定且收敛速度快。     

三维动态裂纹问题的超奇异积分方程法

基于弹性材料的动态基本方程,结合广义Betti-Rayleigh互易等式与时域下的边界积分方程,推导得到时域下的超奇异积分方程组。引入Laplace域下的动态基本解,将经过主部分析的积分核函数分解为静态和动态部分,其中动态积分核不具有奇异性。在裂纹前沿附近单元,采用与理论分析一致的平方根位移模型。结合Lubich时间卷积实现拉氏变换,采用配置点法计算超奇异积分,获得问题的数值解。并针对椭圆裂纹算例编写Fortran程序,得到冲击荷载作用下张开型裂纹的动态应力强度因子变化规律,数值结果稳定且收敛速度快。     

压电材料中三维I型断裂力学分析

讨论了不可导通情况下三维横观各向刚性压电材料中受拉伸和电载荷作用的平片裂纹Ⅰ型断裂力学问题．使用自限部分概念，从二维线性压电理论出发，严格得到了一组以裂纹面位移间断和电势间断为未知变量的超奇异积分方程组；应用二维超奇异积分的主部分析法，从理论上分析得到了裂纹前沿应力和电势奇性指数以及应力和电位移奇性场，从而找到了以裂纹面位移间断和电势间断表示的应力和电位移强度因子、能量释放率表达式；为所得到的超奇异积分方程组建立了数值法，并用此计算了若干典型的平片裂纹问题，数值结果令人满意．     

Hypersingular integral equation method for a three-dimensional crack in anisotropic electro-magneto-elastic bimaterials

Using Green’s functions, the extended general displacement solutions of a three-dimensional crack problem in anisotropic electro-magneto-elastic (EME) bimaterials under extended loads are analyzed by the boundary element method. Then, the crack problem is reduced to solving a set of hypersingular integral equations (HIE) coupled with boundary integral equations. The singularity of the extended displacement discontinuities around the crack front terminating at the interface is analyzed by the main-part analysis method of HIE, and the exact analytical solutions of the extended singular stresses and extended stress intensity factors (SIFs) near the crack front in anisotropic EME bimaterials are given. Also, the numerical method of the HIE for a rectangular crack subjected to extended loads is put forward with the extended crack opening dislocation approximated by the product of basic density functions and polynomials. At last, numerical solutions of the extended SIFs of some examples are obtained.     

Application of hypersingular integral equation method to three-dimensional crack in electromagnetothermoelastic multiphase composites

A three-dimensional crack problem in electromagnetothermoelastic multiphase composites (EMTE-MCs) under extended loads is investigated in this paper. Using Green’s functions, the extended general displacement solutions are obtained by the boundary element method. This crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations, in which the unknown functions are the extended displacement discontinuities. Then, the behavior of the extended displacement discontinuities around the crack front terminating at the interface is analyzed by the main-part analysis method of hypersingular integral equations. Analytical solutions for the extended singular stresses, the extended stress intensity factors (SIFs) and the extended energy release rate near the crack front in EMTE-MCs are provided. Also, a numerical method of the hypersingular integral equations for a rectangular crack subjected to extended loads is put forward with the extended displacement discontinuities approximated by the product of basic density functions and polynomials. In addition, distributions of extended SIFs varying with the shape of the crack are presented. The results show that the present method accurately yields smooth variations of extended SIFs along the crack front.     

Mixed-mode stress intensity factors of 3D interface crack in fully coupled electromagnetothermoelastic multiphase composites

This contribution presents an extended hypersingular intergro-differential equation (E-HIDE) method for modeling the 3D interface crack problem in fully coupled electromagnetothermoelastic anisotropic multiphase composites under extended electro-magneto-thermo-elastic coupled loads through theoretical analysis and numerical simulations. First, based on the extended boundary element method, the 3D interface crack problem is reduced to solving a set of E-HIDEs coupled with extended boundary integral equations, in which the unknown functions are the extended displacement discontinuities. Then, the behavior of the extended singular stress indices around the interface crack front terminating at the interface is analyzed by the extended main-part analysis. The extended stress intensity factors near the crack front are defined. In addition, a numerical method for a 3D interface crack problem subjected to extended loads is proposed, in which the extended displacement discontinuities are approximated by the product of basic density functions and polynomials. Finally, the radiation distribution of extended stress intensity factors at the interface crack surface are calculated, and the results are presented toward demonstrating the applicability of the proposed method.     

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored. This work was supported by the National Natural Science Foundation of China (No.19772064) and by the project of CAS KJ 951-1-20     

Scattering of harmonic anti-plane shear waves by an interface crack in magneto-electro-elastic composites

IntroductionCompositematerialconsistingofapiezoelectricphaseandapiezomagneticphasehasdrawnsignificantinterestinrecentyears,duetotherapiddevelopmentinadaptivematerialsystems .Itshowsaremarkablylargemagnetoelectriccoefficient,thecouplingcoefficientbetweenst…     

Modelling of dynamical crack propagation using time-domain boundary integral equations

We study dynamic antiplane cracks in the time domain by the boundary integral equation method (BIEM) based on the integral equation for displacement discontinuity (or crack opening displacement, COD) as a function of stress on the crack. This displacement discontinuity formulation presents the advantage, with respect to methods developed by Das and others in seismology, that it has to be solved only inside the crack. This BIEM is, however, difficult to implement numerically because of the hypersingularity of the kernel of the integral equation. Hence it is rewritten into a weakly singular form using a regularization technique proposed by Bonnet. The first step, following a method due to Sladek and Sladek, consists in converting the hypersingular integral equation for the displacement discontinuity into an integral equation for the displacement discontinuity and its tangential derivatives (dislocation density distribution); the latter involves a Cauchy type singular kernel. The second step is based on the observation that the hypersingularity is related to the static component of the kernel; the static singularity is then isolated and can be expressed in terms of weakly singular integrals using a result due to Bonnet. Although numerical applications discussed in this paper are all for the antiplane problem, the technique can be applied as well to in-plane crack dynamics.

The BIEM is implemented numerically using continuous linear space-time base functions to model the COD on the crack. In the present scheme the COD gradient interpolation is discontinuous at the element nodes while the integral equations are collocated at the element midpoints. This leads to an overdetermined discrete problem which is solved by standard least-squares methods. We use the dynamic BIEM to study a set of problems that appear in earthquake source dynamics, including the spontaneous dynamic crack propagation for a very simple rupture criterion. The numerical results compare favorably with the few exact solutions that are available. Then we demonstrate that difficulties experienced with finite difference simulations of spontaneous crack dynamics can be removed with the use of BIEM. The results are improved by the use of singular crack tip elements.     

A contour integral method for dynamic stress intensity factors

The contour integral method previously used to determine static stress intensity factors is applied to dynamic crack problems. The required derivatives of the traction in the reference problem are obtained numerically by the displacement discontinuity method. Stress intensity factors are determined by an integral around a contour which contains a crack tip. If the contour is chosen as the outer boundary of the body, the stress intensity factor is obtained from the boundary values of traction and displacement. The advantage of this path-independent integral is that it yields directly both the opening-mode and sliding-mode stress intensity factors for a straight crack. For dynamic problems, Laplace transforms are used and the dynamic stress intensity factors in the time domain are determined by Durbin's inversion method. An indirect boundary element method, incorporating both displacement discontinuity and fictitious load techniques, is used to determine the boundary or contour values of traction and displacement numerically.     

双轴载荷作用下源于椭圆孔的分支裂纹的一种边界元分析

利用一种边界元方法来研究双轴载荷作用下无限大板中源于椭圆孔的分支裂纹．该边界元方法由Crouch与Starfied建立的常位移不连续单元和笔者提出的裂尖位移不连续单元构成．在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界,文中算例说明本数值方法对计算平面弹性裂纹的应力强度因子是非常有效的。该文对双轴载荷作用下无限大板中源于椭圆孔的分支裂纹的数值结果进一步证实本数值方法对计算复杂裂纹的应力强度因子的有效性,同时该数值结果可以揭示双轴载荷及裂纹体几何对应力强度因子的影响。     

Weakly-singular,weak-form integral equations for cracks in three-dimensional anisotropic media

Singularity-reduced integral relations are developed for displacement discontinuities in three-dimensional, anisotropic linearly elastic media. An isolated displacement discontinuity is considered first, and a systematic procedure is followed to develop relations for the displacement and stress fields induced by the discontinuity. The singularity-reduced relation for the stress is particularly important since it is in a form which allows a weakly-singular, weak-form traction integral equation to be readily established. The integral relations obtained for a general displacement discontinuity are then specialized to an isolated crack and to dislocations; the relations for dislocations are introduced to emphasize their direct connection to corresponding results for cracks and to allow earlier independent findings for these two types of discontinuities to be put into proper context. Next, the singularity-reduced integral equations obtained for an isolated crack are extended to allow treatment of cracks in a finite domain, and a pair of weakly-singular, weak-form displacement and traction integral equations is established. These integral equations can be combined to obtain a final formulation which is in a symmetric form, and in this way they serve as the basis for a weakly-singular, symmetric Galerkin boundary element method suitable for analysis of cracks in anisotropic media.