单裂纹问题的虚边界无网格伽辽金法分析

使用含裂纹复变基本解,虚边界无网格伽辽金法被进一步推广应用于弹性材料的单裂纹问题求解.为了清晰地说明单裂纹问题的虚边界元法实现过程,单裂纹问题的虚边界元法示意图、复变坐标平面下含裂纹问题的复变位移和复变面力基本解示意图被展示.含裂纹复变基本解,因自动满足裂纹处边界条件,故使用虚边界无网格伽辽金法计算单裂纹问题,无需在裂纹处布置节点或单元.给出含裂纹复变基本解中的Φ'(x)的详细表达式、裂纹左右裂尖应力强度因子的虚边界无网格离散公式,方便了其他学者使用本方法计算裂纹问题.数值计算两端受拉长方形钢板中心含有裂纹的应力强度因子的算例,计算结果证明了本方法的精确性与稳定性.     

双材料界面裂纹平面问题的半权函数法

应用半权函数法求解双材料界面裂纹的平面问题．由平衡方程、应力应变关系、界面的连续条件以及裂纹面零应力条件推导出裂尖的位移和应力场,其特征值为lambda及其共轭．设置特征值为lambda的虚拟位移和应力场,即界面裂纹的半权函数A·D2由功的互等定理得到应力强度因子KⅠ和KⅡ以半权函数与绕裂尖围道上参考位移和应力积分关系的表达式．数值算例体现了半权函数法精度可靠、计算简便的特点．     

幂函数型曲线裂纹平面问题的一般解

通过构造一个新的、精确的和通用的保角映射,利用Muskhelishvili复势法研究了任意自然数次幂的幂函数型曲线裂纹的平面弹性问题,给出了远处受单向拉伸载荷下裂纹尖端Ⅰ型和Ⅱ型应力强度因子的一般解．当幂次取不同的自然数时,可以退化为若干已有的结果．通过数值算例,讨论了幂函数型曲线裂纹的系数、幂次及在x轴上的投影长度对Ⅰ型和Ⅱ型应力强度因子的影响规律．     

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.     

八次对称二维准晶Ⅱ型单边裂纹的动力学问题

依据准晶弹性-流体动力学模型,采用有限差分方法,探讨了八次对称二维准晶Ⅱ型单边裂纹的动力学问题.首先分析了相同载荷的不同加载时间、不同的加载位置以及不同的试样尺寸对裂纹尖端处声子场应力强度因子的影响;其次分析了不同的声子场相位子场耦合弹性常数对相位子场位移分量的影响;最后分析了板端加载与裂纹面加载对动态应力强度因子的影响.计算结果表明:大小相同的脉冲载荷,加载的时间越长,无量纲化的应力强度因子越大,其曲线逐渐趋近于阶跃载荷下的曲线;试样宽度越宽,应力强度因子由零到非零需要的时间越长,无量纲化的应力强度因子值越小,说明应力强度因子与试样的尺寸有关系;声子场相位子场耦合弹性常数越大相位子场的位移分量也越大,这是因为相位子场的边界没有载荷,相位子场位移的作用力来自声子场,声子场起主导作用;而裂纹面加载和板端加载是不等价的,前者的无量纲化应力强度因子的变化幅度比后者大,这与板端加载更容易导致材料断裂的事实相一致.     

Ⅱ型平面动力裂纹线场的弹塑性精确解

本采用线场分析方法对理想弹塑性Ⅱ型平面应力裂纹裂纹线附近的应力场及弹塑性边界进行了精确分析，本完全放弃了小范围屈服条件，探讨了弹塑性边界上弹塑性应力场匹配条件的正确提法，通过将裂纹线附近塑性区应力场的通解（而不是过去采用的特解）与弹性应力场的精确解（而不是通常的裂尖应力强度因子Ｋ场）在裂纹线附近的弹塑性边界上匹配，本得出了塑性区应力场，塑性区长度及弹塑性边界的单位法向量在裂纹线附近的足够精确     

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．     

Ⅱ型平面应力裂纹线场的弹塑性精确解

本文采用线场分析方法对理想弹塑性Ⅱ型平面应力裂纹裂纹线附近的应力场及弹塑性边界进行了精确分析。本文完全放弃了小范围屈服条件,探讨了弹塑性边界上弹塑性应力场匹配条件的正确提法,通过将裂纹线附近塑性区应力场的通解(而不是过去采用的特解)与弹性应力场的精确解(而不是通常的裂尖应力强度因子K场)在裂纹线附近的弹塑性边界上匹配,本文得出了塑性区应力场,塑性区长度及弹塑性边界的单位法向量在裂纹线附近的足够精确的表达式。     

裂纹问题的非局部弹性力学分析

求解并给出非局部弹性力学平面问题的单位集中不连续位移基本解,基于这些基本解和经典弹性力学中的不连续位移边界积分方程＿边界元方法,提出了一种非局部弹性力学平面问题的一般解法·利用该解法,研究分析了Ｇｒｉｆｉｔｈ裂纹、边缘裂纹等断裂力学中基本的但又很重要的问题·结果表明,裂纹前沿的应力集中系数与裂纹长度有关,给出了裂纹长度对断裂韧性ＫⅠｃ的影响·所得结果与已有实验结果一致·     

剪切载荷作用下含损伤胶接材料界面动应力强度因子的研究

主要针对剪切载荷作用下,胶接材料接合区域界面裂纹尖端动态应力强度因子进行了分析,其中考虑了裂尖区域的损伤．通过积分变换,引入位错密度函数,奇异积分方程被简化为代数方程,并采用配点法求解;最后经过Laplace逆变换,得到动态应力强度因子的时间响应．Ⅱ型动应力强度因子随着黏弹性胶层的剪切松弛参量、弹性基底的剪切模量和Poisson比的增加而增大;随膨胀松弛参量的增加而减小．损伤屏蔽发生在裂纹扩展的起始阶段．裂纹尖端的奇异性指数(-0.5)是与材料参数、损伤程度和时间无关的,而振荡指数由黏弹性材料参数控制．     

A boundary element analysis for stress intensity factors of multiple circular arc cracks in a plane elasticity plate

In this paper, a numerical approach for analyzing interacting multiple cracks in infinite linear elastic media is presented. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks, the original problem is divided into a homogeneous problem (the one without cracks) subjected to remote loads and a multiple crack problem in an unloaded body with applied tractions on the crack surfaces. Thus, the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements proposed recently by the author. Test examples are given to illustrate that the numerical approach is very accurate for analyzing interacting multiple cracks in an infinite linear elastic media under remote uniform stresses. In addition, the displacement discontinuity method with crack-tip elements is used to analyze a multiple crack problem in a finite plate. It is found that the boundary element method is also very accurate for investigating interacting multiple cracks in a finite plate. Specially, a generalization of Bueckner’s principle and the displacement discontinuity method with crack-tip elements are used to analyze multiple circular arc crack problems in infinite plate in tension (including: Two Collinear Circular Arc Cracks, Three Collinear Circular Arc Cracks, Two Parallel Circular Arc Cracks, Three Parallel Circular Arc Cracks and Two Circular Arc Cracks) in a plane elasticity plate. Many results are given.     

Multiple crack fatigue growth modeling by displacement discontinuity method with crack-tip elements

This paper presents a numerical approach for modeling multiple crack fatigue growth in a plane elastic infinite plate. It involves a generation of Bueckner’s principle, a displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author and an extension of Paris’ law to a multiple crack problem under mixed-mode loading. Because of an intrinsic feature of the boundary element method, a general multiple crack growth problem can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. Fatigue growth modeling of an inclined crack in an infinite plate under biaxial cyclic loads is taken into account to illustrate the effectiveness of the present numerical approach. As an example, the present numerical approach is used to study the fatigue growth of three parallel cracks with same length under uniaxial cyclic load. Many numerical results are given.     

Interaction of multiple cracks in a rectangular plate

This paper is concerned with interaction of multiple cracks in a finite plate by using the hybrid displacement discontinuity method (a boundary element method). Detail solutions of the stress intensity factors (SIFs) of the multiple-crack problems in a rectangular plate are given, which can reveal the effect of geometric parameters of the cracked body on the SIFs. The numerical results reported here illustrate that the boundary element method is simple, yet accurate for calculating the SIFs of multiple crack problems in a finite plate.     

A new boundary element technique for solving plane problems of linear elasticity: improved theory and an application to fracture mechanics

An improved boundary element method for solving plane problems of linear elasticity theory is described. The method is based on the Muskhelishvili complex variable representation for the displacement and stress fields. The paper shows how to take account of symmetry about the x and/or y axes.The potential accuracy of the method is illustrated by its application to the calculation of stress intensity factors associated with cracks in both a square and a circular plate. The crack problem is solved using a Gauss-Chebyshev representation of a singular integral equation by a set of linear algebraic equations. The integral equation involves an analytic function which takes account of the presence of the external boundary. This function is determined directly using the boundary element method.Numerical results are believed to be more accurate than the existing published values which are quoted to four significant figures.     

Analysis of arbitrarily shaped planar cracks in two-dimensional hexagonal quasicrystals with thermal effects. Part I: Theoretical solutions

An extended displacement discontinuity (EDD) boundary integral equation method is proposed for analysis of arbitrarily shaped planar cracks in two-dimensional (2D) hexagonal quasicrystals (QCs) with thermal effects. The EDDs include the phonon and phason displacement discontinuities and the temperature discontinuity on the crack surface. Green's functions for unit point EDDs in an infinite three-dimensional medium of 2D hexagonal QC are derived using the Hankel transform method. Based on the Green's functions and the superposition theorem, the EDD boundary integral equations for an arbitrarily shaped planar crack in an infinite 2D hexagonal QC body are established. Using the EDD boundary integral equation method, the asymptotic behavior along the crack front is studied and the classical singular index of 1/2 is obtained at the crack edge. The extended stress intensity factors are expressed in terms of the EDDs across crack surfaces. Finally, the energy release rate is obtained using the definitions of the stress intensity factors.     

有一条裂纹的圆形焊接问题

本文讨论了在带圆孔的无限平面中焊接一个不同材料的带裂纹的近似圆板的问题.该问题化为求解解析函数边值问题然后又转化为求解沿裂纹的奇异积分方程.后者的数字解法也已给出.文末并对Ⅰ型、Ⅱ型情况得出了应力强度因子的公式以及数字结果.     

On magnetoelastic problems of a plane with an arbitrarily shaped hole under stress and displacement boundary conditions

An analytical method for the static plane problem of magnetoelasticityis developed for an infinite plane containing a hole of arbitraryshape under stress and displacement boundary conditions in aprimary uniform magnetic field. The magnetic field influencesthe elastic field by introducing a body force called the Lorentzponderomotive force in the equilibrium equations. The body forcecan be further described in a form relating with the electromagneticstress tensor. The complex variable method in conjunction withthe rational mapping function technique is used in the analysisfor both magnetic field and mechanical field. Governing equationsand boundary conditions are expressed in terms of complex functions.Complex magnetic potential and stress functions are obtainedusing Cauchy integrals for the paramagnetic and soft ferromagneticmaterials, respectively. The distributions of magnetic fieldand the stress components are shown for certain directions ofprimary magnetic fields in an infinite plane with a square hole,as an example. It is found that the stress distributions forthe two types of materials are identical despite the differenceof magnetic fields. The extreme cases of a free and a fixedhole reduced to a crack and a rigid fibre, respectively, arealso investigated. The stress intensity factors at the tipsof crack and rigid fibre are computed, and their variation forcertain directions of primary magnetic field is shown.     

Boundary collocation method for a cracked rectangular plate with double external tension

In this article, the boundary collocation method is employed to investigate the problems of a central crack in a rectangular plate which applied double external tension on the outer boundary under the assumption that the dimensions of the plate are much larger than that of the crack. A set of stress functions has also been proposed based on the theoretical analysis which satisfies the condition that there is no external force on the crack surfaces. It is only necessary to consider the condition on the external boundary. Using boundary collocation method, the linear algebra equations at collocation points are obtained. The least squares method is used to obtain the solution of the equations, so that the unknown coefficients can be obtained. According to the expression of the stress intensity factor at crack tip, we can obtain the numerical results of stress intensity factor. Numerical experiments show that the results coincide with the exact solution of the infinite plate. In particular, this case of the double external tension applied on the outer boundary is seldom studied by boundary collocation method.     

Mathematical model for crack arrest of an infinite plate weakened by a finite and two semi-infinite cracks

The problem of an unbounded plate weakened by three quasi-static coplanar and collinear straight cracks: two semi-infinite cracks and a finite crack situated symmetrically between two semi-infinite cracks, is investigated. The plate is subjected to uniform unidirectional in-plane tension at infinite boundary. Developed plastic zones are arrested by distributing cohesive yield point stress over their rims. The solution is obtained using complex variable technique. Closed form analytic expressions are derived for load bearing capacity and crack-tip-opening displacement (CTOD). A case study is presented for CTOD and load bearing capacity versus crack length, plastic zone length and inter-crack distance etc. Results are presented graphically and analyzed.     

Stress Concentration in an Anisotropic Half Space with Cylindrical Cavities and Plane Cracks

A method is proposed for determining the two-dimensional stressed state of a half space with a general rectilinear anisotropy. General representations of the complex potentials are obtained and studied, as well as expressions for the stresses and displacements, along with the boundary conditions for determining these functions. As an example, we solve for the stressed state of and calculate the stress intensity factors for a half plane (in the presence of a single elastic symmetry plane) with a circular (elliptical) hole and edge cracks. It is shown how the crack length, the closeness of a hole with a crack to the boundary, and the anisotropy of the material affect the stress concentration and stress intensity factors.