THREE-DIMENSIONAL INTERACTIONS OF A HALF-PLANE CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

I. INTRODUCTIONBecause of the widespread application and intrinsic brittleness of piezoelectric ceramics, significantattention is being paid to the crack problems of piezoelectric ceramics. The last decade has seen a lotof three-dimensional studies of crack in piezoelectric ceramics[1??9]. In addition, the electroelastic fieldin a transversely isotropic piezoelectric space with a half-plane crack subjected to symmetric normalpoint forces, antisymmetric tangential point forces and point ch…     

THREE-DIMENSION INTERACTIONS OF CIRCULAR CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

Exact solutions in form of elementary functions were derived for the stress and electric displacement intensity factors of a circular crack in a transversely isotropic piezoelectric space interacting with various stress and charge sources: force dipoles, electric dipoles, moments, force dilatation and rotation. The circular crack includes penny-shaped crack and external circular crack and the locations and orientations of these resultant sources with respect to the crack are arbitrary. Such stress and charge sources may model defects like vacancies, foreign particles, and dislocations. Numerical results are presented at last.     

横观各向同性三维热弹性力学通解及其势理论法

通过引入两个位移函数，对用位移表达的运动平衡方程作了简化．利用算子理论，严格地导出了横观各向同性非耦合热弹性动力学问题的通解．对于静力学问题，通解的形式可进一步简化成用4个准调和函数来表示．具体考察了横观各向同性体内平面裂纹上下表面有对称分布温度作用的问题，推广了势理论方法，导出了一个积分方程和一个微分-积分方程．针对币状裂纹表面受均布温度作用情形，给出了具体的解。     

复合型运动荷载作用下横观各向同性体三维裂纹的应力强度因子

讨论横观各向同性体中含一半平面裂纹,在裂纹面上作用有运动点荷载的三维复合型应力强度因子历史.通过积分变换技术,最终将问题归结为求解Wiener-Hopf型积分方程组.该文给出了求解这一类积分方程组的一般性方法.在此基础上,基于Abel定理和Cagniard-de H oop方法,求得了Ⅱ、Ⅲ型复合应力强度因子的解析解.最后通过数值结果揭示了横观各向同性材料三维裂纹尖端场的动态特性.     

横观各向同性压电材料中裂纹问题的边界元法

采用Somigiliana公式给出了三维横观各向同性压电材料中的非渗漏裂纹问题的一般解和超奇异积分方程,其中未知函数为裂纹面上的位移间断和电势间断．在此基础上,使用有限部积分和边界元结合的方法,建立了超奇异积分方程的数值求解方法,并给出了一些典型数值算例的应力强度因子和电位移强度因子的数值结果,结果令人满意．     

横观各向同性层状场地对环形简谐荷载的位移响应

本文采用横观各同性层状粘弹性模型拟半空间上之的层状场地,用阻尼器取代其下部的半空间以吸收振动能量。     

含刚性线夹杂及裂纹的各向异性压电材料耦合场分析

采用各向异性弹性力学中Ｓｔｒｏｈ方法对含刚性线夹杂及裂纹的无限大各向异性压电材料耦合的弹性场和电场进行了分析。并得到夹杂和基体界面间耦合场的实型显函表达式及夹杂尖端的１／２阶奇异性。     

横观各向同性圆柱体自由振动的弹性力学解

本文由横观各向同性的弹性力学方程出发，研究有限长圆柱体的自由振动问题。利用文献「１」的通解，将位移分量和应力分量分别表达成傅里叶－塞尔级数和双曲－贝塞尔级数的形式。通过边界条件和级数的正交关系，得到关于有限长圆柱自由振动频率的特征方程。利用数值方法求解特征根，从而得到圆柱体三维振动的自振频率。     

THE PERIODIC CRACK PROBLEM IN BONDED PIEZOELECTRIC MATERIALS

The problem of a periodic array of parallel cracks in a homogeneous piezoelectric strip bonded to a functionally graded piezoelectric material is investigated for inhomogeneous continuum.It is assumed that the material inhomogeneity is represented as the spatial varia- tion of the shear modulus in the form of an exponential function along the direction of cracks. The mixed boundary value problem is reduced to a singular integral equation by applying the Fourier transform,and the singular integral equation is solved numerically by using the Gauss- Chebyshev integration technique.Numerical results are obtained to illustrate the variations of the stress intensity factors as a function of the crack periodicity for different values of the material inhomogeneity.     

压电材料裂纹顶端条状电饱和区模型的力学分析

在线性压电本构方程框架下,对裂纹顶端条状电饱和区模型进行了严格的数学分析．完整地考虑了各向异性力电耦合效应．建立了电饱和区尺寸与外加电场的依赖关系．证实了当裂纹垂直极化轴时,压电材料的断裂应力随着外加正电场的增加而减小,随着外加负电场的增加而增加．当裂纹平行于极化轴时,与极化轴平行的外加电场对断裂应力无影响     

THE BASIC SOLUTION OF A 3-D RECTANGULAR PERMEABLE CRACK IN A PIEZOELECTRIC/PIEZOMAGNETIC COMPOSITE MATERIAL

The solution of a 3-D rectangular permeable crack in a piezoelectric/piezomagnetic composite material was investigated by using the generalized Almansi’s theorem and the Schmidt method.The problem was formulated through Fourier transform into three pairs of dual integral equations,in which the unknown variables are the displacement jumps across the crack surfaces.To solve the dual integral equations,the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials.Finally,the relations between the electric filed,the magnetic flux field and the stress field near the crack edges were obtained and the efects of the shape of the rectangular crack on the stress,the electric displacement and magnetic flux intensity factors in a piezoelectric/piezomagnetic composite material were analyzed.     

偏心裂纹板在裂纹面受一对集中拉应力作用时弹塑性解析解

利用裂纹线场方法对理想弹塑性材料偏心裂纹板在裂纹面受一对集中拉力问题进行了弹塑性分析,并且获得了理论解.这个解包括:裂纹线附近弹塑性边界上的单位法向矢量,裂纹线附近的弹塑性解析解、最大塑性区长度、裂纹线上的塑性区长度随荷载的变化规律及其承载力.该分析不受小范围屈服假设的限制,并且不附加假使条件.结果在裂纹线附近足够精确.     

压电材料裂纹顶端条状电饱和区模型的力学分析

在线性压电本构方程框架下,对裂纹顶端条状电饱和区模型进行了严格的数学分析．完整地考虑了各向异性力电耦合效应．建立了电饱和区尺寸与外加电场的依赖关系．证实了当裂纹垂直极化轴时,压电材料的断裂应力随着外加正电场的增加而减小,随着外加负电场的增加而增加．当裂纹平行于极化轴时,与极化轴平行的外加电场对断裂应力无影响     

横观各向同性饱和层状地基的三维稳态动力响应

首先引入状态向量,将直角坐标系下横观各向同性饱和土的Biot波动方程转化为一组状态方程,然后基于双重Fourier变换,求解了状态方程,得到传递矩阵.进而利用传递矩阵,并结合饱和地基的边界条件、排水条件及层间接触和连续条件,求解了横观各向同性饱和层状地基的稳态动力响应问题.     

受有集中力的样条边界元法

本文应用Ｂｅｔｔｉ定理，建立弹性体边界和体内受有有限个集中力时的样条边界积分方程，将集中力的影响表征为边界积分方程中的自由项，从客观实际出发，对具有两套奇性交会的积分方程给出一种方便有效的处理方法，使得集中力下的边界元法得以实施，在样插值基础上，即使稀疏剖分也能给出很高精度的位移场。应力场和未知集中反力。     

压电陶瓷中圆币形裂纹在横向剪力下的机－电耦合行为

以弹性位移分量和电势函数为基本未知量时，横观各向同性压电介质三维问题的场方程可化为四个联立的二阶线性偏微分方程组，本文导出了用四个调和函数表示位移分量及电势函数的表达式，即得到了该场方程的势函数通解，作为通解的应用举例，文中求解了圆币形裂纹受横向剪切作用的问题，得到了裂尖附近应力场及电位移场的解析表达式，结果表明，在横向剪切载荷下圆币形裂纹的尖端场及应力、电位移强度因子均具有明显的机－电耦合性质，而应力和电位移分量在裂尖仍具有－１／２的奇异性。     

ANALYSIS OF THE DYNAMIC BEHAVIOR OF A GRIFFITH PERMEABLE CRACK IN PIEZOELECTRIC MATERIALS WITH THE NON-LOCAL THEORY

The dynamic behavior ofa Griffith permeable crack under harmonic anti-plane shearwaves in the piezoelectric materials is investigated by use of the non-local theory.To overcome themathematical difficulties,a one-dimensional non-local kernel is used instead of a two-dimensionalone for the anti-plane dynamic problem to obtain the stress and the electric displacement near thecrack tips.By means of Fourier transform,the problem can be solved with a pair of dual integralequations that the unknown variable is the jump of the displacement across the crack surfaces.These equations are solved with the Schmidt method and numerical examples are provided.Con-trary to the previous results,it is found that no stress and electric displacement singularities arepresent at the crack tip.The finite hoop stress and the electric displacement depend on the cracklength,the lattice parameter of the materials and the circle frequency of the incident waves.Thisenables us to employ the maximum stress hypothesis to deal with fracture problems in a naturalway.     

ANALYSIS OF DAMAGE NEAR A CONDUCTING CRACK IN A PIEZOELECTRIC CERAMIC

The finite element formulation for analyzing static damage near a conducting crack in a thin piezoelectric plate is established from the virtual work principle of piezoelectricity. The damage fields under various mechanical and electrical loads are calculated carefully by using an effective iterative procedure. The numerical results show that all the damage fields around a crack tip are fan-shaped and the electric field applied has great influence on the mechanical damage,which is related to the piezoelectric properties.     

不均匀裂纹体疲劳裂纹扩展的实验研究和分析

本文提出了裂纹在硬区的软对硬不均匀裂纹体的力学分析模型.疲劳实验研究表明,这种不均匀性影响疲劳裂纹扩展速率.文中的疲劳载荷下不均匀裂纹体的边界元数值计算结果表明,随着疲劳裂纹的扩展,在相同扩展步下,裂纹距软硬区界面越近,裂纹张开位移的幅值△COD 越小,J 积分幅值△J 亦越小.不均匀性对疲劳裂纹扩展速率的影响,主要通过影响△J 来实现.裂纹与软硬区界面的距离越近,疲劳裂纹扩展速率越小.     

压电材料平面应力状态的直线裂纹问题一般解

研究了含直线裂纹系的压电材料平面应力问题单个裂纹和双裂纹问题的封闭解答表明，在裂纹尖端，应力、电场强度和电位移有１／２阶的奇异性并与前人结果比较了产生电场奇异性的物理因素