圆形界面裂纹反平面问题的基本奇异解

本文研究反平面集中力作用下,不同弹性材料的圆形界面上有多条裂纹的问题。运用复变函数的解析延拓技术与奇性主部分析方法,首次获得该问题的一般解答,求出了几种典型情况的封闭解;算出了应力强度因子,并由此导出一系列特殊结果,其中几个与已有文献完全吻合。     

不同材料界面共圆弧裂纹的反平面问题

本文首次将不同弹性材料界面共圆弧裂纹版平面问题,化为解析函数边值问题,获得了一般解答,由此求出了几种典型情况的精确解,算出了应力强度因子。当两种材料相同时,本文结果与文[S]完全吻合。     

不同压电材料反平面应变状态的共圆弧界面裂纹问题

应用复变函数解析延展原理，并通过求解Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ问题，得到了含共圆弧界面裂纹系的压电材料反平面应变问题的一般解；对单个圆弧界面裂纹的情形，给出了封闭形式的复函数解和场强度因子     

压电材料反平面应变状态的椭圆夹杂及界面裂纹问题

本文采用共法求解了压电材料反平面变形的椭圆夹杂及界面裂纹问题，前者的解答表明当远场外力均匀分布对夹杂内的应力场及电位移场是常量，后者解答表明在界面裂纹的裂尖处，应力及电位移都具有γ＾－１／２的奇异性。     

压电介质平面问题的基本解

应用复变函数的方法,对于压电介质平面问题,分析导出了无限介质或半无限介质受任意 集中载荷作用时的复势函数基本解;这些结果可作为边界元法的基本解,以求解具有复杂边界压电体的平面问题。     

压电材料反平面界面裂纹的杂交元分析

基于奇异性电弹场数值特征解开发了一种新型反平面界面裂纹尖端单元。将新型单元与四节点压电P-S单元组装,求解从绝缘到导通的任意电边界条件下,压电结构反平面界面裂纹尖端电弹场的数值解。考察了层厚、载荷类型和裂纹面间电边界条件等对反平面界面裂纹尖端断裂参数的影响。算例证明新型单元能使P-S单元数显著降低,计算结果更为精确。     

压电介质平面问题的一般解和基本解

本文从压电介质平面问题基本方程出发，得到了含体积力的基本方程组的一般解。对状态方程进行Ｆｏｕｒｉｅｒ变换，由一般解得到Ｆｏｕｒｉｅｒ变换下状态方程的通解，对于单位集中力和单位点电荷情形，给出了压电介质平面问题各种情况下的有限形式的基本解。     

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     

功能梯度条共线Griffith裂纹反平面剪切冲击

研究正交各向异性功能梯度条中多个共线Griffith裂纹的反平面剪切冲击问题．材料两个方向的剪切模量假定按比例同时以特定的梯度变化．采用Laplace和Fourier变换及引进位错密度函数将问题化为求解Cauchy奇异积方程，进而化为代数方程数值求解．考查材料非均匀性、正交性和功能梯度条高度对裂尖动态断裂特性的影响．动应力强度因子的数值结果显示：增加剪切模量的梯度和(或)增加垂直于裂纹面方向的剪切模量，可以抑制动应力强度因子的幅度；若功能梯度条较薄，增大条形域的高度也可抑制裂纹扩展．     

压电材料反平面运动裂纹的能量释放率与分叉角

用复变函数方法,研究了压电材料中反平面运动裂纹的动态断裂问题,研究表明：介质内的耦合场与裂纹运动速度有关,在裂纹尖端有奇异。应力强度因子与裂纹运动速度无关,与纯弹性结构一致,沿裂纹延长线扩展的动态能量释放率可用应力强度因子表示,而与电载荷无关,裂纹运动的高速度具有止裂作用,在一定条件下,裂纹有扩展成曲线裂纹或分叉的趋势。     

压电材料中心裂纹问题

以电位移法向分量及电势连通过裂纹面为边界条件,对均匀电材料的裂纹问题及两种不同压材料界面裂纹问题进行了系统分析,得到了含中心裂纹无限大体封闭形的全场解。证实了裂纹引起的非均匀扰动场只信赖于外加场而外加电场无关。     

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.     

INVESTIGATION OF BEHAVIOR OF MODE-I INTERFACE CRACK IN PIEZOELECTRIC MATERIALS BY USING SCHMIDT METHOD

The behavior of a Mode-Ⅰinterface crack in piezoelectric materials was investigated under the assumptions that the effect of the crack surface overlapping very near the crack tips was negligible. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. It is found that the stress and the electric displacement singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials. The solution of the present paper can be returned to the exact solution when the upper half plane material is the same as the lower half plane material.     

ON THE PLANE PIEZOELECTRIC PROBLEM OF A LOADED CRACK TERMINATING AT A MATERIAL INTERFACE

The plane problem of a crack terminating at the interface of a bimaterial piezoelectric,and loaded on its faces, is treated. The emphasis is placed on how to transform this problem into anon-homogeneous Hilbert problem. To make the derivation tractable, the concept of the axial conju-gate is introduced and related to the complex conjugate. The angle between the crack line and the inter-face may be arbitrary. Numerical results are given to illustrate the stress singularity at crack tip.     

两种正交异性材料界面上裂纹冲击后的动态响应

本文研究了两种不同正交异性材料界面半无限长裂纹，在冲击荷载下的动态弹塑性响应。通过积分变换，Ｗｉｅｎｅｒ－Ｈｏｐｆ方法和Ｃａｇｎｉａｒｄ－ｄｅＨｏｏｐ反演围通技术，求得一般解析解，获得了该裂纹的动应力强度因子；通过采用Ｄｕｇｄａｌｅ模型，建立了裂纹尖端塑性区延伸速度与裂纹扩展速度的关系，以及动态ＣＯＤ与裂纹扩展速度的关系。     

FRACTURE ASSESSMENT OF AN INTERFACE CRACK BETWEEN TWO DISSIMILAR MAGNETOELECTROELASTIC MATERIALS UNDER HEAT FLOW AND MAGNETOELECTROMECHANICAL LOADINGS

A magnetoelectrically permeable interface crack between two semi-infinite magnetoelectroelastic planes under the action of a heat flow and remote magnetoelectromechanical loadings is considered, where the assumption of frictionless contact between two dissimilar halfplanes is adopted. Not only the solutions of the interface crack problem are presented in an explicit form, but also the general condition for the transition from a perfect thermal contact of two magnetoelectroelastic bodies to their separation is given.     

Anti-plane crack moving along the interface of dissimilar piezoelectric materials

The problem of an anti-plane Griffith crack moving along the interface of dissimilar piezoelectric materials is solved by using the integral transform technique. It is shown from the result that the intensity factors of anti-plane stress and electric displacement around the crack tip are dependent on the speed of the Griffith crack as well as the material coefficients. When the two piezoelectric materials are identical, the present result will be reduced to the result for the problem of an anti-plane moving Griffith crack in homogeneous piezoelectric materials. Supported by the National Natural Science Foundation and the National Post-doctoral Science Foundation of China.     

压电材料动态裂纹问题的奇异积分方程法

利用广义Betti-Rayleigh 互易公式给出了二维压电材料非渗透裂纹问题的一般解和奇异积分方程,其中未知函数为裂纹上的位移间断和电势间断的导数. 在理论分析的基础上,使用高斯-切比雪夫求积公式及Lubich 卷积积分方法建立了问题的数值求解方法,并给出典型算例的广义动应力强度因子随时间变化的规律.     

平面问题中弹性压电材料的本构关系及应用

本文在三维压电材料本构方程的基础上,推导出二维压电材料的机电耦合方程系统,并分析了受轴向力,弯矩作用时的位移和电势分布情况。     

各向异性压电材料平面裂纹的耦合场分析

用Stroh方法分析了各向异性压电材料电导通型裂纹问题的耦合场.结果表明,裂纹面上的切向电场强度和法向电位移均为常数,在裂纹尖端有由弹性场的耦合作用产生的奇异;电导通裂纹模型中的静电场对裂纹尖端扩展的能量释放率不作贡献.