承受弯曲板断裂问题的特征根

把Rekner型平板裂纹尖端位移场展开式推广到任意切口、任意边界的多材料问题．证明了Reissner型平板断裂问题的特征根等价于相类似的反平面切口问题和平面切口问题两部分的特征根迭加．     

中厚扁壳断裂问题的特征根及特征函数

证明了含任意切口、任意切口边界的多材料中厚扁壳问题的特征根等于相应的平面切口问题和平板弯曲切口问题两部分的特征根组合。进而证明了中厚扁壳切口问题的特征根等于相应反平面切口问题和平面切口问题的组合。中厚扁壳切口问题的特征根及其对应的0级特征函数均可直接按相应的两类基本问题（反平面切口问题和平面切口问题）进行求解。     

二维切口问题完备特征解的研究现状与进展

简要回顾和介绍了文献中常见的几种求解二维切口问题特征根的方法,评述这些方法 的特点及其求解范围．重点介绍了在求解二维切口问题完备特征根方面的一些进展,包括特征 根的求解方法、特征根的重根探讨以及相应的特征函数计算,这一问题基本上得到了解决．为 基于特征展开研究二维断裂问题打下了基础．     

多材料反平面断裂问题特征值的超逆幂迭代求解

从反平面切口问题的特征方程入手，采用换元逆幂迭代法并利用特征函数解析表达式已知及一些有效技巧研究了可以精确有效地求解具有任意张角、多种不同材料及不同边界条件的反平面切口问题的完备特征解的求解方法。     

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。     

一种求解方管稳定性问题的简化方法

采用材料力学中的平面弯曲理论、以及弹性理论中平面应力问题和平面应变问题的转换关系，分析方管在均匀外压作用下的变形、临界压力和应力，得到了方管最大变形、临界压力和最大应力的求解公式．运用有限元分析软件Marc建立有限元模型，分析了方管在外压作用下的变形、临界压力和应力情况．分析结果表明，最大应力出现在凹角处，最大位移出现在各面的中截面处，并将有限元解与本文解作比较，从而验证文本解的正确性．     

反平面断裂问题的无单元伽辽金比例边界法

将比例边界法与无单元伽辽金法相结合,建立了反平面断裂分析的无单元伽辽金比例边界法。这是一种边界型无网格法,在环向方向上采用无单元伽辽金法进行离散,因此计算时仅需要边界上的节点信息,不需要边界元所要求的基本解。为了便于施加本质边界条件,通过建立节点值和虚拟节点值之间的关系给出了修正的移动最小二乘形函数。在径向方向上,该方法利用解析的方法求解,因此是一种半解析的数值方法。最后,给出了数值算例,并验证了所提方法后处理简单和计算精度高的特点,适合于求解反平面断裂问题。     

单向复合材料纤维断裂对局部应力集中的影响

本文采用剪切滞后理论，对单向辅设的增强复合材料中，纤维根数有限时纤维断裂所引起的局部应力集中的进行研究，确证了以往研究中假定纤维无限根的可行性，并定量展示了在断裂纤维和邻近纤维中的应力重分布。     

双周期裂纹压电材料反平面剪切问题断裂力学分析

研究压电材料双周期裂纹反平面剪切与平面电场作用的问题．运用复变函数方法，获得了该问题严格的闭合解，并由此给出了裂纹尖端应力强度因子和电位移强度因子的精确公式．数值算例显示了裂纹分布特征对材料断裂行为的重要影响．叠间小裂纹能够对主裂纹的应力和电位移场起着屏蔽作用，相反行间小裂纹却起着放大作用，至于钻石形分布裂纹的影响规律则更为复杂．对于某些特殊情形给予了解答并导出一系列有意义的结果。     

不同压电介质界面上的反平面运动裂纹

利用积分变换技术,得到不同压电介质界面上的平面运动裂纹问题的分析解。结果表明应力及电位移强度因子均与界面裂纹扩展速度及材料参数相关,这不同于均匀压电介质中运动裂纹的结论,当两种压电介质完全相同时,本文结果将退化为均匀压电介质中反平面运动裂纹问题的解。     

ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｅｔｏｔｈｅｉｎｔｒｉｎｓｉｃｃｏｕｐｌｉｎｇｃｈａｒａｃｔｅｒｉｓｔｉｃｓｂｅｔｗｅｅｎｅｌｅｃｔｒｉｃａｎｄｅｌａｓｔｉｃｂｅｈａｖｉｏｒｓ,ｔｈａｔｉｓ,ａｐｐｌｉｅｄｍｅｃｈａｎｉｃａｌｌｏａｄｉｎｇｐｒｏｄｕｃｅｓｅｌａｓｔｉｃｄｅｆｏｒｍａｔｉｏｎ ,ａｓｗｅｌｌａｓｅｌｅｃｔｒｉｃｆｉｅｌｄ ,ａｎｄｃｏｎｖｅｒｓｅｌｙｅｌｅｃｔｒｉｃｆｉｅｌｄｃａｎｇｉｖｅｒｉｓｅｔｏｅｌａｓｔｉｃｄｅｆｏｒｍａｔｉｏｎ ,ｐｉｅｚｏｅｌｅｃｔｒｉｃｍａｔｅｒｉａｌｓｈａｖｅ…     

Electroelastic field for an impermeable anti-plane shear crack in a piezoelectric ceramics plate

Electroelastic behavior of a cracked piezoelectric ceramics plate subjected to four cases of combined mechanical-electrical loads is analyzed. The integral transform method is applied to convert the problem involving an impermeable anti-plane crack to dual integral equations. Solving the resulting equations, the explicit analytic expressions for electroelastic field along the crack line and the intensity factors of relevant quantities near the crack tip and the mechanical strain energy release rate are obtained. The known results for an infinite piezoelectric ceramics plane containing an impermeable anti-plane crack are recovered from the present results only if the thickness of the plate h → ∞. Biography: LI Xian-fang (1964-)     

Rectangular tensile sheet with a center notch root crack

This paper deals with the rectangular tensile sheet with a center notch crack. Such a crack problem is called a center notch crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, two center notch models are analyzed in detail. By changing the geometrical forms and parameters of the center notch, and by comparing the SIFs of the center notch crack problem with those of the center cracked plate tension specimen (CCT), which is a model frequently used in fracture mechanics, the effect of the geometrical forms and parameters of the center notch on the stress intensity factors (SIFs) of the center cracked plate tension specimen, is revealed. Some geometric characterestic parameters are introduced here, which are used to formulate the notch length and the branch crack length, which are to be determined in mechanical machining of the center cracked plate tension specimen. So we can say that the geometric characterestic parameters and the formulae used to determine the notch length and the branch crack length presented in this paper perhaps have some guidance role for mechanical machining of the center cracked plate tension specimen. In addition, the numerical investigation proves that the conventional angular notched specimen is much less sensitive to the size of notch than is the circular notched specimen.     

A MIXED ELECTRIC BOUNDARY VALUE PROBLEM FOR AN ANTI－PLANE PIEZOELECTRIC CRACK

The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation. The crack face is partly conductive and partly impermeable. The results show that the stress intensity factor is identical with the mode III stress intensity factor independent of the conducting length. But the electric field and the electric displacement are dependent on the electric boundary conditions on the crack faces and are singular not only at the crack tips but also at the junctures between the impermeable part and conducting portions.     

Out-of-plane interface cracks in dissimilar piezoelectric materials

Summary This paper investigates the problem of an anti-plane interfacial crack between two dissimilar piezoelectric material layers. A single crack is first considered. The effect of interaction of two collinear cracks in the medium on the field intensity factors is investigated. The solutions of several particular cases, including an infinite piezoelectric bi-material and a piezoelectric material bonded to an elastic medium, are given. The bi-material constants governing the behavior of the crack tip fields are identified. By considering the crack as a notch of finite thickness, it is shown that the thickness of the notch has a pronounced influence on the crack tip field. The results for the assumption of a permeable crack represent the limit case where the notch thickness is reduced to zero.BLW would like to thank the National Science Foundation of China (#10102004) and the City University of Hong Kong (DAG #7100219) for the support of this work. YGS also thanks the Multidiscipline Scientific Research Foundation Project (HIT. MD 2001. 39) of the Harbin Institute of Technology and the SRF for ROCS, SEM.accepted for publication 3 April 2003     

Dynamic fracture behaviors of cracks in a functionally graded magneto-electro-elastic plate

In this paper the dynamic anti-plane problem for a functionally graded magneto-electro-elastic plate containing an internal or an edge crack parallel to the graded direction is investigated. The crack is assumed to be magneto-electrically impermeable. Integral transforms and dislocation density functions are employed to reduce the problem to Cauchy singular integral equations. Field intensity factors and energy release rate are derived, analyzed and partially calculated numerically. The effects of material graded index, loading combination parameter (including size and direction) and geometry criterion of the plate on the dynamic energy release rate are shown graphically. Numerical results indicate that increasing the graded index can all retard the crack extension, and that both the applied magnetic field loadings and electric field loadings play a dominant role in the dynamic fracture behaviors of crack tips.     

功能梯度压电板条中电绝缘型运动裂纹的电弹性场

基于三维弹性理论和压电理论，对材料系数按指数函数规律分布的功能梯度压电板条中的反平面运动裂纹问题进行了求解。利用Fourier积分变换方法将电绝缘型运动裂纹问题化为对偶积分方程，并进一步归结为易于求解的第二类Fredholm积分方程。通过渐近分析，获得了裂纹尖端应力、应变、电位移和电场的解析解，给出了裂纹尖端场各个变量的角分布函数，并求得了裂纹尖端场的强度因子，分析了压电材料物性梯度参数、几何尺寸及裂纹运动速度对它们的影响。结果表明，对于电绝缘型裂纹，功能梯度压电板条中运动裂纹尖端附近的各个场变量都具有-1／2阶的奇异性；当裂纹运动速度增大时，裂纹扩展的方向会偏离裂纹面。