On the interaction between dislocations and cracks in one-dimensional hexagonal quasi-crystals

The solution of elasticity problems involving the interaction between dislocations and cracks plays a fundamental role in many practical and theoretical applications. Although elasticity problems involving dislocation or cracks in quasi-crystals have been investigated in many papers, the analysis is limited to a single defect. This paper investigates the interaction of defects in one-dimensional hexagonal quasi-crystals using the complex variable function method. The interaction force between two parallel dislocations is presented and the analytic solutions of elastic fields of interaction between a dislocation and a crack are obtained. A version of the well-known Peach－Koehler formula in one-dimensional hexagonal quasi-crystals is given.     

Plastic analysis of the crack problem in two-dimensional decagonal Al-Ni-Co quasicrystalline materials of point group 10,■

The fundamental plastic nature of the quasicrystalline materials remains an open problem due to its essential complicacy.By developing the proposed generalized cohesive force model,the plastic deformation of crack in point group 10,10 decagonal quasicrystals is analysed strictly and systematically.The crack tip opening displacement(CTOD) and the size of the plastic zone around the crack tip are determined exactly.The quantity of the crack tip opening displacement can be used as a parameter of nonlinear fracture mechanics of quasicrystalline material.In addition,the present work may provide a way for the plastic analysis of quasicrystals.     

A MODE-Ⅱ GRIFFITH CRACK IN DECAGONAL QUASICRYSTALS

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Non-equilibrium statistical theory about microscopic fatigue cracks of metal in magnetic field

This paper develops the non-equilibrium statistical fatigue damage theory to study the statistical behaviour of micro-crack for metals in magnetic field. The one-dimensional homogeneous crack system is chosen for study. To investigate the effect caused by magnetic field on the statistical distribution of micro-crack in the system, the theoretical analysis on microcrack evolution equation, the average length of micro-crack, density distribution function of micro-crack and fatigue fracture probability have been performed. The derived results relate the changes of some quantities, such as average length, density distribution function and fatigue fracture probability, to the applied magnetic field, the magnetic and mechanical properties of metals. It gives a theoretical explanation on the change of fatigue damage due to magnetic fields observed by experiments, and presents an analytic approach on studying the fatigue damage of metal in magnetic field.     

狭长体中非对称快速传播裂纹的分析解

用复变函数方法得到了弹性狭长体中含有一非对称半元限裂纹的动力学问题的分析解，当裂纹速度Ｖ→０时，此动力学的解可还原静力学的解，该问题Ｉ型与ＩＩ型静态与动态应力强度因子ＫＩ，ＫＩＩ得以确定，并且具有解析的形式。     

刚性电极夹持的压电陶瓷层中含Ⅲ型裂纹的解析解

分析了刚性电极所夹持的压电陶瓷层的中平面上含有Ⅲ型穿透裂纹的电弹性问题，利用积分变换和对偶积分方程方法，采用绝缘型和导电型裂纹两种假设，分别获得了有限长和半无限长裂纹的电弹性行为的精确解析解，并给出了相应的场强度因子和能量释放度。     

非线性断裂理论基本问题的精确分析解

用构造函数法对非线性断裂力学的基本问题——HRR问题作了严格的分析,给出了H问题与RR问题在数学上的等价性的证明,用统一的方法构造其精确分析解,证明了解的绝对一致收敛性和唯一性,取前3项作为近似,就得到优于Hutchinson数值解的结果,同时第1次提供了RR问题应力分布的具体结果.在N→1(n→1)情形,此解还原为线性弹性解,在N→0(n→∞)情形,此解还原为增量塑性理论中经典Prandtl场.     

一般变换下的Jacobi椭圆函数展开法及应用

将在行波变换下的Jacobi椭圆函数展开法推广到范围非常广泛的一般函数变换下进行，利用这一方法求得了一些非线性发展方程的精确周期解，这些解包括了在行波变换下所求得的周期解. 证明了一些非线性发展方程的周期解一定是行波解. 关键词： 非线性发展方程 周期解 行波解 Jacobi椭圆函数     

Periodic solutions of nonlinear Schro^edinger type equations

By using the solutions of an auxiliary elliptic equation, a direct algebraic method is proposed to construct the exact solutions of nonlinear Schrfdinger type equations. It is shown that many exact periodic solutions of some nonlinear Schro^edinger type equations are explicitly obtained with the aid of symbolic computation, including corresponding envelope solitary and shock wave solutions.     

八次对称二维准晶材料接触问题

本文通过引入位移函数和应用Fourier分析与对偶积分方程理论圆满解决了在一个刚性平头冲头作用下八次对称二维准晶材料的接触问题，得到了此材料接触问题应力与位移的解析表达式。结果表明，如果接触位移在接触区域内为一常数，则接触应力在接触边缘具有1／2阶奇异性，这为准晶材料的接触变形提供了重要的力学量。