非对称Ⅲ型界面裂纹扩展的动态问题

通过复变函数论的方法,对非对称Ⅲ型界面裂纹扩展的动态问题进行了研究.采用自相似函数的方法可以轻易地将所论问题转化为Riemann-Hilbert问题,并求得了裂纹坐标原点分别受到变载荷Pt/z,Px3/t2作用下的解析解的一般表达式.通过Muskhelishvili方法可以相当简单地得到问题的闭合解.利用这些解并采用叠加原理.可以求得任意复杂问题的解.     

运动变载荷作用下的非对称Ⅲ型界面裂纹的解析解

通过复变函数论的方法,对Ⅲ型非对称动态界面裂纹的扩展问题进行了研究.采用自相似函数的途径和利用相应的微分、积分运算,就可以很容易地获得解析解的一般表达式.应用该法可以迅速地将所讨论的问题转化为Riemann-Hilbert问题,并求得了运动变载荷ptn/xn、ptn 1/xn分别作用下Ⅲ型非对称动态界面裂纹解析解.利用这些解并采用叠加原理,就可以求得任意复杂问题的解.     

Ⅲ型界面裂纹面受变载荷Pxmtn作用下的自相似解

通过复变函数论的方法,对Ⅲ型界面裂纹表面受变载荷$Px^mt^n$作用下的动态扩 展问题进行了研究. 采用自相似函数的方法可以获得解析解的一般表达式. 应用 该法可以很容易地将所讨论的问题转化为Riemann-Hilbert问题, 然后应 用Muskhelishvili方法就可以较简单地得到问题的闭合解. 利用这些解 并采用叠加原理,就可以求得任意复杂问题的解.     

反平面动态扩展裂纹问题的研究

应用复变函数论，对反平面动态扩展裂纹问题进行了研究。通过自相似函数的方法可以获得若干问题的解析解。应用该法可以迅速地将所论问题转化为Riemann-Hilbert问题，并可以相当简单地得到问题的闭合解。通过叠加原理利用这些解，就可以求得任意复杂问题的解。     

Asymmetrical dynamic propagation problems on mode Ⅲ interface crack

By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approaches of self-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.     

动态扩展裂纹的若干反平面问题的研究

采用复变函数论,对反平面条件下的动态裂纹扩展问题进行研究。通过自相似函数的方法可以获得解析解的一般表达式。应用该法可以很容易地将所讨论的问题转化为Riemann—Hilbert问题,并可以相当简单地得到问题的闭合解。文中分别对裂纹面受均布载荷、坐标原点受集中增加载荷、坐标原点受瞬时冲击载荷以及裂纹面受运动集中载荷Px／t作用下的动态裂纹扩展问题进行求解,得到了裂纹扩展位移、裂纹尖端的应力和动态应力强度因子的解析解。应用该解并通过叠加原理,就可以求得任意复杂问题的解。     

界面裂纹非对称扩展模型

提出了一种新的复合材料结构中层间脱层裂纹扩展模型，该模型能够揭示裂纹扩展对裂纹左右尖端能量释放率的相对大小及界面材料性能的依赖性，能够比较真实地揭示复合材料结构层间脱层裂纹扩展复杂性的特点．     

正交异性复合材料界面上反平面动态自相似扩展裂纹问题的解

采用复变函数论的方法，对复合材料界面上的裂纹扩展问题进行研究。并根据任意的自相似指数的断裂动力学问题，进行自相似求解，导出解析解的一般表示。应用该法可以迅速地将所论问题转化为Riemann-Hil-bert问题，并可以相当简单地得到问题的闭合解。文中分别对裂纹中心受阶跃载荷，裂纹面受到瞬时脉冲载荷作用下的界面裂纹扩展问题进行求解。得到了裂纹的位移。尖端的应力和动态应力强度因子的解析解。应用该解并通过叠加原理。就可以很容易的求得任意复杂问题的解。     

界面裂纹尖端的动态奇异特性

本文研究了界面裂纹尖端的动态应力场的奇异特性.引入尖端无摩擦接触的界面裂纹模型并采用具有运动边界的控制积分方程.证明了在动态界面裂纹尖端仅存在平方根奇异的应力场.数值结果表明接触区中的正应力确保持为压应力.为表现界面裂纹的动态特性,给出了应力强度因子和裂纹面接触区尺寸的数值结果.     

Dynamic propagation problems concerning surfaces of asymmetrical mode III crack subjected to moving loads

With the theory of complex functions, dynamic propagation problems concerning surfaces of asymmetrical mode III crack subjected to moving loads are investigated. General representations of analytical solutions are obtained with self-similar functions. The problems can be easily converted into Riemann-Hilbert problems using this technique. Analytical solutions to stress, displacement and dynamic stress intensity factor under constant and unit-step moving loads on the surfaces of asymmetrical extension crack, respectively, are obtained. By applying these solutions, together with the superposition principle, solutions of discretionarily intricate problems can be found. Project supported by the Post-Doctoral Science Foundation of China (No. 2005038199) and the Natural Science Foundation of Heilongjiang Province of China (No. ZJG04-08)     

Asymmetrical dynamic propagation problems on mode III interface crack

By the application of the theory of complex functions, asymmetrical dynamic propagation problems on modeⅢinterface crack are studied. The universal representations of analytical solutions are obtained by the approaches of self-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.     

DYNAMIC PROPAGATION PROBLEM ON DUGDALE MODEL OF MODE Ⅲ INTERFACE CRACK

By the theory of complex functions, the dynamic propagation problem on Dugdale model of mode Ⅲ interface crack for nonlinear characters of materials was studied. The general expressions of analytical solutions are obtained by the methods of self-similar functions. The problems dealt with can be easily transformed into Riemann-Hilbert problems and their closed solutions are attained rather simply by this approach. After those solutions were utilized by superposition theorem, the solutions of arbitrarily complex problems could be obtained.     

Asymmetrical dynamic propagation problems on mode Ⅲ interface crack

By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approaches of serf-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.     

Singular fields of a mode III interface crack in a power-law hardening bimaterial

A high order of asymptotic solution of the singular fields near the tip of a mode III interface crack for pure power-law hardening bimaterials is obtained by using the hodograph transformation. It is found that the zero order of the asymptotic solution corresponds to the assumption of a rigid substrate at the interface, and the first order of it is deduced in order to satisfy completely two continuity conditions of the stress and displacement across the interface in the asymptotic sense. The singularities of stress and strain of the zeroth order asymptotic solutions are −1/(n ₁+1) and −n/(n ₁+1) respectively. (n=n ₁,n ₂ is the hardening exponent of the bimaterials.) The applicability conditions of the asymptotic solutions are determined for both zeroth and first orders. It is proved that the Guo-Keer solution^[10] is limited in some conditions. The angular functions of the singular fields for this interface crack problem are first expressed by closed form. The project supported by National Natural Science Foundation of China     

Dynamic propagation problems concerning surfaces of asymmetrical mode Ⅲ crack subjected to moving loads

With the theory of complex functions, dynamic propagation problems concerning surfaces of asymmetrical mode Ⅲ crack subjected to moving loads are investigated. General representations of analytical solutions are obtained with self-similar functions. The problems can be easily converted into Riemann-Hilbert problems using this technique. Analytical solutions to stress, displacement and dynamic stress intensity factor under constant and unit-step moving loads on the surfaces of asymmetrical extension crack, respectively, are obtained. By applying these solutions, together with the superposition principle, solutions of discretionarily intricate problems can be found.     

Mode III interface crack propagation in two joined media with weak dissimilarity and strong orthotropy

By application of the theory of complex functions, the analytical solutions are obtained for mode III interface crack that propagates along the interface of two joined media with weak dissimilarity and strong orthotropy. The Riemann–Hilbert problem is formulated. Several examples are given for different loadings on a moving crack. By superposition, the case of arbitrary loading can be obtained.