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。     

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.     

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$Pt/ x$, $Px^3 /t^2$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.      

复合材料桥纤维拔出的动态裂纹模型

在无限大正交各向异性体弹性平面上对复合材料桥纤维平行自由表面的内部中央裂纹提出了桥纤维拔出的动态裂纹模型。通过复变函数将其转化为Reimann-Hilbert混合边界值问题。求得了裂纹在坐标原点受载荷Px/t、Px2/t作用的解析解。利用这一解析解可通过迭加原理求得任意复杂问题的解。     

界面超高速自相似动态分层分析：反平面情况

对材料界面超高速自相似动态分层的反平面问题进行了解析分析。分层模拟为界面裂纹由零长度自相似扩展，扩展速度为蹭音速或超音速。首先考虑运动集中载荷作用下界面动态分层的情况，利用界面裂纹自相似扩展的运动位错模型将问题归结为奇异积分方程，并求得解析解，分析了裂纹尖端的应力奇性，获得了动应力强度因子。最后，利用叠加原理给出了ｘ＾ｎ型载荷作用下界面动态分层的解。     

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.     

集中载荷作用下各向异性平面内的椭圆孔或裂纹问题

应用复变函数Cauchy积分的方法,对含有椭圆孔或裂纹的各向异性平面,系统地导出了当其在面内受任意集中载荷作用时的复应力函数解或裂纹应力强度因子解析解,即基本解;并通过基本解的迭加,得到了在椭圆孔周或裂纹表面作用一般外载时的解,其特例证实了上述解的正确性。     

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.     

复合材料的裂纹动力学问题的模型

复合材料产生裂纹后，其纤维处形成“桥连”，这是一个不可避免的现象。由于桥连问题很复杂，在数学方法的处理上有很大困难，至今人们研究的大多是桥连的静力学问题，而对其动力学问题研究得很少。只有建立复合材料的桥连动力学模型，才能更好地研究复合材料的断裂动力学问题。为了便于分析复合材料的问题，将桥连处用载荷代替，当裂纹高速扩展时，其纤维也连续地断裂。通过复变函数论的方法，将所讨论的问题转化为Riemann-Hilbet问题。利用建立的动态模型和自相似方法，得到了正交异性体中扩展裂纹受运动的集中力Px/t及均布载荷作用下位移、应力和动态应力强度因子的解析解，并通过迭加原理，最终求得了该模型的解。     

复合材料桥连的断裂动力学模型

复合材料产生裂纹后，其纤维处形成“桥连”，这是一个不可避免的现象。由于桥连问题很复杂．在数学方法的处理上有很大困难，至今人们研究大多是桥连的静力学问题．而对其动力学问题研究得很少。为了便于分析复合材料的问题，将桥连处用载荷代替，当裂纹高速扩展时．其纤维也连续地断裂。只有建立复合材料的桥连动力学模型，才能更好地研究复合材料的断裂动力学问题。通过复变函数论的方法，将所讨论的问题转化为Riemann—Hilbert问题。利用建立的动态模型和自相似方法，得到了正交异性体中扩展裂纹受运动的集中力P及阶跃载荷作用下位移、应力和动态应力强度因子的解析解，并通过叠加原理，最终求得了该模型的解。     

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.     

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.     

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.     

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 RiemannHilbert 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.     

DYNAMIC CRACK MODELS ON PROBLEM OF BRIDGING FIBER PULL-OUT OF COMPOSITE MATERIALS

An elastic analysis of an internal central crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane was performed. A dynamic model of bridging fiber pull-out of composite materials was presented. Resultingly the fiber failure is governed by maximum tensile stress, the fiber breaks and hence the crack extension should occur in self-similar fashion. By the methods of complex functions, the problem studied can be transformed into the dynamic model to the Reimann-Hilbert mixed boundary value problem, and a straightforward and easy analytical solution is presented. Analytical study on the crack propagation subjected to a ladder load and an instantaneous pulse loading is obtained respectively for orthotropic anisotropic body. By utilizing the solution, the concrete solutions of this model are attained by ways of superposition.