均布载荷作用下Ⅲ型非对称裂纹动态扩展问题

Dynamic propagation of Mode Ⅲ asymmetrical crack under homogeneous loads

为了研究均布载荷作用下的Ⅲ型非对称裂纹动态扩展问题,利用复变函数论方法,根据正交异性体弹性动力学反平面问题运动方程的相应关系,采用自相似函数的方法可以获得解析解的一般表达式。应用该法可以迅速地将所讨论的问题转化为Riemann-Hilbert问题,后一问题可以用通常的Muskhel-ishvili方法求解,并求得了应力、位移和动态应力强度因子解析解。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。这些解在断裂动力学以及弹性动力学、静力学问题当中具有重要的应用价值和理论意义。

Based on the theory of complex functions,the dynamic propagation of Mode Ⅲ asymmetrical crack under homogenous loads was investigated in this paper.In terms of the relationship to motion equation of the elastodynamics anti-plane problem for an orthotropic anisotropic body,the universal representations of analytical solutions were obtained using the techniques of self-similar functions.Therefore the problems considered can be translated into Riemann-Hilbert problems,which can be solved using traditional Muskhelishvili method to obtain analytical solutions on the stress,the displacement and dynamic stress intensity factor.Also,based on superposition principle and those solutions,the solutions for any complex problems can be achieved.Those solutions are of significance in application and theory for fracture dynamics,ealstodynamics and elastostatics.