非对称Ⅰ型动态裂纹尖端后部区受均布载荷作用

Rear sections of asymmetrical modeⅠdynamic crack tips subjected to homogeneous loads

通过复变函数论的方法,对非对称Ⅰ型裂纹尖端后部区受均布载荷作用下的动态扩展问题进行了研究。根据正交异性体弹性动力学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。应用该法可以很容易地将所讨论的问题转化为Riemann-Hilbert问题,而后一问题可以用通常的Muskhel-ishvili方法进行求解,并且可以相当简单地得到问题的闭合解。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。

By means of the theory of complex functions, dynamic propagation problem on the rear sections of asymmetrical mode I crack tips subjected to homogeneous loads was researched. In terms of relevant relationship to equation of motion of the elastodynamics plane problem for an orthotropic anisotropic body, the universal representations of analytical solutions are obtained with the method of self-similar functions. The problems considered can be very facilely translated into Riemann-Hilbert problem by application of the approaches which are resolved by usual Muskhelishvili＇s methods, and their closed solutions are acquired rather straightforward. Those solutions have an important applied value and theoretical significance in the problems concerning fracture dynamics, ealstodynamics as well as elastostatics.