动态Ⅲ型裂纹表面受不同载荷作用下的解析解

ANALYTICAL SOLUTIONS TO THE SURFACE OF DYNAMIC MODE Ⅲ CRACK SUBJECTED TO DIFFERENT LOADS

通过复变函数论的方法,对Ⅲ型动态裂纹表面受双重载荷、瞬时冲击载荷作用下的问题分别进行研究。采用自相似函数的方法可以获得应力、位移、应力强度因子、应变能密度因子和位错分布函数的解析解。应用该法可以迅速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。利用这些解并采用叠加原理,就可以很容易地求得任意复杂问题的解。

By the measures of theory for complex functions, the problems on the surface of a mode Ⅲ dynamic crack subjected to superimpose loads and impact loads were studied, respectively. Analytical solutions to the stress, displacement, stress intensity factor, strain energy density factor and dislocation distribution function are attained by the approaches of self-similar functions. The problem researched can be very facilely translated into Riemarm-Hilbert problem and its closed solution will be obtained rather straightforward by this technique. Using the solution and superposition theorem, the solution of an arbitrarily complex problem can be acquired.