Ⅲ型界面裂纹的非对称动态扩展问题

Asymmetrical Dynamic Propagation Problems on Mode Ⅲ Interface Crack

采用复变函数论的方法,对Ⅲ型界面裂纹的非对称动态扩展问题进行了研究.通过自相似函数的方法可以获得解析解的一般表达式.应用该法可以迅速地将所论问题转化为Riemann-Hilbert问题,并求得了非对称扩展裂纹分别在集中载荷、阶跃载荷作用下的解析解.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.

By 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 functions. The problems researched can be facilely transfotmed into Riemann-Hilbert problems and analytical solutions to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, are acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.