I型裂纹非对称动态扩展解的基本形式

Radical format of solution of asymmetrically dynamic propagation of mode Ⅰ crack

采用复变函数论方法,对Ⅰ型裂纹非对称动态扩展解的基本形式进行推导.用自相似函数的方法获得解析解的一般表达式,使问题相应地简化,并具有一定的普遍性.应用该法可以迅速地将所论问题转化为Keldysh-Sedov问题,而这一类问题容易用通常的Muskhelishvili方法解决.利用已获得的解析解和叠加原理,即可求得任意复杂问题的解.

By the methods of the theory of complex functions, radical format of solution to asymmetrically dynamic propagation of model Ⅰ crack was deduced. General representations of analytical solutions are obtained by the approaches of self-similar functions. The issues considered become accordingly simple and have definitive catholicity. By application of this method, the problems can be easily transformed into Keldysh-Sedov problems which are facilely resolved by the ways of Muskhelishvili. Utilizing superposition theorem, the solutions of arbitrarily complex problems could be acquired.