轴对称断裂动力学问题的自相似解

通过复变函数论的方法,对复合材料的圆盘状裂纹的轴对称性扩展问题进行研究.采用自相似方法,并根据任意的自相似指数的断裂动力学问题,进行自相似求解,导出解析解的一般表示.应用该法可以迅速地将所论问题转化为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,就可以求得任意复杂问题的解.

Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry

By the theory of complex functions, a penny_shaped crack on axially symmetric propagating problems for composite materials was studied. The general representations of the analytical solutions with arbitrary index of self_similarity were presented for fracture elastodynamics problems on axially symmetry by the ways of self_similarity under the ladder_shaped loads. The problems dealt with can be transformed into Riemann_Hilbert problems and their closed analytical solutions are obtained rather simple by this method. After those analytical solutions are utilized by using the method of rotational superposition theorem in conjunction with that of Smirnov_Sobolev, the solutions of arbitrary complicated problems can be obtained.