中心区域受均布载荷的轴对称裂纹扩展问题

Axially symmetric propagation of crack under action of homogeneous load in central zone

针对复合材料的圆盘状裂纹面中心区域受均布载荷作用下的轴对称性扩展问题,采用复变函数论方法和自相似方法,对任意自相似指数的断裂动力学方程进行了自相似求解,导出了解析解的一般表示.应用该法可将所论问题转化为Riemann-Hilbert问题,并可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.

The axially symmetric propagation of a penny-shaped crack in composite materials subjected to locally homogeneous load is studied by using the theory of complex functions. The general representations of the analytical solutions with arbitrary index of self-similarity are reduced for axisymmetric fracture elastodynamics problems by the ways of self-similarity. The problems under investigation can be transformed into Riemann-Hilbert problems and their closed analytical solutions are obtained rather simply by this method. After those analytical solutions are utilized by superposition theorem, the solutions of arbitrary completed problems can be obtained.