求解无限板圆孔边四不等长裂纹应力强度因子问题

THE PROBLEM FOR THE INFINITE PLATE WITH FOUR ASYMMETRY CRACKS EMANATING FROM A CIRCULAR HOLE

复变函数法和有限截项法是解决孔边裂纹问题的常用方法,复变函数法是解析方法,有限截项法是半解析半数值的方法,采用这两种方法需要引入适当的保角映射函数,将问题转化为可求解的模型.本文分别用复变函数法和有限截项法求解无限远处受任意角度双向均匀拉伸应力、无限大板圆孔边四不等长裂纹的应力强度因子.结果表明,当水平裂纹对称,右裂纹长与半径的比值大于1时,有限截项法与复变函数法所得结果吻合较好;当水平裂纹不对称,右裂纹长与半径的比值大于1.5时,上述两种方法所得结果吻合较好.圆孔边四条裂纹退化为共线的两条裂纹时,复变函数法的结果与文献中已有的结果一致.

The complex variable function method and the truncated conformal mapping approach are common methods for solving the problem of cracks emanating from a hole.The complex function method is an analytical method,and the truncated conformal mapping approach is a semi-analytical and semi-numerical method.The two met hods need to introduce conformal mapping.A mapping function that turns a problem into a model that can be solved.In this paper,the complex variable function method and the truncated conformal mapping approach are used to solve the stress intensity factors for the infinite plate with four cracks emanating from a circular hole,which is under remote uniform tension in the bidirectional at an arbitrary angle.The results show that when the horizontal crack is symmetrical and the ratio of crack length to radius is greater than 1,the results of the complex variable function and the truncated conformal mapping approach have good approaching effect.When the horizontal crack is asymmetrical and the ratio of crack length to radius is greater than 1.5,the results obtained by the above two methods are consistent.When the vertical crack length is equal to zero,The results of the complex variable function are consistent with the existing results in the literature.