拉伸半无限圆孔板应力集中系数研究

A Study of Stress Concentration Factors for Tension Semi-infinite Plate with a Circular Hole

用近似解析方法推出了拉伸半无限圆孔板孔边最大应力集中系数的显式表达式 ,此式不但形式简单而且具有良好的精度。对该式的精度验证采用两条路径 :1)与应力集中系数手册结果 (无显式表达式 ,只有曲线 )比较 ;2 )与有限元计算结果比较 ,所推公式 (当d/a≥ 1.2 ) 的精度得到证实。同时应该指出 ,Jeffery给出的仅有的几个具体理论值在圆孔比较靠近直线边界时误差较大 ,但至今Jeffery的结果仍被当成经典数据或准确值被引用 ,本文的工作支持西田正孝编著的应力集中系数手册认为Jeffery解“有错误”的指正。此外 ,分别用Koiter的近似解析方法和有限元法证实 ,采用本文新定义的应力集中系数 (即用最大应力点所在的邻近一侧截面上的平均应力为基准应力 ) ,当圆孔非常靠近直线边界 (1<d/a <1.2 ) 时有一个极限值 2。

The explicit expression of the maximum stress concentration factor for the tension semi-infinite plate with a circular hole is formulated by using an approximate analytical method. This expression is both simple and adequately accurate. The accuracy of the proposed expression is testified by two approaches: 1)Comparison with the results collected in the stress concentration factor handbook (there is no explicit formula, only curves are available). 2)Comparison with the calculated results from finite element method. Good accuracy of the expression (d/a≥1.2)is thus proved. Meanwhile, it should be pointed out that the only several concrete theoretical values given by Jeffery are proved to be with relatively large error, especially when the circular hole gets closer to the straight line, unfortunately, Jeffery's results have been considered classic and exact up to now, the research presented here supports the rectification of Jeffery's 'erroneous' solution, which is stated in the stress concentration factor handbook authored by Nishida. Furthermore, both the approximate analytical method proposed by Koiter and the finite element method are used to verify that, under the new definition of the stress concentration factor given in this paper, a limit value 2 is approached when the circular hole is very near to the straight line boundary (1<d/a<1.2).