含孔边非均匀材料圆环的无限大薄板的应力集中系数

Stress Concentration Factor in an Infinite Thin Plate with a Nonhomogeneous Ring around a Hole

对于含圆孔及孔边非均匀材料圆环的无限大薄板,假设非均匀材料的弹性模量沿径向按照指数函数变化,而泊松比为常数,分别导出了双轴拉伸和纯剪切作用时孔边及界面处的应力集中系数的解析解.通过数值算例详细分析了非均匀材料圆环的弹性模量的变化对无限大薄板的孔边及界面处的应力集中系数的影响.研究结果表明,合理选择孔边非均匀材料圆环的材料性能变化参数可有效地缓解薄板的孔边应力集中程度.本文的研究结果可为含圆孔的薄板的设计提供一定的参考.

For an infinite thin plate with a circular hole and a nonhomogeneous ring, the analytical solution of stress concentration factor under biaxial tension and the series solution under pure shear are derived by assuming that the elastic modulus varies exponentially while Poisson’s ratio keeps constant. The influence of the variation of the elastic modulus on the stress concentration factor is analyzed in detail. The results of numerical examples show that the stress concentration can be relieved effectively by tuning the material parameters of the nonhomogeneous material. The solutions obtained in this paper can provide some reference for the design of the thin plate with a circular hole.