三维切口应力奇性指数计算

EVALUATION OF THE STRESS SINGULARITY ORDER FOR THREE-DIMENSIONAL V-NOTCH

将三维切口根部的位移渐近展开式引入线弹性力学平衡方程,导得关于切口应力奇性指数的特征微分方程组.再采用插值矩阵法,一次性地计算出三维切口的各阶应力奇性指数,它们具有同阶精度,并可同时获取相应的特征角函数.算例显示该法是分析三维切口应力奇异指数的一个有效的路径.计算结果表明,三维切口的部分应力奇性指数收敛于平面应变切口应力奇性指数理论值,但若直接用平面应变理论预测三维切口应力奇性指数将导致部分奇性指数缺失.

By introducing the expression of displacement asymptotic expansion into the linear elastic- ity equilibrium equation, the characteristic differential equations with respect to the stress singularity order of 3-D V-notch are proposed. The interpolating matrix method is employed to solve them, all the stress sin- gularity orders and the corresponding characteristic stress angle functions can be obtained synchronously. All the calculated stress singularity orders have the same high accuracy by comparing with the existed re- sults. The numerical results show that, part of the singularity orders converges to the theory solution of the plane strain V-notch problem. However, the value of the singularity orders for 3-D V-notch is more than that of 2-D plane strain V-notch. If the plane strain theory is used to predict the stress singularity order of 3-D V-notch, some the important orders are lost.