三维切口应力奇性指数计算

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.

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

After the expression of displacement asymptotic expansion is introduced into the linear elasticity equilibrium equation, the characteristic differential equation with respect to the stress singularity order of 3-D V-notch is proposed. By applying the interpolating matrix method to solving the established equation, all the stress singularity orders companying with the corresponding characteristic angle functions can be yielded at a time. All the calculated stress singularity orders have the same high accuracy by comparing with the existed results. The numerical results show that, part of the singularity orders is converging to the theory resolution of the plane strain V-notch problem. However, the number of the singularity orders for 3-D V-notch is more than the one of 2-D plane strain V-notch. If the plane strain theory is used to predict the stress singularity orders of 3-D V-notch, part of the important singularity orders will be lost.