论文标题
在双轴载荷下，无限板的孔附近的压力的数值解决方案
Numerical solution for the stress near a hole with corners in an infinite plate under biaxial loading
论文作者
论文摘要
我们考虑双轴应力下无限板的孔附近的弹性应力。弹性问题是使用复杂的Goursat函数提出的，从而在边界上产生了一组单数的截见方程。所得的边界积分方程是使用Chebyshev搭配方法来数字求解的，该方法通过分数功率项增强，该方法通过渐近区域的渐近分析得出，以解决孔的拐角处的应力奇异性。我们将数值方法应用于由两个部分重叠的圆圈形成的孔的测试用例，该圆圈可以包括指向固体指向固体的角的角。对于适度的计算工作，我们的数值结果将边界上的确切应力恢复到相对错误$ 10^{-3} $内的确切应力。
We consider the elastic stress near a hole with corners in an infinite plate under biaxial stress. The elasticity problem is formulated using complex Goursat functions, resulting in a set of singular integro-differential equations on the boundary. The resulting boundary integral equations are solved numerically using a Chebyshev collocation method which is augmented by a fractional power term, derived by asymptotic analysis of the corner region, to resolve stress singularities at corners of the hole. We apply our numerical method to the test case of the hole formed by two partially-overlapping circles, which can include either a corner pointing into the solid or a corner pointing out of the solid. Our numerical results recover the exact stress on the boundary to within relative error $10^{-3}$ for modest computational effort.
