Numerical solution to stress distribution of a hole with corners on infinite plane

02/10/2020

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by   Weiqi Wang, et al.

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In this paper, we consider the stress of a hole with the given fourfold shape (with corner) on an infinite plane under uniaxial tension. Complex Goursat functions formulation by Muskhelishvili (1953) gives a set of singular integral equations on the boundary to solve this problem. We develope a numerical method using a set of Chebyshev polynomial with some constraints to represent the Goursat function on the boundary and apply the collocation method on roots of Legendre polynomial to solve integral equations. Our results show that the numerical method spectrally converges to the known exact solution when boundary shape is a circle, ellipse. We also applied our numerical method on two overlapped circle shape (with corner) and find the result also converge to the exact solution on Ling (1948).