Analytical solution to calculate the stress distribution around a triangular hole in finite isotropic plates under in-plane loading

In this paper, stress distribution around a triangular hole in finite isotropic plate under in-plane loading is studied. With the assumption of plane stress conditions, the method employed is based on the analytical solution of Muskhelishvili’s complex variable method and conformal mapping. The finite plate (the ratio of the length of the biggest side of the hole to side of the plate is greater than 0.2) can be considered as isotropic and linearly elastic. For solving the problem, the finite area with a triangular hole in z plan is mapped onto finite area outside a unite circle in ζ plan using the conformal mapping function. The stress function in finite plate with triangular hole is presented by superposition of the stress function for an infinite plate with a triangular hole and ones for a finite plate without a hole. The unknown coefficients in stress function are obtained by using the least square boundary collocation method and applying the appropriate boundary conditions. The effect of hole curvature, hole orientation, plate’s aspect ratio, hole size, type of loading as the effective parameters is investigated. The results based on analytical solution are in a good agreement with the results obtained from the finite element method. The results show that the analysis of the stress distribution in perforated plates that the ratio of the length of the biggest side of the hole to the smallest side of the plate is greater than 0.2, by using the infinite plate theory has a great error.