An accurate and efficient computational method for seeking two equi-tangential stress hole shapes

As an infinite elastic plane containing two holes subjected to uniform remote loading, the tangential stress concentration degree around the holes is related to the hole shapes. Conformal transformation in the complex variable method is used to achieve optimal hole shapes, in which equi-tangential stress is produced at the edge of the holes. An effective method and algorithm determining equi-stress hole shapes are proposed. The key of this method is how to map the outer domain of the two holes in physical plane into an annulus in image plane. The mapping function adopted in this article has a general explicit expression, so it is different from the previous ones. Coefficients of the mapping function are design variables in the optimization algorithm of mixed penalty function (Mult-SUMT method) to find optimal holes. The approach presented has a significant computational advantage. The numerical simulations present in detail the influence of hole sizes and external loads on the shape of the optimal holes. Some of the results are verified by ANSYS numerical method.