Shape optimization of two interacting holes with different areas in an infinite plate

Abstract This paper presents an effective optimization approach based on the equi-stress criterion and conformal transformation to determine two equi-stress holes with different areas in an infinite plate subjected to biaxial loads at infinity and internal uniform pressure on hole boundaries. Conformal transformation in the complex variable method is used to map the outer domain of two holes in the physical plane onto an annulus in the image plane. Mathematically, the hole shapes are parameterized and expressed in one mapping function, therefore, the shape of two holes can be determined by obtaining the coefficients of the mapping function. In the process of optimization, the coefficients are used as design variables in the differential evolution (DE) algorithm to determine the hole shapes. As examples, the results has high accuracy, the optimal hole shapes under different conditions are given and the effect of each parameter are analyzed. What's more, the contour plots of principal stresses are presented to clearly show the stress distribution in the domain for the optimal hole shape.