Stress minimization around a hole with a stochastically simulated micro-rough edge in a loaded elastic plate

A conformal mapping technique is used to simulate a variety of highly oscillating roughness profiles and further to analytically solve the stress field induced around a hole in a thin elastic plate under equibiaxial tension at infinity. This framework is combined with genetic algorithm scheme to minimize the hoop stress concentration factor (SCF) by appropriately shaping the profile at given integral-type roughness parameters embedded in the optimization as non-linear lower constraints. The effectiveness of the proposed approach is demonstrated by extensive numerical tests aiming to find the SCF-roughness dependence which finally assumes a simple and accurate analytical form applicable in a representative micro-scale range.