Vol. 15, No. 2, 2020

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

Shmuel Vigdergauz and Isaac Elishakoff

Vol. 15 (2020), No. 2, 277–289

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 equi-biaxial 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.

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2D elastostatic problem, Kolosov–Muskhelishvili potentials, stress concentration factor, shape optimization, surface micro-roughness, genetic algorithm
Received: 3 March 2020
Revised: 12 March 2020
Accepted: 19 March 2020
Published: 8 April 2020
Shmuel Vigdergauz
Research and Development Division
The Israel Electric Corporation Ltd.
Isaac Elishakoff
Department of Ocean and Mechanical Engineering
Florida Atlantic University
Boca Raton, FL
United States