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
Abstract

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.

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