Vol. 16, No. 4, 2021

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Stress-smoothing holes in a regularly perforated elastic plate with a given effective bulk modulus

Shmuel Vigdergauz and Isaac Elishakoff

Vol. 16 (2021), No. 4, 511–525

A thin elastic plate with a square lattice of traction-free holes is considered as a setup for the optimization problem of finding the hole shapes which minimize the (nonnegative) variation of the hoop stresses (MSV) induced by unit bulk load at given perforation rate and effective bulk modulus (Ke) of the structure. In this context, there is the well-known correspondence between the local and the averaged stress-strain field. The starting point of this study is the analytically proven existence of the specially shaped (equistress) holes which together provide the global maximum of the structure’s bulk modulus and a zero-variation (constant) stress distribution around the hole’s face. Here, using an effective optimization scheme we numerically analyze the Ke-to-MSV relation for nonoptimal Ke and hence nonzero MSV across certain representative intervals of their values depending on the structure’s porosity. This is performed by explicitly finding the optimal hole shapes and the attendant stress distributions. The results obtained are detailed in tables and graphs.

2D elastostatic problem, Kolosov–Muskhelishvili potentials, hoop stress variations, shape optimization, bulk effective modulus, genetic algorithm
Received: 13 February 2021
Revised: 5 May 2021
Accepted: 11 May 2021
Published: 9 November 2021
Shmuel Vigdergauz
Research and Development Division
The Israel Electric Corporation Ltd.
Haifa 31000
Isaac Elishakoff
Department of Ocean and Mechanical Engineering
Florida Atlantic University
Boca Raton, FL 33431-0991
United States