Vol. 14, No. 1, 2019

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Energy-maximizing holes in an elastic plate under remote loading

Shmuel Vigdergauz and Isaac Elishakoff

Vol. 14 (2019), No. 1, 139–154

A single hole in an infinite elastic plate is used as the simplest setup to find the hole shape which induces the maximum energy increment in a homogeneous stress field given at infinity. In order to avoid the energy unboundedness trivially caused by jagged shapes with an arbitrarily large number of sharp notches, we restrict our attention to only fully concave shapes with everywhere negative curvature. It goes in parallel with the well-known fact that the energy-minimizing hole shapes are invariably convex. Though rather empirical, this easily verified condition allows us to obtain finite and stable energy maxima at moderate computation cost using the same flexible scheme as in the first author’s previous research on optimal shaping of the single energy-minimizing hole. The scheme combines a standard genetic algorithm optimization with an efficient semianalytic direct solver and with an economic shape parametrization, both formulated in complex-variable terms. The results obtained are detailed in tables and graphs. They may stimulate further studies in both theoretical and practical directions.

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2-D elastostatic problem, Kolosov–Muskhelishvili potentials, shape extremization, effective energy, surface roughness, genetic algorithm
Received: 4 November 2018
Revised: 21 November 2018
Accepted: 26 November 2018
Published: 7 April 2019
Shmuel Vigdergauz
R&D Division
The Israel Electric Corp. Ltd.
Isaac Elishakoff
Department of Ocean and Mechanical Engineering
Florida Atlantic University
Boca Raton, FL
United States