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Stress-smoothing
holes in a regularly perforated elastic plate with a given
effective bulk modulus
Shmuel Vigdergauz and Isaac Elishakoff |
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Vol. 16 (2021), No. 4, 511–525
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Abstract |
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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 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 -to-MSV relation for nonoptimal 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. |
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Keywords
2D elastostatic problem, Kolosov–Muskhelishvili potentials,
hoop stress variations, shape optimization, bulk effective
modulus, genetic algorithm
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Milestones
Received: 13 February 2021
Revised: 5 May 2021
Accepted: 11 May 2021
Published: 9 November 2021
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Authors |
| Shmuel Vigdergauz | |
| Research and Development
Division The Israel Electric Corporation Ltd. Haifa 31000 Israel |
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| Isaac Elishakoff | |
| Department of Ocean and Mechanical
Engineering Florida Atlantic University Boca Raton, FL 33431-0991 United States |
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