| Issue |
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
|
|
|---|---|---|
| Page(s) | 1137 - 1151 | |
| DOI | https://doi.org/10.1051/m2an/2024036 | |
| Published online | 26 June 2024 | |
Optimal design of elastic plates
1
School of Applied Mathematics and Informatics, University of Osijek, Osijek, Croatia
2
Department of Mathematics, Faculty of Science University of Zagreb, Zagreb, Croatia
* Corresponding author: petar@math.hr
Received:
26
April
2023
Accepted:
13
May
2024
This paper is concerned with optimal design problems in the setting of the Kirchhoff–Love model for pure bending of a thin solid symmetric plate under a transverse load. For two isotropic elastic materials with a prescribed amount, the goal is to find their rearrangement within the domain that forms a least compliant structure. The homogenization method is used as a relaxation tool to overcome the lack of a classical solution of optimal design problem. Neccessary conditions of optimality were derived and an optimality criteria method for the single state compliance minimization problems is developed and tested on several examples.
Mathematics Subject Classification: 49M05 / 49J20 / 74Q05 / 74K20 / 35J30
Key words: Kirchhoff–Love model of elastic plate / optimal design / optimality criteria method / Hashin–Shtrikman bounds
© The authors. Published by EDP Sciences, SMAI 2024
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