Issue |
ESAIM: COCV
Volume 26, 2020
|
|
---|---|---|
Article Number | 82 | |
Number of page(s) | 29 | |
DOI | https://doi.org/10.1051/cocv/2020053 | |
Published online | 21 October 2020 |
On material optimisation for nonlinearly elastic plates and shells
1
Fakultät Mathematik, TU Dresden,
01062
Dresden, Germany.
2
Institut für Numerische Simulation, Universität Bonn,
53115
Bonn, Germany.
* Corresponding author: s6stsimo@uni-bonn.de
Received:
28
February
2020
Accepted:
26
July
2020
This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate functional with incorporated material hardness function are investigated and a compliance cost functional is taken into account. Under symmetry assumptions on the material distribution and the load it is shown that cylindrical solutions are stationary points. Furthermore, it is demonstrated that the optimal design of cylindrically deforming, clamped rectangular plates is non trivial, i.e. with a material distribution which is not just depending on one axial direction on the plate. Analytical results are complemented with numerical optimization results using a suitable finite element discretization and a phase field description of the material phases. Finally, using numerical methods an outlook on the optimal design of non isometrically deforming plates and shells is given.
Mathematics Subject Classification: 49K15 / 49Q10 / 74P05 / 74S05
Key words: Elastic plates and shells / isometries / shape optimization / phase-field model
© EDP Sciences, SMAI 2020
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