Volume 26, 2020
|Number of page(s)||29|
|Published online||21 October 2020|
On material optimisation for nonlinearly elastic plates and shells
Fakultät Mathematik, TU Dresden,
2 Institut für Numerische Simulation, Universität Bonn, 53115 Bonn, Germany.
* Corresponding author: firstname.lastname@example.org
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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