On Material Optimisation for Nonlinearly Elastic Plates and Shells
| Autor: | Stefan Simon, Martin Rumpf, Peter Hornung |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Optimal design
Control and Optimization Field (physics) Discretization Numerical analysis 010102 general mathematics Mathematical analysis Numerical Analysis (math.NA) 010103 numerical & computational mathematics 01 natural sciences Stationary point Finite element method Symmetry (physics) Computational Mathematics Mathematics - Analysis of PDEs Control and Systems Engineering FOS: Mathematics Shape optimization Mathematics - Numerical Analysis 0101 mathematics Analysis of PDEs (math.AP) Mathematics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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