Phase field model for multi-material shape optimization of inextensible rods
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914775463624704 |
|---|---|
| author | Dondl, Patrick Maione, Alberto Wolff-Vorbeck, Steve |
| author_facet | Dondl, Patrick Maione, Alberto Wolff-Vorbeck, Steve |
| contents | We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both rigidities as objectives. We then formulate a phase field approximation of the optimization problem and show the convergence to the aforementioned sharp interface model via $Γ$-convergence. In the final part of this work we numerically approximate minimizers of the phase field problem by using a steepest descent approach and relate the resulting optimal shapes to the development of the morphology of plant stems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_04538 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Phase field model for multi-material shape optimization of inextensible rods Dondl, Patrick Maione, Alberto Wolff-Vorbeck, Steve Optimization and Control Numerical Analysis Mathematical Physics 35Q74, 41A60, 49J45, 49Q10, 74B20, 74P10 We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both rigidities as objectives. We then formulate a phase field approximation of the optimization problem and show the convergence to the aforementioned sharp interface model via $Γ$-convergence. In the final part of this work we numerically approximate minimizers of the phase field problem by using a steepest descent approach and relate the resulting optimal shapes to the development of the morphology of plant stems. |
| title | Phase field model for multi-material shape optimization of inextensible rods |
| topic | Optimization and Control Numerical Analysis Mathematical Physics 35Q74, 41A60, 49J45, 49Q10, 74B20, 74P10 |
| url | https://arxiv.org/abs/2209.04538 |