Elastic membranes spanning deformable boundaries
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911934087954432 |
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| author | Ballarin, Francesco Bevilacqua, Giulia Lussardi, Luca Marzocchi, Alfredo |
| author_facet | Ballarin, Francesco Bevilacqua, Giulia Lussardi, Luca Marzocchi, Alfredo |
| contents | We perform a variational analysis of an elastic membrane spanning a closed curve which may sustain bending and torsion. First, we deal with parametrized curves and linear elastic membranes proving the existence of equilibria and finding first-order necessary conditions for minimizers computing the first variation. Second, we study a more general case, both for the boundary curve and for the membrane, using the framed curve approach. The infinite dimensional version of the Lagrange multipliers' method is applied to get the first-order necessary conditions. Finally, a numerical approach is presented and employed in several numerical test cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_13614 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Elastic membranes spanning deformable boundaries Ballarin, Francesco Bevilacqua, Giulia Lussardi, Luca Marzocchi, Alfredo Analysis of PDEs Mathematical Physics 2020: 49J45, 49Q05, 74K15, 74B20, 74S05 We perform a variational analysis of an elastic membrane spanning a closed curve which may sustain bending and torsion. First, we deal with parametrized curves and linear elastic membranes proving the existence of equilibria and finding first-order necessary conditions for minimizers computing the first variation. Second, we study a more general case, both for the boundary curve and for the membrane, using the framed curve approach. The infinite dimensional version of the Lagrange multipliers' method is applied to get the first-order necessary conditions. Finally, a numerical approach is presented and employed in several numerical test cases. |
| title | Elastic membranes spanning deformable boundaries |
| topic | Analysis of PDEs Mathematical Physics 2020: 49J45, 49Q05, 74K15, 74B20, 74S05 |
| url | https://arxiv.org/abs/2207.13614 |