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EnglishWe study the asymptotic behavior of one-dimensional functionals associated with the energy of a thin nonlinear elastic spherical shell in the limit of vanishing thickness ( proportional to a small parameter) epsilon and under the assumption of radial deformations. The functionals are characterized by the presence of a nonlocal potential term and defined on suitable weighted functional spaces. The shell-membrane transition is studied at three different relevant scales. For each we give a compactness result and compute the Gamma-limit. In particular, we show that if the energies on a sequence of configurations scale as epsilon(3/2), then the limit configuration describes a ( locally) finite number of transitions between the undeformed and the everted configurations of the shell. We also highlight a kind of "Gibbs phenomenon" by showing that nontrivial optimal sequences restricted between the undeformed and the everted configurations must have energy scaling of at least epsilon(4/3).
Ansini, N., Braides, A., & Valente, V. (2006). Multiscale analysis by Gamma-convergence of a one-dimensional nonlocal functional related to a shell-membrane transition. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 38(3), 944-976.
| Tipologia: | Articolo su rivista | |
| Citazione: | Ansini, N., Braides, A., & Valente, V. (2006). Multiscale analysis by Gamma-convergence of a one-dimensional nonlocal functional related to a shell-membrane transition. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 38(3), 944-976. | |
| Lingua: | English | |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica | |
| Revisione (peer review): | Sì, ma tipo non specificato | |
| Tipo: | Articolo | |
| Rilevanza: | Rilevanza internazionale | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1137/050630829 | |
| Stato di pubblicazione: | Pubblicato | |
| Data di pubblicazione: | 2006 | |
| Titolo: | Multiscale analysis by Gamma-convergence of a one-dimensional nonlocal functional related to a shell-membrane transition | |
| Autori: | ||
| Autori: | Ansini, N; Braides, A; Valente, V | |
| Appare nelle tipologie: | 01 - Articolo su rivista |
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http://hdl.handle.net/2108/35528
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