An asymptotic variational problem modeling a thin elastic sheet on a liquid, lifted at one end. (English) Zbl 1445.49008
Summary: We discuss a 1D variational problem modeling an elastic sheet on water, lifted at one end. Its terms include all forces that are relevant in the experiment. By studying a suitable Gamma-limit, we identify a parameter regime in which the sheet is inextensible, and the bending energy of the sheet is negligible. In this regime, the problem simplifies to one with an explicit solution. In order to prove \(\Gamma\)-convergence, we introduce a retardation argument in order to deal with the possibly infinite bending energy of the ansatz. This model involves a variational problem set in an unbounded domain and non reflexive topology, and hence requires special care.
MSC:
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 49S05 | Variational principles of physics |
| 74B05 | Classical linear elasticity |
References:
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