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.

Elastic membranes spanning deformable curves / Ballarin, Francesco; Bevilacqua, Giulia; Lussardi, Luca; Marzocchi, Alfredo. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK. - ISSN 0044-2267. - 104:6(2024), pp. 1-33. [10.1002/zamm.202300890]

Elastic membranes spanning deformable curves

Bevilacqua, Giulia;Lussardi, Luca;
2024

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2989732