Calculus of Variations and Geometric Measure Theory

F. Ballarin - G. Bevilacqua - L. Lussardi - A. Marzocchi

Elastic membranes spanning deformable boundaries

created by bevilacqua on 23 Aug 2022
modified by lussardi on 25 Dec 2022


Submitted Paper

Inserted: 23 aug 2022
Last Updated: 25 dec 2022

Year: 2022

ArXiv: 2207.13614 PDF


We perform a variational analysis of an elastic membrane spanning a 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 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.