We introduce a modified Kirchhoff-Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. In a specific setting, we characterize quantitatively some properties of minimizers. Indeed, choosing three different geometrical shapes for the cross-section, we derive Euler-Lagrange equations for a planar version of the Kirchhoff-Plateau problem. We show that in the physical range of the parameters, there exists a unique critical point satisfying the imposed constraints. Finally, we analyze the effects of the surface tension on the shape of the cross-sections at the equilibrium.
Bevilacqua, G., Lonati, C., Effects of surface tension and elasticity on critical points of the Kirchhoff–Plateau problem, <<BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA>>, 2023; 17 (2): 221-240. [doi:10.1007/s40574-023-00392-6] [https://hdl.handle.net/10807/294597]
Effects of surface tension and elasticity on critical points of the Kirchhoff–Plateau problem
Lonati, Chiara
2023
Abstract
We introduce a modified Kirchhoff-Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. In a specific setting, we characterize quantitatively some properties of minimizers. Indeed, choosing three different geometrical shapes for the cross-section, we derive Euler-Lagrange equations for a planar version of the Kirchhoff-Plateau problem. We show that in the physical range of the parameters, there exists a unique critical point satisfying the imposed constraints. Finally, we analyze the effects of the surface tension on the shape of the cross-sections at the equilibrium.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.