Soap film spanning an elastic link

TL;DR

This paper models the equilibrium configuration of multiple Kirchhoff rods linked together and tied by a soap film, proving the existence of a minimum energy solution and experimentally validating the predicted surface shapes.

Contribution

It introduces a variational framework for analyzing soap films spanning elastic rods and proves the existence of solutions with potentially irregular surfaces.

Findings

Existence of a minimum energy configuration is established.

Experimental results confirm the theoretical surface predictions.

The model accommodates complex rod linkages and irregular surfaces.

Abstract

We study the equilibrium problem of a system consisting by several Kirchhoff rods linked in an arbitrary way and tied by a soap film, using techniques of the Calculus of Variations. We prove the existence of a solution with minimum energy, which may be quite irregular, and perform experiments confirming the kind of surface predicted by the model.