Stability of boundary conditions for the Sadowsky functional

TL;DR

This paper proves that the Gamma-convergence of the Sadowsky functional remains stable under affine boundary conditions, including those modeling a Möbius band, for a rectangular strip as its height tends to zero.

Contribution

It demonstrates the stability of Gamma-convergence of the Sadowsky functional under affine boundary conditions, extending previous results.

Findings

Gamma-convergence is stable with affine boundary conditions.

Includes boundary conditions modeling Möbius bands.

Supports the robustness of the Sadowsky functional analysis.

Abstract

It has been proved by the authors that the (extended) Sadowsky functional can be deduced as the Gamma-limit of the Kirchhoff energy on a rectangular strip of height $\varepsilon$, as $\varepsilon$ tends to 0. In this paper we show that this Gamma-convergence result is stable when affine boundary conditions are prescribed on the short sides of the strip. These boundary conditions include those corresponding to a M\"obius band.