It has been proved by the authors that the (extended) Sadowsky functional can be deduced as the Γ -limit of the Kirchhoff energy on a rectangular strip, as the width of the strip tends to 0. In this paper, we show that this Γ -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 Möbius band. This provides a rigorous justification of the original formal argument by Sadowsky about determining the equilibrium shape of a free-standing Möbius strip. We further write the equilibrium equations for the limit problem and show that, under some regularity assumptions, the centerline of a developable Möbius band at equilibrium cannot be a planar curve.

Stability of Boundary Conditions for the Sadowsky Functional

Mora M. G.
;
Paroni R.
2022-01-01

Abstract

It has been proved by the authors that the (extended) Sadowsky functional can be deduced as the Γ -limit of the Kirchhoff energy on a rectangular strip, as the width of the strip tends to 0. In this paper, we show that this Γ -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 Möbius band. This provides a rigorous justification of the original formal argument by Sadowsky about determining the equilibrium shape of a free-standing Möbius strip. We further write the equilibrium equations for the limit problem and show that, under some regularity assumptions, the centerline of a developable Möbius band at equilibrium cannot be a planar curve.
2022
Freddi, L.; Hornung, P.; Mora, M. G.; Paroni, R.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1161363
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact