Stability of boundary conditions for the Sadowsky functional

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 $\epsilon$, as $\epsilon$ 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 Möbius band.

References in corpus (8)

• Numerical modeling of static equilibria and bifurcations in bigons and bigon rings
• Translation of Michael Sadowsky's paper "An elementary proof for the existence of a developable Möbius band and the attribution of the geometric problem to a variational problem"
• Translation and interpretation of Michael Sadowsky's paper "Theory of elastically bendable inextensible bands with applications to the Möbius band"
• Simple deformation measures for Discrete elastic rods and ribbons
• Bistability and equilibria of creased annular sheets and strips
• Hierarchy of Geometrical Frustration in Elastic Ribbons: shape-transitions and energy scaling obtained from a general asymptotic theory
• Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons
• Deformation of Framed Curves

Cited by in corpus (2)

• Elastic membranes spanning deformable boundaries
• Existence of optimal flat ribbons