Mahadevan, L.; Keller, Joseph B. The shape of a Möbius band. (English) Zbl 0786.73041 Proc. R. Soc. Lond., Ser. A 440, No. 1908, 149-162 (1993). Summary: The shape of a Möbius band made of a flexible material, such as paper, is determined. The band is represented as a bent, twisted elastic rod with a rectangular cross-section. Its mechanical equilibrium is governed by the Kirchhoff-Love equations for the large deflections of elastic rods. These are solved numerically for various values of the aspect ratio of the cross-section, and an asymptotic solution is found for large values of this ratio. The resulting shape is shown to agree well with that of a band made from a strip of plastic. Cited in 11 Documents MSC: 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 74B20 Nonlinear elasticity Keywords:twisted elastic rod; rectangular cross-section; Kirchhoff-Love equations; large deflections; asymptotic solution PDFBibTeX XMLCite \textit{L. Mahadevan} and \textit{J. B. Keller}, Proc. R. Soc. Lond., Ser. A 440, No. 1908, 149--162 (1993; Zbl 0786.73041) Full Text: DOI