Get The Mechanics of Ribbons and Möbius Bands PDF

By Roger Fosdick, Eliot Fried

ISBN-10: 9401772991

ISBN-13: 9789401772990

Recent advancements in biology and nanotechnology have prompted a speedily growing to be curiosity within the mechanics of skinny, versatile ribbons and Mobius bands.

This edited quantity includes English translations of 4 seminal papers in this subject, all initially written in German; of those, Michael A. Sadowsky released the 1st in 1929, through others in 1930, and Walter Wunderlich released the final in 1962.

The quantity additionally includes invited, peer-reviewed, unique learn articles on comparable topics.

Previously released within the magazine of Elasticity, quantity 119, factor 1-2, 2015.

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Gottingen 6, 1823–1827 (1827) 9. : Recherches sur la théorie des surfaces élastiques. Huzard-Courcier (1821) 10. : Statistical mechanics of developable ribbons. Phys. Rev. Lett. 104(23), 238104 (2010) Reprinted from the journal 46 Gamma-Limit of a Model for the Elastic Energy of an Inextensible Ribbon 11. : Differential Geometry. , New York (1935) 12. : Mémoire sur les surfaces élastiques. Mém. Cl. Sci. Mathém. Phys. Inst. de Fr. 2, 167–226 (1812) 13. : Sides of the Möbius strip. Arch. Math. 66(6), 511–521 (1996) 14.

Synonymous with ideal point. vi. The order of Figs. 5 and 6 is herein reversed from the original for clarity. vii. The use of X¨ i in the original instead of X¨ appears to be an error. viii. Imaginary circle was chosen for the German nullteiliger Kreis. 1007/s10659-014-9475-4 Gamma-Limit of a Model for the Elastic Energy of an Inextensible Ribbon Nicholas O. Kirby · Eliot Fried Received: 7 November 2013 / Published online: 20 March 2014 © Springer Science+Business Media Dordrecht 2014 Abstract A Γ -convergence result involving the elastic bending energy of a narrow inextensible ribbon is established.

O. Kirby, E. Fried Given the centerline r, consider the energy of an elastic ribbon S of width 2w parameterized by x. Wunderlich [19] shows that the nonvanishing principal curvature κ1 of S is given by κ1 = κ(1 ˜ + η2 ) , |1 + ζ η| ˙ (9) where the dot denotes differentiation with respect to arclength. The bending energy E of S therefore takes the form E= D 2 S κ12 dA = D 2 w 0 −w κ˜ 2 (ξ )(1 + η2 (ξ ))2 dζ dξ, |1 + ζ η(ξ ˙ )| (10) where D is a measure of flexural rigidity. Evaluating the integral on the far right-hand side of (10) over the width 2w of the ribbon yields 2 E = Dw κ˜ 2 (ξ ) 1 + η2 (ξ ) g 2wη(ξ ˙ ) dξ, (11) 0 where g : R → [1, +∞] is defined by ⎧ ⎪ ⎨1, g(x) = x1 ln( 2+x ), 2−x ⎪ ⎩ +∞, if x = 0, if |x| < 2 and x = 0, if |x| ≥ 2.

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