Triangular buckling patterns of twisted inextensible strips

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 467, Issue 2125, 2011, Pages 285-303

  Korte, A P ^a   Starostin, E L ^a   Van Der Heijden, G H M ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Boundary value problem; Calculus of variations; Load displacement behaviour; Triangular buckling pattern; Twisted inextensible strip

Indexed keywords

CALCULATIONS;

BUCKLING PATTERNS; CALCULUS OF VARIATIONS; CRITICAL LOAD; ELASTIC STRIPS; EQUILIBRIUM SHAPE; FORCE-EXTENSION; GEOMETRICALLY EXACT; HIGHER MODE; LOAD DISPLACEMENTS; MODE NUMBER; POSTBUCKLING; TRIANGULAR BUCKLING PATTERN; TRIANGULAR FACETS; TWISTED INEXTENSIBLE STRIP; TWISTED STRIP;

BUCKLING;

EID: 79251510565     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2010.0200     Document Type: Article

References (28)

1. Anderson, I. M. 1989 The variational bicomplex. Technical report, Utah State University, Logan. See http://www.math.usu.edu/∼fg-mp/Publications/VB/ vb.pdf.
2. Ashwell D. G. 1962 The inextensional twisting of a rectangular plate. Q. J. Mech. Appl. Math. 15, 91-107. (doi:10.1093/qjmam%2F15.1.91)
3. Capovilla, R., Chryssomalakos, C. & Guven, J. 2002 Hamiltonians for curves. J. Phys. A: Math. Gen. 35, 6571-6587. (doi:10.1088/0305-4470/35/31/304)
4. Clebsch, A. 1862 Theorie der Elasticität fester Körper. Leipzig, Germany: Teubner.
5. Coman, C. D. & Bassom, A. P. 2008 An asymptotic description of the elastic instability of twisted thin elastic plates. Acta Mech. 200, 59-68. (doi:10.1007/s00707-007-0572-3)
6. Crispino, D. J. & Benson, R. C. 1986 Stability of twisted orthotropic plates. Int. J. Mech. Sci. 28, 371-379. (doi:10.1016/0020-7403(86)90056-1)
7. Doedel, E. J., Champneys, A. R., Fairgrieve, T. R., Kuznetsov, Y. A., Sandstede, B. & Wang, X. J. 2007 AUTO-07p: continuation and bifurcation software for ordinary differential equations. See http://indy.cs.concordia.ca/ auto/.
8. Goldstein, H. 1980 Classical mechanics. Reading, MA: Addison-Wesley Publishing Company, Inc.
9. Graustein, W. C. 1966 Differential geometry. New York, NY: Dover.
10. Green, A. E. 1936 The equilibrium and elastic stability of a thin twisted strip. Proc. R. Soc. Lond. A 154, 430-455. (doi:10.1098/rspa.1936.0061)
11. Green, A. E. 1937 The elastic stability of a thin twisted strip. II. Proc. R. Soc. Lond. A 161, 197-220. (doi:10.1098/rspa.1937.0141)
12. Hangan, T. 2005 Elastic strips and differential geometry. Rend. Sem. Mat. Univ. Pol. Torino 63, 179-186.
13. Hornung, P. 2009 Minimizers of Kirchhoff's plate functional: Euler-Lagrange equations and regularity. C. R. Acad. Sci. Paris 347, 647-650. (doi:10.1016/j.crma.2009.03.031)
14. Kogan, I. A. & Olver, P. J. 2003 Invariant Euler-Lagrange equations and the invariant variational bicomplex. Acta Applicandae Mathematicae 76, 137-193. (doi:10.1023/A:1022993616247)
15. Langer, J. & Perline, R. 1991 Poisson geometry of the filament equation. J. Nonlinear Sci. 285, 131-144. (doi:10.1007/BF01209148)
16. Love, A. E. H. 1927 A treatise on the mathematical theory of elasticity. Cambridge, UK: Cambridge University Press.
17. Mansfield, E. H. 1989 The bending and stretching of plates, 2nd edn. Cambridge, UK: Cambridge University Press.
18. Mockensturm, E. M. 2001 The elastic stability of twisted plates. J. Appl. Mech. Trans. ASME 68, 561-567. (doi:10.1115/1.1357517)
19. Randrup, T. & Røgen, P. 1996 Sides of the Möbius strip. Arch. Math., 66, 511-521.
20. Sadowsky, M. 1931 Theorie der elastisch biegsamen undehnbaren Bänder mit Anwendungen auf das Möbius'sche Band. Verhandl. des 3. Intern. Kongr. f. Techn. Mechanik, 1930, Teil II, 444-451.
21. Starostin, E. L. & van der Heijden, G. H. M. 2007 The shape of a Möbius strip. Nat. Mater. 6, 563-567. (doi:10.1038/nmat1929)
22. Starostin, E. L. & van der Heijden, G. H. M. 2009 Force and moment balance equations for geometric variational problems on curves. Phys. Rev. E 79, 066602. (doi:10.1103/PhysRevE.79.066602)
23. Thamwattana, N., McCoy, J. A. & Hill, J. M. 2008 Energy density functions for protein structures. Q. J. Mech. Appl. Math. 61, 431-451. (doi:10.1093/qjmam%2Fhbn012)
24. van der Heijden, G. H. M. & Thompson, J. M. T. 2000 Helical and localised buckling in twisted rods: a unified analysis of the symmetric case. Nonlinear Dynm. 21, 71-99. (doi:10.1023/A:1008310425967)
25. Wakamatsu, H., Yamasaki, T., Arai, E. & Hirai S. 2007 Modeling of flexible belt objects toward their manipulation. In Proc. 2007 IEEE Int. Symp. Assembly and Manufacturing, Ann Arbor, MI, 22-25 July 2007, pp. 1-6. (doi:10.1109/ISAM.2007.4288440)
26. Witten, T. A. 2007 Stress focusing in elastic sheets. Rev. Mod. Phys. 79, 643-675. (doi:10.1103/RevModPhys.79.643)
27. Wunderlich, W. 1962 Über ein abwickelbares Möbiusband. Monatsh. Math. 66, 276-289. (doi:10.1007/BF01299052)
28. Yoshimura, Y. 1951 On the mechanism of buckling of a circular cylindrical shell under axial compression. Reports of the Institute of Science and Technology of the University of Tokyo, vol. 5(5), 179-198. [English translation: Technical Memorandum 1390 of the National Advisory Committee for Aeronautics, Washington DC, 1955.]