Acta Mechanica

, Volume 230, Issue 11, pp 3825–3838 | Cite as

Elastic belt extended by two equal rigid pulleys

  • Milan BatistaEmail author
Original Paper


In this paper, we provide an analytical solution for the contact problem of an elastic belt extended by two equal smooth rigid pulleys. The belt is treated as a Bernoulli–Euler rod, and the expressions for pulley displacement and pulley reaction force are given in terms of Jacobi elliptical functions. Theoretical considerations are enhanced by examples in tabular and graphical form.


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  1. 1.
    Belyaev, A., Eliseev, V., Irschik, H., Oborin, E.: Nonlinear statics of extensible elastic belt on two pulleys. PAMM 16, 11–14 (2016)CrossRefGoogle Scholar
  2. 2.
    Belyaev, A.K., Eliseev, V.V., Irschik, H., Oborin, E.A.: Contact of two equal rigid pulleys with a belt modelled as Cosserat nonlinear elastic rod. Acta Mech. 228, 4425–4434 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Belyaev, A.K., Eliseev, V.V., Irschik, H., Oborin, E.A.: Contact of flexible elastic belt with two pulleys. In: Irschik, H. (ed.) Dynamics and Control of Advanced Structures, pp. 195–203. Springer, Berlin (2017)CrossRefGoogle Scholar
  4. 4.
    Denoel, V., Detournay, E.: Eulerian formulation of constrained elastica. Int. J. Solids Struct. 48, 625–636 (2011)CrossRefGoogle Scholar
  5. 5.
    Huynen, A., Detournay, E., Denoel, V.: Eulerian formulation of elastic rods. Proc R. Soc. A Math. Phys. 472, 1–23 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Huynen, A., Detournay, E., Denoel, V.: Surface constrained elastic rods with application to the sphere. J. Elast. 123, 203–223 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Majidi, C., O’Reilly, O.M., Williams, J.A.: On the stability of a rod adhering to a rigid surface: shear-induced stable adhesion and the instability of peeling. J. Mech. Phys. Solids 60, 827–843 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Steinbrecher, I., Humer, A., Vu-Quoc, L.: On the numerical modeling of sliding beams: a comparison of different approaches. J. Sound Vib. 408, 270–290 (2017)CrossRefGoogle Scholar
  9. 9.
    Antman, S.S.: Nonlinear Problems of Elasticity, 2nd edn. Springer, New York (2005)zbMATHGoogle Scholar
  10. 10.
    Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity, 4th edn. Dover Publications, New York (1944)zbMATHGoogle Scholar
  11. 11.
    Frisch-Fay, R.: Flexible Bars. Butterworths, London (1962)zbMATHGoogle Scholar
  12. 12.
    Batista, M.: Elfun18 A Collection of Matlab functions for the computation of Elliptical Integrals and Jacobian elliptic functions of real arguments. arXiv:1806.10469 [cs.MS] (2018)
  13. 13.
    Popov, E.P.: Theory and Calculation of Flexible Elastic Bars. Nauka, Moscow (1986)Google Scholar
  14. 14.
    Batista, M.: Analytical treatment of equilibrium configurations of cantilever under terminal loads using Jacobi elliptical functions. Int. J. Solids Struct. 51, 2308–2326 (2014)CrossRefGoogle Scholar
  15. 15.
    Batista, M.: A closed-form solution for Reissner planar finite-strain beam using Jacobi elliptic functions. Int. J. Solids Struct. 87, 153–166 (2016)CrossRefGoogle Scholar
  16. 16.
    Goss, V.G.A.: Snap buckling, writhing and loop formation in twisted rods. In: Center for Nonlinear Dynamics, University Collage London, PhD. thesis (2003)Google Scholar
  17. 17.
    Reinhardt, W.P., Walker, P.L.: Jacobian elliptic functions. In: Olver, F.W.J. (ed.) NIST Handbook of Mathematical Functions, p. xv. Cambridge University Press, NIST, Cambridge; New York (2010)Google Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Maritime Studies and TransportUniversity of LjubljanaLjubljanaSlovenia

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