Elastic belt extended by two equal rigid pulleys. (English) Zbl 1431.74091

Batista, Milan

Acta Mech. 230, No. 11, 3825-3838 (2019).

Summary: 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.

MSC:

74M15	Contact in solid mechanics
74G05	Explicit solutions of equilibrium problems in solid mechanics

Software:

Elfun18

References:

[1]	Belyaev, A., Eliseev, V., Irschik, H., Oborin, E.: Nonlinear statics of extensible elastic belt on two pulleys. PAMM 16, 11-14 (2016)
[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) · Zbl 1380.74065
[3]	Belyaev, AK; Eliseev, VV; Irschik, H.; Oborin, EA; Irschik, H. (ed.), Contact of flexible elastic belt with two pulleys, 195-203 (2017), Berlin
[4]	Denoel, V., Detournay, E.: Eulerian formulation of constrained elastica. Int. J. Solids Struct. 48, 625-636 (2011) · Zbl 1236.74143
[5]	Huynen, A., Detournay, E., Denoel, V.: Eulerian formulation of elastic rods. Proc R. Soc. A Math. Phys. 472, 1-23 (2016) · Zbl 1371.74166
[6]	Huynen, A., Detournay, E., Denoel, V.: Surface constrained elastic rods with application to the sphere. J. Elast. 123, 203-223 (2016) · Zbl 1334.74048
[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)
[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)
[9]	Antman, S.S.: Nonlinear Problems of Elasticity, 2nd edn. Springer, New York (2005) · Zbl 1098.74001
[10]	Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity, 4th edn. Dover Publications, New York (1944) · Zbl 0063.03651
[11]	Frisch-Fay, R.: Flexible Bars. Butterworths, London (1962) · Zbl 0124.18001
[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]	Popov, E.P.: Theory and Calculation of Flexible Elastic Bars. Nauka, Moscow (1986)
[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)
[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)
[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)
[17]	Reinhardt, WP; Walker, PL; Olver, FWJ (ed.), Jacobian elliptic functions, xv (2010), Cambridge; New York