Stability of Two Planar Loop Elasticas

Zajac, E. E.

doi:10.1115/1.3636445

Cited by 102 publications

(65 citation statements)

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“…The onset of snarling is only evident beyond a critical value of R, and for nitinol this was found experimentally to be at R ≈ 4.5π radians, a result consistent with the theoretical amount of end rotation that can be input into a ring before it buckles spatially, given in [27]:…”

Section: Inspection Of the T D Diagram Insupporting

confidence: 63%

Experiments on snap buckling, hysteresis and loop formation in twisted rods

Goss

Heijden

Thompson

et al. 2005

Experimental Mechanics

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We give results of large deflection experiments involving the bending and twisting of 1 mm diameter nickel-titanium alloy rods, up to 2 m in length. These results are compared to calculations based on the Cosserat theory of rods. Details of this theory, formulated as a boundary value problem are presented. The mathematical boundary conditions model the experimental set up. The rods are clamped in aligned chucks and the experiments are carried out under rigid loading conditions. An experiment proceeds by either twisting the ends of the rod by a certain amount and then adjusting the slack, or fixing the slack and varying the amount of twist. In this way commonly encountered phenomena such as snap buckling, the formation of loops, and buckling into and out of planar configurations are investigated. The effect of gravity is discussed.

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Section: Inspection Of the T D Diagram Insupporting

confidence: 63%

Experiments on snap buckling, hysteresis and loop formation in twisted rods

Goss

Heijden

Thompson

et al. 2005

Experimental Mechanics

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“…In combination with the definition (3.3) 2 of μ, (6.25) yields the well-known critical value Ω = (n 2 − 1)a/Rc of the twist density for a twisted elastic ring, which was obtained independently by Michell [9], Zajac [10] and Benham [11]. In particular, (6.25) demonstrates that a twisted ring first buckles at μ = √ 3, corresponding to the mode n = 2.…”

Section: Solution To the Linearized Equilibrium Conditionsmentioning

confidence: 99%

Buckling of a soap film spanning a flexible loop resistant to bending and twisting

Biria

Fried

2014

Proc. R. Soc. A.

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A generalization of the Euler–Plateau problem to account for the energy contribution due to twisting of the bounding loop is proposed. Euler–Lagrange equations are derived in a parametrized setting and a buckling analysis is performed. A pair of dimensionless parameters govern buckling from a flat, circular ground state. While one of these is familiar from the Euler–Plateau problem, the other encompasses information about the ratio of the torsional rigidity to the bending rigidity, the twist density and the size of the loop. For sufficiently small values of the latter parameter, two separate groups of buckling modes are identified. However, for values of that parameter exceeding the critical twist density arising in Michell's study of the stability of a twisted elastic ring, only one group of buckling modes exists. Buckling diagrams indicate that a loop with greater torsional rigidity shows more resistance to transverse buckling. Additionally, a twisted flexible loop spanned by a soap film buckles at a value of the twist density less that the value at which buckling would occur if the soap film were absent.

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“…Examples are the study of coiling and loop formation of sub-oceanic cables [1,2,3,4], filamentary structures of biomolecules [5,6,7,8,9] and bacterial fibers [10,11], the phenomenon of helix hand reversal in climbing plants [12] and the shape and dynamics of cracking whips [13].…”

Section: Introductionmentioning

confidence: 99%

Solving the boundary value problem for finite Kirchhoff rods

Fonseca¹,

Aguiar²

2003

Physica D: Nonlinear Phenomena

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The Kirchhoff model describes the statics and dynamics of thin rods within the approximations of the linear elasticity theory. In this paper we develop a method, based on a shooting technique, to find equilibrium configurations of finite rods subjected to boundary conditions and given load parameters. The method consists in making a series of small changes on a trial solution satisfying the Kirchhoff equations but not necessarily the boundary conditions. By linearizing the differential equations around the trial solution we are able to push its end point to the desired position, step by step. The method is also useful to obtain configurations of rods with fixed end points but different mechanical parameters, such as tension, components of the moment or inhomogeneities.

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Stability of Two Planar Loop Elasticas

Cited by 102 publications

References 0 publications

Experiments on snap buckling, hysteresis and loop formation in twisted rods

Experiments on snap buckling, hysteresis and loop formation in twisted rods

Buckling of a soap film spanning a flexible loop resistant to bending and twisting

Solving the boundary value problem for finite Kirchhoff rods

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