A critical review of the heavy elastica

Wang, C.Y.

doi:10.1016/0020-7403(86)90052-4

Cited by 93 publications

(54 citation statements)

References 69 publications

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“…Assuming everything remains two-dimensional, we describe the position of the plate in terms of arc length s at time t: (X(s, t), Z(s, t)). Denoting the local stress resultant by (N X , N Z ), the equations of motion of the ruck, where it is lifted off the plane, are [1,19] where κ is the local curvature. The moment and curvature are related by M = Bκ, where B is the bending stiffness.…”

Section: Ruck Dynamics (A) Mathematical Formulationmentioning

confidence: 99%

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The speed of an inclined ruck

Balmforth

Hewitt

2015

Proc. R. Soc. A.

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Steady rucks in an elastic beam can roll at constant speed down an inclined plane. We examine the dynamics of these travelling-wave structures and argue that their speed can be dictated by a combination of the physical conditions arising in the vicinity of the 'contact points' where the beam is peeled off the underlying plane and stuck back down. We provide three detailed models for the contact dynamics: viscoelastic fracture, a thermodynamic model for bond formation and detachment and adhesion mediated by a thin liquid film. The results are compared with experiments.

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Section: Ruck Dynamics (A) Mathematical Formulationmentioning

confidence: 99%

“…[2,19]) where the order-one constant m and the small constantN Z (0) are to be determined. Hence, to leading order…”

Section: Ruck Dynamics (A) Mathematical Formulationmentioning

confidence: 99%

The speed of an inclined ruck

Balmforth

Hewitt

2015

Proc. R. Soc. A.

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“…Conditions of buckling can be found using standard theory [1,5] where the strip deformation in the outof-plane direction w is described by (6) where the buckling is being described in the directions of the principal stresses ( ) Y X , as shown in Figure 2b, and D is the flexural rigidity with ν the Poisson's ratio.…”

Section: Determining Camber Tolerances To Avoid Upstream Strip Bucklingmentioning

confidence: 99%

“…Consider a strip, containing a localised buckle, being in contact with the roll away from the buckle. The Elastica Equation [6] describing the bending of strip from the applied moments can be approximated by:…”

Section: Stability Of Buckle Over a Rollmentioning

confidence: 99%

Crease formation in the processing of thin web material

Dixon¹,

Yuen²

2008

Australian Journal of Mechanical Engineering

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A mathematical model is developed to describe the conditions for buckling of steel strip between transport rolls due to strip camber, together with conditions necessary for the subsequent "ironing-in" of the buckle as it passes over the downstream roll. For a permanent crease to form, the buckle must be sufficiently stable so that it is prohibited by friction to spread laterally, and the stresses from the buckle defect must be large enough for plastic deformation to occur as it travels over the downstream roll. Once the conditions to produce a permanent crease are known they can be avoided in plant operations.

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“…This more sophisticated model, also known as the heavy elastica (Levien 2008;Wang 1986), offers two boundary conditions and therefore the possibility of fixing both end inclinations θ 0 and θ ℓ .…”

Section: The Considered Problemmentioning

confidence: 99%

Patching Asymptotics Solution of a Cable with a Small Bending Stiffness

Denoël

Canor

2013

J. Struct. Eng.

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The analysis of a cable with a small bending stiffness is a problem encountered in many engineering applications such as the fatigue assessment of stay cables, the modeling of pipeline laying operation or the determination of bending stresses in drillpipe assemblies. Because this phenomenon is modeled by a singularly perturbed equation, standard numerical techniques fail to solve these problems efficiently. As an alternative, provided the complexity of the analytical developments does not preclude their application, these problems may be tackled with appealing analytical procedures such as matching asymptotics or multiple scales. Otherwise advanced numerical simulations combining patching asymptotics within a numerical framework are the only possible approach for problems where the governing equations are too complex. Patching asymptotics also features a number of merits such as the possibility of using a boundary layer with a finite extent. Aiming at a better understanding of this latter technique, it is considered here to determine the solution of a cable with a small bending stiffness. Interesting details about patchability conditions and about how to restore higher derivatives continuity are included. The accuracy of the patching asymptotics approach is also compared with that of matched asymptotics.

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A critical review of the heavy elastica

Cited by 93 publications

References 69 publications

The speed of an inclined ruck

The speed of an inclined ruck

Crease formation in the processing of thin web material

Patching Asymptotics Solution of a Cable with a Small Bending Stiffness

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