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Snap buckling, writhing and loop formation in twisted rods

Goss, V.G.A.; (2003) Snap buckling, writhing and loop formation in twisted rods. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

A plethora of literature has appeared over the last twenty years with respect to large deflection rod theory. Some of this has been purely theoretical, and some has been applied. However there is a marked absence of experimental research. One of the aims of this thesis is to help fill that gap. A suitable rigid loading device was designed for this purpose. The rig facilitates the input of end rotation and end shortening (slack), and the measurements of torque and axial force at the ends of the rod. The rods were generally fixed in chucks. The thesis begins with an extensive review of the history of rod theory. This is followed by an outline of the mathematical model, in which we formulate a well defined boundary value problem for computing spatial (non-planar) solutions for finite length uniformly isotropic rods. The experimental apparatus and procedure, including details of the rods used in the experiments are outlined. Classical solutions (the helix and the localised homoclinic) are reviewed. Bent rods buckling into and out of planar configurations are investigated. We derive analytical solutions to four qualitatively different types of planar elastica with aligned welded ends. Our work includes some new analytical results. Data obtained from experiments on bent rods are compared with planar elastica theory. We find a secondary bifurcation not previously reported upon in the literature. Data obtained from experiments on rods under combined compression and twisting are compared to numerical results, exploring commonly encountered phenomena such as snap-buckling, hysteresis and the formation of loops. We include in our report, experimental data for which we have no numerical results to compare with. These experiments involve highly twisted rubber rods investigating such phenomena as snarling and pop-out. The isotropic case is rather special because the equations are integrable. However the theory for flat rods, which cannot bend about one axis, (i.e. "strips") is not well-established. We include some results from experiments on strips which could be useful for future research. We end the thesis with an industrial application of rod theory. Combining a version of our mathematical model with some simple experiments and some analysis, we study the out of plane deflections which arise during pipe-laying operations in deep seas.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Snap buckling, writhing and loop formation in twisted rods
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Thesis digitised by ProQuest.
Keywords: Applied sciences; Deflection rods
URI: https://discovery.ucl.ac.uk/id/eprint/10102437
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