Sébastien Neukirch
Institut Jean le Rond d'Alembert
Centre National de la Recherche Scientifique
Sorbonne Université, Campus Pierre et Marie Curie
Paris, Francetel: +33 1 44 27 72 61
e-mail: sebastien.neukirch (-atat-) upmc.fr
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Instability and self-contact phenomena in the writhing of clamped rods
G. van der Heijden, Sébastien Neukirch, V. G. A. Goss & J.M.T. Thompson
International Journal of Mechanical Science 45 (2003) 161-196
Abstract : We use the Cosserat rod theory to present a unified picture of jump phenomena, associated with looping, snap-through, pop-out, etc., in twisted clamped rods undergoing large deections. Both contact-free rods and rods with isolated points of self-contact are considered. Taking proper account of the symmetries of the problem we find that an arbitrary contact-free solution is fully characterised by four parameters; each point contact adds another two. A shooting method is used for solving the boundary value problem. An intricate bifurcation picture emerges with a strong interplay between planar and spatial rod configurations. We find new jump phenomena by treating the ratio of torsional to bending stiffness of the rod as a bifurcation parameter. Load-deection curves are computed and compared with results from carefully conducted experiments on contact- free as well as self-contacting metal-alloy rods.
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