Sébastien Neukirch
Institut Jean le Rond d'Alembert
Centre National de la Recherche Scientifique
Université Pierre et Marie Curie
Paris, France

tel: +33 1 44 27 72 61
fax : +33 1 44 27 52 59
e-mail: sebastien.neukirch (-atat-) upmc.fr

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Classification of the spatial equilibria of the clamped elastica: symmetries and zoology of solutions

Sébastien Neukirch & Michael E. Henderson

Journal of Elasticity, 68 (2002) 95-121

Abstract : We investigate the configurations of twisted elastic rods under applied end loads and clamped boundary conditions. We classify all the possible equilibrium states of inextensible, unshearable, isotropic, uniform and naturally straight and prismatic rods. The Kirchhoff equations which describe the equilibria of these rods are integrated in a formal way which enable us to describe the boundary conditions in terms of 2 closed form equations involving 4 free parameters. We show that only reversible solutions of the Kirchhoff equations fulfil the clamped boundary conditions and we sort them according to their period in the phase plane. We show how planar untwisted configurations as well as circularly closed configurations play an important role in the classification.

Mathematics Subject Classifications (2000) : 74B20, 74K10, 74G05, 74G60, 37J35, 70K42.

Keywords : classification of boundary value problem solutions for elastic rods.

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