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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Classification of the spatial clamped elastica: numerical continuation of the solution set
Michael E. Henderson & Sébastien Neukirch
International Journal of Bifurcation and Chaos, vol 14, no 4 (2004) 1223-1239
Abstract : We consider equilibrium configurations of inextensible, unshearable, isotropic, uniform and naturally straight and prismatic rods when subject to end loads and clamped boundary conditions. In a first paper, we discussed symmetry properties of the equilibrium configurations of the centre line of the rod. Here we are interested in the set of all parameter values that yield equilibrium configurations that fulfill clamped boundary conditions. We call this set the solution manifold and we compute it unsing a recently introduced continuation algorithm. We then describe the topology of this manifold and how it comprises different interconneted layers. We show that the border set of the different layers is the well known solution set of buckled rings.
Mathematics Subject Classifications (2000) : 74B20, 74K10, 74G60, 65P30, 65L10.
Keywords : numerical continuation, boundary value problem for twisted rods, surface following algorithm.
download the preprint version gzipped PS or PDF
download the figures :
1+- (fig 8 & 9)
2+- (fig 10 & 11)
3+- (fig 12 & 13)
4+- (fig 14 & 15)
All layers (fig 16 & 17)
border 1+/1-/2+ (fig 18)
download the journal version PDF
