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DOI: 10.1080/14689360802691037

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Dynamical Systems An International Journal (2009) 1-27

On the connection of isolated branches of a bifurcation diagram: the truss arch system

Nathalie M.M. N.M.M. Cousin-Rittemard (  Corresponding author ) 1, Isabelle Gruais 1

(2009-02-06)

One of the important basic issues of bifurcation theory is the determination of the set of the fixed points of non-linear evolution equations as a function of its parameters. The branching of branches of solutions rarely occurs in real applications for which imperfections tend to distort these sharp transitions. Furthermore, bifurcation theory may a priori indicate that there are {\it disjoint} branches of solutions. In the present work, the truss arch system is considered and described. The bifurcation diagram is carried out numerically. It is shown that the truss arch system is a simple example of coexistence of disjoint branches. Moreover, it is shown that the emergence of the subcritical bifurcations of the non-shallow configuration is the result of the connection of these disjoint branches. The analytic solutions are derived and the connection of the branches is studied.

1:	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne

Subject

:

Mathematics/Dynamical Systems Engineering Sciences/Mechanics/Mechanics of the solides Physics/Mechanics/Mechanics of the solides

Keyword(s): bifurcation – truss arch – disjoint solution – connection – stability

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From: Nathalie Rittemard <>

Submitted on: Tuesday, 31 March 2009 18:17:52

Updated on: Friday, 19 February 2010 10:02:15