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

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

1 IRMAR - Institut de Recherche Mathématique de Rennes

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 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.

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Systèmes dynamiques [math.DS]

Nathalie M. M. Cousin-Rittemard, Isabelle Gruais. On the connection of isolated branches of a bifurcation diagram: the truss arch system. Dynamical System : an international journal, 2009, 24 (3), pp.315-341. ⟨10.1080/14689360802691037⟩. ⟨hal-00833032⟩