On the catastrophic bifurcation diagram of the truss arch system

Yannick G. Cantin; Nathalie M.M. Cousin-Rittemard; Isabelle Gruais

doi:10.1016/j.crme.2008.07.001

On the catastrophic bifurcation diagram of the truss arch system

Presented by: Jean-Baptiste Leblond

Yannick G. Cantin ¹; Nathalie M.M. Cousin-Rittemard ² ; Isabelle Gruais ²

¹ Université de technologie de Belfort–Montbéliard, 90010 Belfort cedex, France
² I.R.M.A.R., Université de Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France

Comptes Rendus. Mécanique, Volume 336 (2008) no. 9, pp. 699-703.

Abstract
Résumé

Non-linear physical models depend on parameters. One of the important basic issues of bifurcation theory is the determination of the fixed points of the system under investigation. Nevertheless, the branching of solutions rarely occurs in the real applications for which imperfections tend to distort these sharp transitions. In the present Note, the truss arch system is considered as a simple example of the coexistence of disjoint branches, even in a perfect case. 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.

Les modèles des phénomènes physiques non linéaires dépendent de paramètres. Une première étape de la théorie des bifurcations est la détermination des points fixes du système étudié. Néanmoins, les intersections de branches de solutions sont rarement observées dans les applications réelles pour lesquelles des imperfections tendent à distordre ces transitions parfaites. Dans ce travail, le système plan de deux barres articulées, même sans imperfections, est considéré comme un exemple simple de coexistence de branches isolées pour une configuration géométrique large. De plus, on montre que l'émergence des bifurcations sous-critiques est le résultat de la connection de ces branches disjointes.

Received: 2008-05-06
Accepted: 2008-07-07
Published online: 2008-08-22

DOI: 10.1016/j.crme.2008.07.001

Keywords: Solids and structures, Bifurcation, Truss arch, Disjoint branch, Stability
Mots-clés : Solides et structures, Bifurcation, Barres articulées, Branche disjointe, Stabilité

Author's affiliations:

Yannick G. Cantin ¹; Nathalie M.M. Cousin-Rittemard ²; Isabelle Gruais ²

¹ Université de technologie de Belfort–Montbéliard, 90010 Belfort cedex, France
² I.R.M.A.R., Université de Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France

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Yannick G. Cantin; Nathalie M.M. Cousin-Rittemard; Isabelle Gruais. On the catastrophic bifurcation diagram of the truss arch system. Comptes Rendus. Mécanique, Volume 336 (2008) no. 9, pp. 699-703. doi : 10.1016/j.crme.2008.07.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.07.001/

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