[A propos d'un diagramme de bifurcation catastrophique : le système de deux barres articulées]
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.
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.
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Mot clés : Solides et structures, Bifurcation, Barres articulées, Branche disjointe, Stabilité
@article{CRMECA_2008__336_9_699_0,
author = {Yannick G. Cantin and Nathalie M.M. Cousin-Rittemard and Isabelle Gruais},
title = {On the catastrophic bifurcation diagram of the truss arch system},
journal = {Comptes Rendus. M\'ecanique},
pages = {699--703},
publisher = {Elsevier},
volume = {336},
number = {9},
year = {2008},
doi = {10.1016/j.crme.2008.07.001},
language = {en},
}
TY - JOUR AU - Yannick G. Cantin AU - Nathalie M.M. Cousin-Rittemard AU - Isabelle Gruais TI - On the catastrophic bifurcation diagram of the truss arch system JO - Comptes Rendus. Mécanique PY - 2008 SP - 699 EP - 703 VL - 336 IS - 9 PB - Elsevier DO - 10.1016/j.crme.2008.07.001 LA - en ID - CRMECA_2008__336_9_699_0 ER -
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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