Comptes Rendus
Confined buckling of inextensible rods by convex difference algorithms
Comptes Rendus. Mécanique, Volume 330 (2002) no. 12, pp. 819-824.

In this Note we present an approach to determine the local minima of a specific class of minimization problems. Attention is focused on the inextensibility condition of flexible rods expressed as a nonconvex constraint. Two algorithms are derived from a special splitting of the Lagrangian into the difference of two convex functions (DC). They are compared to the augmented Lagrangian methods used in this context. These DC formulations are easily extended to contact problems and applied to the determination of confined buckling shapes.

Dans cette Note nous présentons une approche permettant de déterminer les minima locaux d'une classe spécifique de problèmes de minimisation. On s'intéresse à la condition d'inextensibilité d'une poutre flexible exprimée comme une contrainte non convexe. Deux algorithmes découlent alors de la décomposition du Lagrangien en la différence de deux fonctions convexes (DC). Ils sont comparés à la méthode du Lagrangien augmenté utilisée dans ce contexte. La gestion de conditions de contact est aisément intégrable dans le schéma DC et application est faite au flambement confiné.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-0721(02)01547-4
Keywords: computational solid mechanics, nonlinear mechanics, local minimization, convex difference, augmented Lagrangian, confined buckling
Mot clés : mécanique des solides numérique, mécanique non linéaire, minimisation locale, différence convexe, Lagrangien augmenté, flambement confiné

Pierre Alart 1; Stéphane Pagano 1

1 LMGC, CNRS-Université de Montpellier II, place E. Bataillon CC048, 34005 Montpellier cedex, France
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Pierre Alart; Stéphane Pagano. Confined buckling of inextensible rods by convex difference algorithms. Comptes Rendus. Mécanique, Volume 330 (2002) no. 12, pp. 819-824. doi : 10.1016/S1631-0721(02)01547-4. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01547-4/

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