Confined buckling of inextensible rods by convex difference algorithms

Pierre Alart (1) , Stéphane Pagano (1)

1 LMGC - Laboratoire de Mécanique et Génie Civil

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. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

Mots clés: computational solid mechanics; nonlinear mechanics; local minimization; convex difference; augmented Lagrangian; confined buckling; NONCONVEX

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Equations aux dérivées partielles [math.AP]

Pierre Alart, Stéphane Pagano. Confined buckling of inextensible rods by convex difference algorithms. Comptes Rendus Mécanique, 2002, 330, pp.819-824. ⟨10.1016/S1631-0721(02)01547-4⟩. ⟨hal-00514568⟩