A Lagrangian approach to intrinsic linearized elasticity

Oana Iosifescu (1) , Philippe G. Ciarlet (2) , Patrick Ciarlet (3) , Zou Jun (4) , Stefan Sauter (5)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 HKU - Department of Mathematics
3 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
4 Department of Mathematics [Hong Kong]
5 Institut für Mathematik [Zürich]

We consider the pure traction problem and the pure displacement problem of three-dimensional linearized elasticity. We show that, in each case, the intrinsic approach leads to a quadratic minimization problem constrained by Donati-like relations. Using the Babuška-Brezzi inf-sup condition, we then show that, in each case, the minimizer of the constrained minimization problem found in an intrinsic approach is the first argument of the saddle-point of an ad hoc Lagrangian, so that the second argument of this saddle-point is the Lagrange multiplier associated with the corresponding constraints.

Domaines: Equations aux dérivées partielles [math.AP]

Oana Iosifescu, Philippe G. Ciarlet, Patrick Ciarlet, Zou Jun, Stefan Sauter. A Lagrangian approach to intrinsic linearized elasticity. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2010, 348, pp.587-592. ⟨10.1016/j.crma.2010.04.011⟩. ⟨hal-00804358⟩