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A Lagrangian approach to intrinsic linearized elasticity

Abstract : 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.
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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, Elsevier, 2010, 348, pp.587-592. ⟨10.1016/j.crma.2010.04.011⟩. ⟨hal-00804358⟩



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