# A Lagrangian approach to intrinsic linearized elasticity

Ciarlet, P G; Iosifescu, J O; Sauter, S; Zou, J (2010). A Lagrangian approach to intrinsic linearized elasticity. Comptes Rendus Mathematique, 348(9-10):587-592.

## 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.

## 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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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English May 2010 11 Nov 2010 11:55 05 Apr 2016 14:15 Elsevier 1631-073X https://doi.org/10.1016/j.crma.2010.04.011 http://www.ensta.fr/~ciarlet/Resumes/10_CRAS.pdf

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