Lagrange multipliers in intrinsic elasticity

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

2 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)651-666
Journal / PublicationMathematical Models and Methods in Applied Sciences
Volume21
Issue number4
Publication statusPublished - Apr 2011

Abstract

In an intrinsic approach to three-dimensional linearized elasticity, the unknown is the linearized strain tensor field (or equivalently the stress tensor field by means of the constitutive equation), instead of the displacement vector field in the classical approach. We consider here the pure traction problem and the pure displacement problem and we show that, in each case, the intrinsic approach leads to a quadratic minimization problem constrained by Donati-like relations (the form of which depends on the type of boundary conditions considered). Using the Babuka-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. Such results have potential applications to the numerical analysis and simulation of the intrinsic approach to three-dimensional linearized elasticity. © 2011 World Scientific Publishing Company.

Research Area(s)

  • Babuška-Brezzi inf-sup condition, constrained quadratic optimization, intrinsic elasticity, Lagrange multipliers, Linearized elasticity

Citation Format(s)

Lagrange multipliers in intrinsic elasticity. / Ciarlet, Philippe G.; Ciarlet Jr., Patrick; Iosifescu, Oana et al.
In: Mathematical Models and Methods in Applied Sciences, Vol. 21, No. 4, 04.2011, p. 651-666.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review