A new duality approach to elasticity

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Article number1150003
Journal / PublicationMathematical Models and Methods in Applied Sciences
Volume22
Issue number1
Publication statusPublished - Jan 2012

Abstract

The displacement-traction problem of three-dimensional linearized elasticity can be posed as three different minimization problems, depending on whether the displacement vector field, or the stress tensor field, or the strain tensor field, is the unknown. The objective of this paper is to put these three different formulations of the same problem in a new perspective, by means of LegendreFenchel duality theory. More specifically, we show that both the displacement and strain formulations can be viewed as Legendre-Fenchel dual problems to the stress formulation. We also show that each corresponding Lagrangian has a saddle-point, thus fully justifying this new duality approach to elasticity.

Research Area(s)

  • constrained quadratic optimization, duality, intrinsic elasticity, Lagrangians, Legendre-Fenchel transform, Linearized elasticity

Citation Format(s)

A new duality approach to elasticity. / Ciarlet, Philippe G.; Geymonat, Giuseppe; Krasucki, Françoise.
In: Mathematical Models and Methods in Applied Sciences, Vol. 22, No. 1, 1150003, 01.2012.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review