A new duality approach to elasticity
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Article number | 1150003 |
| Journal / Publication | Mathematical Models and Methods in Applied Sciences |
| Volume | 22 |
| Issue number | 1 |
| Publication status | Published - Jan 2012 |
Link(s)
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.
In: Mathematical Models and Methods in Applied Sciences, Vol. 22, No. 1, 1150003, 01.2012.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
