Legendre–Fenchel duality in elasticity
Philippe G. Ciarlet, Giuseppe Geymonat, Françoise Krasucki · Comptes Rendus Mathématique · 2011
We show that the displacement and strain formulations of the displacement–traction problem of three-dimensional linearized elasticity can be viewed as Legendre–Fenchel dual problems to the stress formulation of the same problem. We also show that each corresponding Lagrangian has a saddle-point, thus fully justifying this new approach to elasticity by means of Legendre–Fenchel duality.