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Another approach to linearized elasticity and a new proof of Korn's inequality

Patrick Ciarlet 1 Philippe G. Ciarlet 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We describe and analyze an approach to the pure traction problem of three-dimensional linearized elasticity, whose novelty consists in considering the linearized strain tensor as the "primary" unknown, instead of the displacement itself as is customary. This approach leads to a well-posed minimization problem, constrained by a weak form of the St Venant compatibility conditions. Interestingly, it also provides a new proof of Korn's inequality.
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Patrick Ciarlet, Philippe G. Ciarlet. Another approach to linearized elasticity and a new proof of Korn's inequality. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2005, 15 (02), pp.259-271. ⟨10.1142/S0218202505000352⟩. ⟨hal-00983006⟩



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