TY - JOUR
T1 - New formulations of linearized elasticity problems, based on extensions of Donati's theorem
AU - Amrouche, Cherif
AU - Ciarlet, Philippe G.
AU - Gratie, Liliana
AU - Kesavan, Srinivasan
PY - 2006/5/15
Y1 - 2006/5/15
N2 - The classical Donati theorem is used for characterizing smooth matrix fields as linearized strain tensor fields. In this Note, we give several generalizations of this theorem, notably to matrix fields whose components are only in H-1. We then show that our extensions of Donati's theorem allow to reformulate in a novel fashion linearized three-dimensional elasticity problems as quadratic minimization problems with the strains as the primary unknowns. To cite this article: C. Amrouche et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006). © 2006 Académie des sciences.
AB - The classical Donati theorem is used for characterizing smooth matrix fields as linearized strain tensor fields. In this Note, we give several generalizations of this theorem, notably to matrix fields whose components are only in H-1. We then show that our extensions of Donati's theorem allow to reformulate in a novel fashion linearized three-dimensional elasticity problems as quadratic minimization problems with the strains as the primary unknowns. To cite this article: C. Amrouche et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006). © 2006 Académie des sciences.
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U2 - 10.1016/j.crma.2006.03.027
DO - 10.1016/j.crma.2006.03.027
M3 - RGC 21 - Publication in refereed journal
VL - 342
SP - 785
EP - 789
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 10
ER -