TY - JOUR
T1 - Recovery of a displacement field on a surface from its linearized change of metric and change of curvature tensors
AU - Ciarlet, Philippe G.
AU - Gratie, Liliana
AU - Mardare, Cristinel
AU - Shen, Ming
PY - 2007/5/1
Y1 - 2007/5/1
N2 - We establish that the components of the linearized change of metric and change of curvature tensors associated with a displacement field of a surface in ℝ3 must satisfy compatibility conditions, which are the analogues 'on a surface' of the Saint Venant equations in three-dimensional elasticity. We next show that, conversely, if two symmetric matrix fields of order two satisfy these compatibility conditions over a simply-connected surface S ⊂ ℝ3, then they are the linearized change of metric and change of curvature tensors associated with a displacement field of the surface S. To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).
AB - We establish that the components of the linearized change of metric and change of curvature tensors associated with a displacement field of a surface in ℝ3 must satisfy compatibility conditions, which are the analogues 'on a surface' of the Saint Venant equations in three-dimensional elasticity. We next show that, conversely, if two symmetric matrix fields of order two satisfy these compatibility conditions over a simply-connected surface S ⊂ ℝ3, then they are the linearized change of metric and change of curvature tensors associated with a displacement field of the surface S. To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).
UR - http://www.scopus.com/inward/record.url?scp=34247887563&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-34247887563&origin=recordpage
U2 - 10.1016/j.crma.2007.03.019
DO - 10.1016/j.crma.2007.03.019
M3 - RGC 21 - Publication in refereed journal
VL - 344
SP - 597
EP - 602
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 9
ER -