Recovery of a displacement field on a surface from its linearized change of metric and change of curvature tensors

Philippe G. Ciarlet; Liliana Gratie; Cristinel Mardare; Ming Shen

doi:10.1016/j.crma.2007.03.019

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Related Research Unit(s)

Detail(s)

Original language	English
Pages (from-to)	597-602
Journal / Publication	Comptes Rendus Mathematique
Volume	344
Issue number	9
Online published	27 Apr 2007
Publication status	Published - 1 May 2007

Link(s)

DOI	DOI https://doi.org/10.1016/j.crma.2007.03.019 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-34247887563&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(8858be44-1c1f-4a0d-8804-9a6d16964b75).html

Abstract

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).

Citation Format(s)

[ RIS ] [ BibTeX ]

Recovery of a displacement field on a surface from its linearized change of metric and change of curvature tensors. / Ciarlet, Philippe G.; Gratie, Liliana ; Mardare, Cristinel et al.
In: Comptes Rendus Mathematique, Vol. 344, No. 9, 01.05.2007, p. 597-602.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Ciarlet, PG , Gratie, L , Mardare, C & Shen, M 2007, 'Recovery of a displacement field on a surface from its linearized change of metric and change of curvature tensors', Comptes Rendus Mathematique, vol. 344, no. 9, pp. 597-602. https://doi.org/10.1016/j.crma.2007.03.019

Ciarlet, P. G., Gratie, L., Mardare, C., & Shen, M. (2007). Recovery of a displacement field on a surface from its linearized change of metric and change of curvature tensors. Comptes Rendus Mathematique, 344(9), 597-602. https://doi.org/10.1016/j.crma.2007.03.019

Ciarlet PG , Gratie L , Mardare C, Shen M. Recovery of a displacement field on a surface from its linearized change of metric and change of curvature tensors. Comptes Rendus Mathematique. 2007 May 1;344(9):597-602. Epub 2007 Apr 27. doi: 10.1016/j.crma.2007.03.019

Ciarlet, Philippe G. ; Gratie, Liliana ; Mardare, Cristinel et al. / Recovery of a displacement field on a surface from its linearized change of metric and change of curvature tensors. In: Comptes Rendus Mathematique. 2007 ; Vol. 344, No. 9. pp. 597-602.