Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates

Philippe G. Ciarlet; Cristinel Mardare; Ming Shen

doi:10.1016/j.crma.2007.03.012

Author(s)

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	535-540
Journal / Publication	Comptes Rendus Mathematique
Volume	344
Issue number	8
Publication status	Published - 15 Apr 2007

Link(s)

DOI	DOI https://doi.org/10.1016/j.crma.2007.03.012 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-34247359562&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(20e20de8-cb53-4921-a02f-e7b7e559c8d2).html

Abstract

We establish that, if a symmetric matrix field defined over a simply-connected open set satisfies the Saint Venant equations in curvilinear coordinates, then its coefficients are the linearized strains associated with a displacement field. Our proof provides an explicit algorithm for recovering such a displacement field, which may be viewed as the linear counterpart of the reconstruction of an immersion from a given flat Riemannian metric.

Citation Format(s)

[ RIS ] [ BibTeX ]

Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates. / Ciarlet, Philippe G.; Mardare, Cristinel; Shen, Ming.
In: Comptes Rendus Mathematique, Vol. 344, No. 8, 15.04.2007, p. 535-540.

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

Ciarlet, PG , Mardare, C & Shen, M 2007, 'Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates', Comptes Rendus Mathematique, vol. 344, no. 8, pp. 535-540. https://doi.org/10.1016/j.crma.2007.03.012

Ciarlet, P. G., Mardare, C., & Shen, M. (2007). Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates. Comptes Rendus Mathematique, 344(8), 535-540. https://doi.org/10.1016/j.crma.2007.03.012

Ciarlet PG , Mardare C, Shen M. Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates. Comptes Rendus Mathematique. 2007 Apr 15;344(8):535-540. doi: 10.1016/j.crma.2007.03.012

Ciarlet, Philippe G. ; Mardare, Cristinel ; Shen, Ming. / Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates. In: Comptes Rendus Mathematique. 2007 ; Vol. 344, No. 8. pp. 535-540.