Unique determination of unknown boundaries in an elastic plate by one measurement

Antonino Morassi; Edi Rosset

doi:10.1016/j.crme.2010.07.011

Unique determination of unknown boundaries in an elastic plate by one measurement
[Détermination unique des frontières inconnues dans une plaque élastique par une mesure]

Antonino Morassi ¹ ; Edi Rosset ²

¹ Dipartimento di Georisorse e Territorio, Università degli Studi di Udine, via Cotonificio 114, 33100 Udine, Italy
² Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, via Valerio 12/1, 34127 Trieste, Italy

Comptes Rendus. Mécanique, Volume 338 (2010) no. 7-8, pp. 450-460.

Résumé
Abstract

Dans cet article, on considère deux problèmes inverses pour une plaque mince élastique soumise à une distribution donnée de moments sur une partie de son bord. Le premier problème consiste à déterminer une portion inconnue du bord, supposée libre d'efforts. Le second problème correspond à l'identification d'une inclusion rigide dans la plaque. Pour les deux problèmes, l'identifiabilité au moyen d'une seule mesure est prouvée, sous l'hypothèse d'un comportement isotrope du matériau constitutif de la plaque.

In this article we study two inverse problems for a thin elastic plate subjected to a given couple field applied at its boundary. One problem consists in determining an unknown portion of the exterior boundary of the plate subjected to homogeneous Neumann conditions, while the other problem concerns with the determination of a rigid inclusion inside the plate. In both cases, under the assumption that the plate is made by isotropic material, we prove uniqueness with one measurement.

Publié le : 2010-07-01

DOI : 10.1016/j.crme.2010.07.011

Keywords: Inverse problems, Elastic plates, Unknown boundaries
Mot clés : Problèmes inverses, Plaques élastiques, Frontières inconnues

Affiliations des auteurs :

Antonino Morassi ¹ ; Edi Rosset ²

¹ Dipartimento di Georisorse e Territorio, Università degli Studi di Udine, via Cotonificio 114, 33100 Udine, Italy
² Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, via Valerio 12/1, 34127 Trieste, Italy

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     author = {Antonino Morassi and Edi Rosset},
     title = {Unique determination of unknown boundaries in an elastic plate by one measurement},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {450--460},
     publisher = {Elsevier},
     volume = {338},
     number = {7-8},
     year = {2010},
     doi = {10.1016/j.crme.2010.07.011},
     language = {en},
}

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Antonino Morassi; Edi Rosset. Unique determination of unknown boundaries in an elastic plate by one measurement. Comptes Rendus. Mécanique, Volume 338 (2010) no. 7-8, pp. 450-460. doi : 10.1016/j.crme.2010.07.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.07.011/

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