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.
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.
Mots-clés : Problèmes inverses, Plaques élastiques, Frontières inconnues
Antonino Morassi 1; Edi Rosset 2
@article{CRMECA_2010__338_7-8_450_0, 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}, }
TY - JOUR AU - Antonino Morassi AU - Edi Rosset TI - Unique determination of unknown boundaries in an elastic plate by one measurement JO - Comptes Rendus. Mécanique PY - 2010 SP - 450 EP - 460 VL - 338 IS - 7-8 PB - Elsevier DO - 10.1016/j.crme.2010.07.011 LA - en ID - CRMECA_2010__338_7-8_450_0 ER -
Antonino Morassi; Edi Rosset. Unique determination of unknown boundaries in an elastic plate by one measurement. Comptes Rendus. Mécanique, Inverse problems, 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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