Emna Jaïem
Abstract:
We study a new framework for a geometric inverse problem in linear elasticity.
This problem concerns the recovery of cavities from the knowledge of
partially overdetermined boundary data. The boundary data available for
the reconstruction are given by the displacement field and the normal
component of the normal stress, whereas there is lack of information about
the shear stress. We propose an identification method based on a
Kohn-Vogelius error functional combined with the shape gradient method.
We put special focus on the identification of cavities and prove uniqueness
for the case of monotonous cavities.
Submitted February 3, 2016. Published September 28, 2016.
Math Subject Classifications: 35R30, 74B05.
Key Words: Geometric inverse problem; cavities identification; linear elasticity;
partially overdetermined boundary data; Kohn-Vogelius error functional;
shape gradient.
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Emna Jaïem Université de Tunis El Manar Ecole Nationale d'Ingénieurs de Tunis LR99ES20 Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur LAMSIN, B.P. 37, 1002 Tunis, Tunisie email: emna23jaiem@gmail.com |
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