Cavities Identification from Partially Overdetermined Boundary Data in Linear Elasticity
Jaiem E*, Abda AB and Rjaibi B
Lamsin Enit Department, University of Tunis El Manar, BP 37, 1002, Tunis, Tunisia
- *Corresponding Author:
- Jaiem E
Lamsin Enit Department
University of Tunis El Manar
BP 37, 1002, Tunis, Tunisia
E-mail: [email protected]
Received Date: February 18, 2016; Accepted Date: March 16, 2016; Published Date: March 22, 2016
Citation: Jaiem E, Abda AB, Rjaibi B (2016) Cavities Identification from Partially Overdetermined Boundary Data in Linear Elasticity. J Appl Computat Math 5:295. doi:10.4172/2168-9679.1000295
Copyright: © 2016 Jaiem E, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Our main interest in this work is an analysis of geometrical inverse problem related to the detection of cavities, in elasticity framework from partially overdetermined boundary data in two spatial dimensions. For the reconstruction, we have only access to the displacement field and to the normal component of the normal stress. We propose an identification method based on the Kohn-Vogelius formulation combined with the topological gradient method. An asymptotic expansion for an energy function is derived with respect to the creation of a small hole. A one-shot reconstruction algorithm based on the topological sensitivity analysis is implemented. Some numerical experiments concerning the cavities identification are finally reported, highlighting the ability of the method to identify multiple cavities.