Topological sensitivity analysis for identification of voids under Navier's boundary conditions in linear elasticity. (4th September 2019)

• Record Type: Journal Article
• Authors: Ben Abda, Amel; Méjri, Bochra
• Is Part Of: Inverse problems. Volume 35:Number 10(2019)
• Publication Date: 2019-09-04
• Subjects: Voids identification -- linear elasticity -- Navier boundary conditions -- energy-like error functional -- topological gradient; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab2c91
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This article is concerned with a geometric inverse problem related to the two-dimensional linear elasticity system. Thereby, voids under Navier's boundary conditions are reconstructed from the knowledge of partially over-determined boundary data. The proposed approach is based on the so-called energy-like error functional combined with the topological sensitivity method. The topological derivative of the energy-like misfit functional is computed through the topological-shape sensitivity method. Firstly, the shape derivative of the corresponding misfit function is presented briefly from previous work Méjri (2018 J. Inverse Ill-Posed Problems ). Then, an explicit solution of the fundamental boundary-value problem in the infinite plane with a circular hole is calculated by the Muskhelishvili formulae. Finally, the asymptotic expansion of the topological gradient is derived explicitly with respect to the nucleation of a void. Numerical tests are performed in order to point out the efficiency of the developed approach.