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Research Article Open Access
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.
Geometrical inverse problems, Cavities identification, Linear elasticity, Partially overdetermined boundary data, Topological derivative, Asymptotic expansion, Smooth Complexities, Adomian Decomposition Method, Applied Mathematics, Number Theory, Sensitivity Analysis, Convection Diffusion Equations, Numerical Solutions, Nonlinear Differential Equations, Differential Transform Method , Balance Law, Quasilinear Hyperbolic Systems, Mixed Initial-boundary Value, Fuzzy Boundary Value, Semi Analytical-Solution, Integrated Analysis, Fuzzy Environments, Molecular Modelling, Fuzzy Quasi-Metric Space, Three Dimensional Steady State, Computational Model