Cavity/Inclusion Detection in Plane Linear Elastic Bodies Using Linear Sampling Method
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In this paper, solution of inverse problems in elastostatic fields is investigated. For this purpose, we propose a qualitative inverse approach based on linear sampling method (LSM) for cavity/inclusion detection in a two-dimensional (2D) isotropic linear elastic body using measurement of data on the boundary. The LSM is an effective approach to image the geometrical features of unknown targets. Although the LSM has been used in the context of inverse scattering problems such as acoustics, and electromagnetism, there is no specific attempt to apply this method for identification of cavities/inclusions in inverse elastostatic problems. This study emphasizes the implementation of the LSM coupled with the finite element method (FEM). A set of numerical simulations on 2D elastostatic problems is presented to highlight many effective features of the proposed LSM fast qualitative identification method.
KeywordsQualitative inverse problems Linear sampling method Inverse elastostatic problems The finite element method
- 13.Karageorghis, A., Lesnic, D., Marin, L.: The method of fundamental solutions for the detection of rigid inclusions and cavities in plane linear elastic bodies. Comput. Struct. 106–107, 176–188 (2010) Google Scholar
- 14.Bakushinsky, A.B., Kokurin, M.Y.: Iterative Methods for Approximate Solution of Inverse Problems, 1st edn. Springer, Berlin (2005) Google Scholar
- 24.Sadd, M.H.: Elasticity: Theory, Applications, and Numerics, 2nd edn. Academic Press, San Diego (2009) Google Scholar
- 26.Hadamard, J.: Lectures on the Cauchy Problem in Linear Partial Differential Equations. Yale University Press, New Haven (1923) Google Scholar