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Article Dans Une Revue International Journal of Solids and Structures Année : 2009

Higher-order topological sensitivity for 2-D potential problems. Application to fast identification of inclusions

Marc Bonnet

Résumé

This article concerns an extension of the topological derivative concept for 2D potential problems involving penetrable inclusions, whereby a cost function $J$ is expanded in powers of the characteristic size $\varepsilon$ of a small inclusion. The $O(\varepsilon^{4})$ approximation of $J$ is established for a small inclusion of given location, shape and conductivity embedded in a 2-D region of arbitrary shape and conductivity, and then generalized to several such inclusions. Simpler and more explicit versions of this result are obtained for a centrally-symmetric inclusion and a circular inclusion. Numerical tests are performed on a sample configuration, for (i) the O(\varepsilon^{4})$ expansion of potential energy, and (ii) the identification of a hidden inclusion. For the latter problem, a simple approximate global search procedure based on minimizing the $O(\varepsilon^{4})$ approximation of $J$ over a dense search grid is proposed and demonstrated.
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Dates et versions

hal-00351820 , version 1 (11-01-2009)
hal-00351820 , version 2 (04-02-2009)

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Marc Bonnet. Higher-order topological sensitivity for 2-D potential problems. Application to fast identification of inclusions. International Journal of Solids and Structures, 2009, 46, pp.2275-2292. ⟨10.1016/j.ijsolstr.2009.01.021⟩. ⟨hal-00351820v2⟩
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