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Journal Articles Engineering Analysis with Boundary Elements Year : 2011

Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems

Marc Bonnet

Abstract

This article concerns an extension of the topological sensitivity (TS) concept for 2D potential problems involving insulated cracks, whereby a misfit functional $J$ is expanded in powers of the characteristic size $a$ of a crack. Going beyond the standard TS, which evaluates (in the present context) the leading $O(a^{2})$ approximation of $J$, the higher-order TS established here for a small crack of arbitrarily given location and shape embedded in a 2-D region of arbitrary shape and conductivity yields the $O(a^{4})$ approximation of $J$. Simpler and more explicit versions of this formulation are obtained for a centrally-symmetric crack and a straight crack. A simple approximate global procedure for crack identification, based on minimizing the $O(a^{4})$ expansion of $J$ over a dense search grid, is proposed and demonstrated on a synthetic numerical example. BIE formulations are prominently used in both the mathematical treatment leading to the $O(a^{4})$ approximation of $J$ and the subsequent numerical experiments.
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Dates and versions

hal-00495407 , version 1 (26-06-2010)

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Marc Bonnet. Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems. Engineering Analysis with Boundary Elements, 2011, 35, pp.223-235. ⟨10.1016/j.enganabound.2010.08.007⟩. ⟨hal-00495407⟩
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