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Topological derivatives for thermo-mechanical semi-coupled system

Esparta, J.E.; Giusti, S.M.;

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The topological derivative measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation. According to the literature, the topological derivative has been fully developed for a wide range of one single physical phenomenon modeled by partial differential equations. In addition, up to our knowledge, the topological asymptotic analysis associated to multi-physics problems has so far not been re- ported in the literature. In this work, we present the topological asymptotic analysis for the total potential mechanical energy associated to a thermo-mechanical system, when a small circular inclusion is introduced at an arbitrary point of the domain. In particular, we con- sider the linear elasticity system (modeled by the Navier equation) coupled with the steady- state heat conduction problem (modeled by the Laplace equation). The mechanical coupling term comes out from the thermal stress induced by the temperature field. Since this term is non-local, we introduce a non-standard adjoint state, which allows to obtain a closed form for the topological derivative. Finally, we provide a full mathematical justification for the de- rived formulas and develop precise estimates for the remainders of the topological asymptotic expansion.

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Palavras-chave: Topological derivative, thermo-mechanical system, multi-physic topology opti- mization, asymptotic analysis.,

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DOI: 10.5151/meceng-wccm2012-19623

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Como citar:

Esparta, J.E.; Giusti, S.M.; "Topological derivatives for thermo-mechanical semi-coupled system", p. 3888-3905 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-19623

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