Article Dans Une Revue International Journal of Solids and Structures Année : 2008

Discussion of "Second order topological sensitivity analysis" by J. Rocha de Faria et al

Marc Bonnet

Résumé

The article by J. Rocha de Faria et al. under discussion is concerned with the evaluation of the perturbation undergone by the potential energy of a domain Ω (in a 2-D, scalar Laplace equation setting) when a disk Bϵ of small radius ϵ centered at a given location $\hat{\boldsymbol{x}\in\Omegaisremovedfrom\Omega,assumingeitherNeumannorDirichletconditionsontheboundaryofthesmallholethuscreated.Ineachcase,thepotentialenergy\psi(\Omega_{\epsilon})ofthepunctureddomain\Omega_{\epsilon}=\Omega\setminus\B_{\epsilon}isexpandedabout\epsilon=0sothatthefirsttwotermsoftheperturbationaregiven.Thefirst(leading)termisthewelldocumentedtopologicalderivativeof\psi$. The article under discussion places, logically, its main focus on the next term of the expansion. However, it contains incorrrect results, as shown in this discussion. In what follows, equations referenced with Arabic numbers refer to those of the article under discussion.
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Dates et versions

hal-00168443 , version 1 (28-08-2007)

Identifiants

Citer

Marc Bonnet. Discussion of "Second order topological sensitivity analysis" by J. Rocha de Faria et al. International Journal of Solids and Structures, 2008, 45, pp.705-707. ⟨hal-00168443⟩
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