Discussion of "Second order topological sensitivity analysis" by J. Rocha de Faria et al
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 $\hat{\boldsymbol{x}\in\Omegaisremovedfrom\Omega,assumingeitherNeumannorDirichletconditionsontheboundaryofthesmall‘hole′thuscreated.Ineachcase,thepotentialenergy\psi(\Omega_{\epsilon})ofthepunctureddomain\Omega_{\epsilon}=\Omega\setminus\B_{\epsilon}isexpandedabout\epsilon=0sothatthefirsttwotermsoftheperturbationaregiven.Thefirst(leading)termisthewell−documentedtopologicalderivativeof\psi$. 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.
Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...