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Une Méthode d'Analyse Asymptotique En Optimisation Topologique by Sy-A

Une Méthode d'Analyse Asymptotique En Optimisation Topologique

by Sy-A
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Book cover type: Paperback
  • ISBN13: 9783841732217
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 80
  • Original Price: GBP 29.0
  • Language: French
  • Edition: N/A
  • Item Weight: 127 grams
  • BISAC Subject(s): General

De manière générale, les problèmes d'optimisation de formes rencontrés dans les sciences de l'ingénieur peuvent ètre modélisés de la façon suivante min Ω∈Σ, J(Ω, u(Ω)), où Σ est un ensemble de domaines admissibles et u(Ω) est solution d'une certaine équation aux dérivées partielles posées dans Ω ⊂ IR n. Le but de l'analyse de la sensibilité topologique est de donner une expression asymptotique d'une fonctionnelle de forme définie sur Ω en inçerant un petit trou dans le domaine. Dans ce document, une telle expression est obtenue et analysée dans le contexte d'élasticité linéaire, pour un trou de forme quelconque et une fonctionnelle générale en utilisant une adaptation de la méthode adjointe à l'optimisation topologique et la technique de troncature du domaine. Pour terminer, les résultats sont appliqués en dimensions N= 2,3 à l'équation de Poisson avec une condition de Dirichlet au bord d'un trou de forme quelconque. Ensuite, des résultats numériques (la sensibilité topologique est utilisée comme direction de descente) sont donnés pour l'équation de Black-Schols, illustrant efficacité de cette méthode en optimisation de forme.

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