Topological sensitivity analysis for a coupled nonlinear problem with an obstacle

• Autorzy: Abdelbari M. , Nachi K. , Sokolowski J.
• Języki publikacji: EN

Abstrakty

EN

The Topological Derivative has been recognized as a powerful tool in obtaining the optimal topology for several kinds of engineering problems. This derivative provides the sensitivity of the cost functional for a boundary value problem for nucleation of a small hole or a small inclusion at a given point of the domain of integration. In this paper, we present a topological asymptotic analysis with respect to the size of singular domain perturbation for a coupled nonlinear PDEs system with an obstacle on the boundary. The domain decomposition method, referring to the SteklovPoincar´epseudo-differential operator, is employed for the asymptotic study of boundary value problem with respect to the size of singular domain perturbation. The method is based on the observation that the known expansion of the energy functional in the ring coincides with the expansion of the Steklov-Poincar´e operator on the boundary of the truncated domain with respekt to the small parameter, which measures the size of perturbation. In this way, the singular perturbation of the domain is reduced to the regular perturbation of the Steklov-Poincar´e map ping for the ring. The topological derivative for a tracking type shape functional is evaluated so as to obtain the useful formula for application in the numerical methods of shape and topology optimization.

Słowa kluczowe

EN

topological derivative; shape optimization; SteklovPoincaroperator; Signorini problem; variational inequality; Helmholtz equation; coupled partial differential equations; conical differential; asymptotic expansions; singular perturbations of geometrical Romains; truncated domain

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2017
• Tom: Vol. 46, no. 1
• Strony: 5--25
• Opis fizyczny: Bibliogr. 21 poz., rys.

Twórcy

autor

Abdelbari M.

• Universit´e d’Oran 1, Ahmed BenBella, Laboratoire de Math´ematique et ses applications BP 1524, El M’naouer, Oran, Alg´erie
• Universit´e Hassiba Benbouali, D´epartement de Math´ematiques, Chlef, Alg´erie

autor

Nachi K.

• Universit´e d’Oran 1, Ahmed BenBella, Laboratoire de Math´ematique et ses applications BP 1524, El M’naouer, Oran, Alg´erie

autor

Sokolowski J.

• Universit´e de Lorraine-Nancy, Institut Elie Cartan, Laboratoire de Math´ematiques, B.P. 239, 54506, Vandoeuvre l`es Nancy cedex, France
• Systems Research Institute of the Polish Academy of Sciences, 01-447 Warszawa, ul. Newelska 6, Poland

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).