Shape and topology optimization of distributed parameter systems

• Autorzy: Sokołowski J. , Żochowski A.
• Języki publikacji: EN

Abstrakty

EN

The energy functional for an elliptic boundary value problem in two spatial dimensions is considered. The variations of shape functional resulting from the small shape-topological domain perturbations with the holes and inclusions in elastic body are determined. The exact representation of solutions to the boundary value problem is exploited for the purposes of asymptotic analysis. To this end the perturbed solutions of the boundary value problem are Expressem as the minimizers of perturbed energy functionals. The proposed method of asymptotic analysis results in the double asymptotic expansions, with respect to the size of a hole and to the contrast parameter of an inclusion with respect to the matrix, of solutions to the boundary value problems as well as of the associated energy functional. The shape sensitivity analysis of the energy functional with respekt of the boundary variations of an inclusion is performed. The further asymptotic analysis allows for the limit passage with the size of inclusion to zero. In this way the topological derivative of the energy functional is obtained. The proposed analysis can be used in the shape and topology optimum design for elastic bodies governed by the stationary as well as by the time dependent elasticity boundary value problems in the framework of selfadjoint extensions of elliptic operators.

Słowa kluczowe

EN

shape optimization; topological derivative; asymptotic analysis; singularly perturbed geometrical domains; asymptotic expansion of energ functional

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: Vol. 42, no. 1
• Strony: 217--226
• Opis fizyczny: Bibliogr. 15 poz., il. wykr.

Twórcy

autor

Sokołowski J.

• Institut Élie Cartan, UMR 7502 Nancy-Université-CNRS-INRIA, Laboratoire de Mathématiques, Université Henri Poincaré Nancy 1, B.P. 239, 54506 Vandoeuvre Lès Nancy Cedex, France
• Systems Research Institute of the Polish Academy of Sciences,ul. Newelska 6, 01-447 Warszawa, Poland

autor

Żochowski A.

• Systems Research Institute of the Polish Academy of Sciences,ul. Newelska 6, 01-447 Warszawa, Poland

Bibliografia

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