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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-49a92c0d-261a-4b08-8f65-df0c468cbefd

Czasopismo

Control and Cybernetics

Tytuł artykułu

Shape and topology optimization of distributed parameter systems

Autorzy Sokołowski, J.  Żochowski, A. 
Treść / Zawartość
Warianty tytułu
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, Jan.Sokolowski@univ–lorraine.fr
  • Systems Research Institute of the Polish Academy of Sciences,ul. Newelska 6, 01-447 Warszawa, Poland
autor Żochowski, A.
Bibliografia
1. Berezin, F.A., Faddeev, L.D. (1961) Remark on the Schrödinger equation with singular potential. Dokl. Akad. Nauk. SSSR, 137, 1011–1014.
2. Garreau, S., Guillaume, Ph. and Masmoudi, M. (2001) The Topological Asymptotic for PDE Systems: The Elasticity Case. SIAM Journal on Control and Optimization, 39, 6, 1756–1778.
3. Gross, W.A. (1957) The second fundamental problem of elasticity applied to a plane circular ring. Zeitschrift für Angewandte Mathematik und Physik, 8,71–73.
4. Kachanov, M., Shafiro, B., Tsukrov, I. (2003) Handbook of Elasticity Solutions. Kluwer Academic Publishers.
5. Kanaun, S.K., Levin, V. (2008) Self-Consistent Methods for Composites. Springer.
6. Kowalewski, A. , Lasiecka, I. & Sokolowski, J. (2012) Sensitivity analysis of hyperbolic optimal control problems. Computational Optimization and Applications, 52, 1, 147–179.
7. Kurasov, P. and Posilicano, A. (2005) Finite speed of propagation and local boundary conditions for wave equations with point interactions. Proc. Amer. Math. Soc., 133, 10, 3071–3078.
8. Lurie, A.I. (2005) Theory of Elasticity. Springer Verlag, Berlin-Heidelberg.
9. Lewinski, T. and Sokolowski, J. (2003) Energy change due to the appearance of cavities in elastic solids. Int. J. Solids Struct. 40, 7, 1765–1803.
10. Muskhelishvili, N.I. (1952) Some Basic Problems on the Mathematical Theory of Elasticity. Noordhoff.
11. Novotny,A.A., Novotny,R.A., Padra,C. and Taroco,E.A. (2003) Topological sensitivity analysis. Computer Methods in Applied Mechanics and Engineering, 192, 7-8, 803–829.
12. Sokolowski J., Żochowski A. (1999) On topological derivative in shape optimization. SIAM Journal on Control and Optimization, 37, 4, 1251–1272.
13. Sokolowski J., Żochowski A. (2003) Optimality conditions for simultaneous topology and shape optimization. SIAM Journal on Control and Optimization, 42, 4, 1198–1221.
14. Sokołowski, J., Żochowski, A. (2005) Modelling of topological derivatives for contact problems. Numerische Mathematik, 102, 1, 145–179.
15. Sokołowski, J., Żochowski, A. (2008) Topological derivatives for optimization of plane elasticity contact problems. Engineering Analysis with Boundary Elements, 32, 11, 900–908.
Kolekcja BazTech
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