Abstract: The method of simultaneous topology and shape optimization of 2D structures by finite topology modification is presented in the paper. Both, structures in a plane state of stress and bending Kirchhoff's plates are analyzed here. Conditions for the introduction of finite topology modification based on the topological derivative are specified. When the respective condition is satisfied, finite holes and finite variations of existing boundaries are introduced into the structure. Next, standard shape optimization of new holes and variable boundaries is performed. Two basic types of modification are considered here, namely the introduction of holes of a prescribed size and shape and the introduction of holes of an unknown size and shape together with the introduction of finite changes of other boundaries. A heuristic algorithm for optimal design of topology and shape is proposed in the paper. Illustrative examples confirm applicability of the proposed approach.
B I B L I O G R A F I A1. Adamski W., 1997, Application of NURBS in numerical modeling of objects, Proceedings of the XIII Polish Conference on Computer Methods in Mechanics, Garstecki A., Rakowski J. (edit.), Politechnika Poznańska, 1, 89-97
2. Bojczuk D., Szteleblak W., 2003, Design optimisation for plane elasticity problems using finite topology variations, Proceedings of the 15th International Conference on Computer Methods in Mechanics, Wisła, CD ROM
3. Bojczuk D., Szteleblak W., 2005, Topology and shape optimization of plates using finite variations, Proceedings of the 16th International Conference on Computer Methods in Mechanics, Częstochowa, CD ROM
4. Burczyński T. (edit.), 2002, Computational sensitivity analysis and evolutionary optimization of systems with geometrical singularities, Zeszyty Naukowe Katedry Wytrzymałości Materiałów i Metod Komputerowych Mechaniki, Politechnika Śląska, Gliwice
5. Burczyński T., Kokot G., 2003, Evolutionary algorithms and boundary element method in generalized shape optimization, J. Theor. and Appl. Mech., 41, 2, 341-364
6. Czarnecki S., Dzierżanowski G., Lewiński T., 2004, Topology optimization of two-component plates, shells and 3D bodies, Optimal shape design and modelling, Selected papers presented at WISDOM 2004, Lewi«ski T., Sigmund O., Sokołowski J., Żochowski A. (edit.), Akademicka Oficyna Wydawnicza EXIT, Warszawa, 15-29
7. Dems K., 1980, Wieloparametrowa optymalizacja ksztaªtu konstrukcji, Zeszyty Naukowe, 371, Politechnika Łódzka, Łódź
8. Eschenauer H.A., Kobelev V.V., Schumacher A., 1994, Bubble method for topology and shape optimization, Struct. Optim., 8, 42-51
9. Gerald C.F., Wheatley P.O., 1995, Applied Numerical Analysis, Addison-Wesley Publishing Company
10. Il&apos
in A.M., 1992, Matching of asymptotic expansions of solutions of boundary value problems, Translations of Mathematical Monographs, 102, AMS
11. Kiciak P., 2005, Podstawy modelowania krzywych i powierzchni, WNT, Warszawa
12. Kleiber M. (edit.), 1995, Komputerowe metody mechaniki ciała stałego, PWN, Warszawa
13. Marczewska I., Sosnowski W., Marczewski A., Bednarek T., 2003, Topology and sensitivity - based optimization of stiffened plates and shells, Short Papers of the Fifth World Congress of Structural and Multidisciplinary Optimization, 271-272
14. Mróz Z., Bojczuk D., 2003, Finite topology variations in optimal design of structures, Struct. Multidisc. Optim., 25, 153-173
15. Sokołowski J., .ochowski A., 1999, On topological derivative in shape optimization, SIAM J. Control and Optimiz., 37, 4, 1251-1272 
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