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Topological sensitivity derivative : application in optimal design and material science

Autorzy
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The concept of topologicai derivative is introduced and applied to optimal design of structural elements and to study the material microstructure evolution. For structural design the objective function and constraints provide the optimal design, for material microstructure the free energy and dissipation function generate the process of evolution such as phase transformation, crack growth or void generation. Three general modes of topology variation have been considered: generation of new elements, removing of the existing elements and a substitution of the existing elements by new elements. The cases of infinitesimal and finite topology variations have been discussed and illustrated by examples.
Rocznik
Tom
Strony
229--259
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
autor
  • Institute of Fundamental Technological Research, Warsaw, Poland Tel: 0048-41-3424-363; fax: 0048-41-3424-306, mecdb@eden.tu.kielce.pl
Bibliografia
  • 1. Allaire G.: Shape optimization by the homogenization method, New York, Springer 2002.
  • 2. Bendsoe M.P.: Optimization of structural topology, shape and materiał, Berlin, Springerl997.
  • 3. Bendsoe M.P., Kikuchi N.: Generating optimal topologies in structural design using a homogenization method, Comp. Meth. Appl. Mech. Eng., 71 (1988), 197-224.
  • 4. Bojczuk D.: Method of optimal reinforcement of structures based on topologi-cal derivative, in: Proc. III Europ. Conf. Comp. Mech., C. Mota Soares et al. (Eds), Lisbon, Springer 2006, on CD.
  • 5. Bojczuk D., Mróz Z.: On optimal design of supports in beam and frame structures, Struct. Optim., 16 (1998), 47-57.
  • 6. Bojczuk D., Mróz Z.: Optimal design of trusses with account for topology yariation, Mech. Struct. Mach., 26 (3998), 21-40.
  • 7. Bojczuk D., Mróz Z.: Optimal topology and configuration design of trusses with stress and buckling constraints, Struct. Optim., 17 (1999), 25-35.
  • 8. Bojczuk D., Szteleblak W.: Application of finite variations to topology and shape optimization of 2D structures, J. Theoret. Appl. Mech., 44 (2006), 323-349.
  • 9. Burczyński T., Kokot G.: Evolutionary algorithms and boundary element method in generalized shape optimization, J. Theor. Appl. Mech., 41 (2003), 341-364.
  • 10. Cherkaev A.V.: Yariational methods for structural optimization, New York, Springer 2000.
  • 11. Dems K., Mróz Z.: Yariational approach by means of adjoint systems to structural optimization and sensitivity analysis. II. Structure shape yariation, Int. J. Solids Struct., 19 (1984), 527-552.
  • 12. Dems K., Mróz, Z.: Optimal design of rib-stiffeners in disks and plates, Int. J. Solids Struct., 25 (1989), 973-998.
  • 13. Eschenauer H.A., Kobelev V.V., Schumacher A.: Bubble method for topology and shape optimization of structures, Struct. Optim., 8 (1994), 42-51.
  • 14. Garstecki A., Mróz Z.: Optimal design of supports of elastic structures sub-jected to loads and initial distortions, Mech. Struct. Mach., 15 (1987), 47-68.
  • 15. Hills R.E., Abbaschian R.: Physical metallurgy principlcs, PWS Publ. Co. 1994.
  • 16. Kirsch U.: Optimal topologies of structures, Appl. Mech. Rev., 42 (1989), 223-239.
  • 17. Lam Y.C., Santhikumar S.: Automated rib location and optimization for piąte structures, Struct. Multidisc. Optim., 25 (2003), 35-45.
  • 18. Lewiński T., Telega J.J.: Plates, laminates and shells. Asymptotic analysis and homogenization, Singapore, World Scientific 2000.
  • 19. Mróz Z., Bojczuk D.: Topological derivative and its application in optimal design of truss and beam structures for displacement, strcss and buckling constraints, in: Topology Optimization of Structures and Composite Con-tinua, G. I. N. Rozvany, N. OlhofN. (Eds.), Kluwer Ac. Publ. 2000, 91-105.
  • 20. Mróz Z., Bojczuk D.: Finite topology variation in optima! design of structures, Struct. Multidisc. Optim., 25 (2003), 153-173.
  • 21. Mróz Z., Garstecki A.: Optimal loading conditions in the design and identifi-cation of structures. Fart 1: discrete formulation, Struct. Multidisc. Optim., 29 (2005), 1-18.
  • 22. Petryk H., Mróz Z.: Time derivatives of integrals and functionals defined on yarying volume and surface domains, Arch. Mech., 38 (1986), 697-724.
  • 23. Sethian J.A.: Level set methods and fast marching methods: evolving inter-faces in computational geometry, Fluid Mechanics Computer Yision and Materials Science, Carnbr. Univ. Press 1999.
  • 24. Sokolowski J., Żochowski T.: On topological derivativc in shape optimiza-tion, SIAM J. Control Optim., 37 (1999), 1251-1272.
  • 25. Wang X., Wang M.Y., Guo D.: Structural shape and topology Optimization in a level-set-based framework of region representation, Struct. Multidisc. Optim., 27 (2004), 1-19
  • 26. Xia Q., Wang M.Y., Wang S., Chen S.: Semi-Lagrange method for level-set based structural topology and shape Optimization, Struct. Multidisc. Optim., 32 (2006), in print.
  • 27. Xie Y.M., Steven G.P.: A simple evolutionary procedurę for structural Optimization, Comp. Struct., 49 (1993), 885-896.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPP1-0064-0067
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