Skip to main content
SpringerLink
Log in

Optimal design of shells against buckling by means of the simulated annealing method

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

In this paper, the problem of optimal design of shells against instability under combined state of loadings is considered. We look for the shape of a meridian as well as the thickness of a shell, which ensures the maximal critical value of the loading parameter. The equality constraining the volume of material and the capacity of a shell are considered. The concept of a shell of uniform stability is applied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Andreev, L.V.; Mossakovsky, V.I.; Obodan, I.N. 1972: On the optimal thickness of a cylindrical shell under external pressure. Prikl Mat i Mekh36(4), 719–725 (in Russian)

    Google Scholar 

  2. Axelrad, E.I. 1985: On local buckling of thin shells. Int J Nonlinear Mech24(4), 249–259

    Google Scholar 

  3. Barski, M.; Krużelecki, J.; Trzeciak, P. 2001: Optimization of axially symmetric shells of uniform stability under torsion and axial force. In: Magnucki, K.; Mielniczuk, J. (eds.) Second Conference on Thin-Walled Vessels (held in Karłów, Poland), pp. 5–16. Zielona Góra: Wyższa Szkoła Pedagogiczna w Zielonej Górze

  4. Błachut, J. 1987: On optimal barrel-shaped shells under buckling constraints. AIAA J25, 186–188

    Google Scholar 

  5. Błachut, J. 1987: Combined axial and pressure buckling of shells having optimal positive gaussian curvature. Comput Struct26(3), 513–519

    Google Scholar 

  6. Bushnell, D. 1993: Optimization of composite, stiffened, imperfect panels under combined loads for service in the postbuckling regime. Comput Methods Appl Mech Eng103, 43–114

    Google Scholar 

  7. Feigen, M. 1952: Minimum weight of tapered round thin-walled columns. J Appl Mech5(3), 375–380

    Google Scholar 

  8. Gajewski, A.; Życzkowski, M. 1988: Optimal structural design under stability constraints. Dordrecht, Boston, Londyn: Kluwer Academic

  9. Gajewski, A. 1991: Multimodal optimization of uniformly compressed cylindrical shells. In: Eschenauer, H.A.; Mattheck, C.; Olhoff, N. (eds.) Engineering Optmization in Design Processes(ICKNC held in Karlsruhe 1990) pp. 275–282. Berlin Heidelberg New York: Springer

  10. Hutchinson, J.W. 1967: Imperfection sensitivity of externally pressurized spherical shells. J Appl Mech 34, 49

    Google Scholar 

  11. Hyman, B.I.; Lucas, A.W. 1971: An optimum design for the instability of cylindrical shells under lateral pressure. AIAA J9(4), 738–740

    Google Scholar 

  12. Kiciak, P. 2000: Basis of modelling of curves and surfaces. Warszawa: Wyd. Naukowo-Techniczne (in Polish)

  13. Kirkpatrick, S.; Gellat, C.D.Jr.; Vecchi, M.P. 1983: Optimization by simulated annealing. Science220, 671–680

    Google Scholar 

  14. Koiter, W.T. 1969: The nonlinear buckling problem of a complete spherical shell under uniform external pressure. Proc K ned Akad Went Series B 72, 40

  15. Krużelecki, J. 1988: Optimal design of a cylindrical shell under overall bending with axial force. Bull Polish Acad Sci Tech Sci36(3/4), 141–150

    Google Scholar 

  16. Krużelecki, J. 1997: On optimal barrel-shaped shells subjected to combined axial and radial compression. In: Gutkowski, W.; Mróz, Z. (eds.) Structural and Multidisciplinary Optimization (WCSMO-2held in Zakopane), pp. 467–472. Lublin: Wydawnictwo Ekoinżynieria

  17. Krużelecki, J.; Trzeciak, P. 1998: Optimal design of axially symmetrical shells under compression using the concept of a shell of uniform stability. In: Magnucki, K.; Mielniczuk, J. (eds.) Zbiorniki Cienkościenne (held in Karłów, Poland), pp. 39–42. Zielona Góra: Wyższa Szkoła Pedagogiczna w Zielonej Górze (in Polish with English summary)

  18. Krużelecki, J.; Życzkowski, M. 1984: Optimal design of an elastic cylindrical shell under overall bending with torsion. Solid Mech Arch9, 269–30

    Google Scholar 

  19. Krużelecki, J.; Życzkowski, M. 1985: Optimal design of shells – a survey. Solid Mech Arch10, 101–170

    Google Scholar 

  20. Krużelecki, J.; Trzeciak, P. 2000: Optimal design of rotationally symmetrical shells for inelastic buckling under hydrostatic pressure. In: Structural and Multidisciplinary Optimization (WCSMO-3 held in Buffalo 1999), (CD-ROM only), ISMO/UBCAD/UB/AIAA, Buffalo 1999

  21. Krużelecki, J.; Trzeciak, P. 2000: Optimal design of axially symmetrical shells under hydrostatic pressure with respect to their stability. Struct Multidisc Optim19(2), 148–154

    Google Scholar 

  22. Krużelecki, J.; Trzeciak, P.; Życzkowski, M. 1999: Optimal design of rotationally symmetric shells for buckling under thermal loadings. In: Skrzypek, J.J.; Hetnarski, R.B. (eds.) Thermal Stresses ’99 (3rd International Congress on Thermal Stresses held in Cracow, Poland), pp. 483–486. Kraków: Bratni Zew

  23. Krzyś, W. 1973: Optimum design of thin-walled cross-section columns. Bull Acad Pol Sci Ser SciTechnol21(9), 409–420

    Google Scholar 

  24. Laarhoven, van P.J.M.; Aarts, E.H.L. 1992: Simulated annealing – theory and applications. Dordrecht, Boston, Londyn: Kluwer Academic

  25. Leit, J.P.B.; Topping, B.H.V. 1999: Parallel simulated annealing for structural optimization. Comput Struct73, 545–564

    Google Scholar 

  26. Magnucki, K. 1993: Some problems of optimization of rod structures and shells with elastic stability condition taken into account. Poznań: Rozprawy No. 292, Polit. Poznańska (in Polish with English summary)

  27. Masters, T. 1993: Practical Neural Network Recipes in C++. Academic Press

  28. Mazurkiewicz, S.; Życzkowski, M. 1966: Optimum design of cross-section of thin-walled bar under torsion and bending. Bull Acad Pol Ser Sci Technol14(4), 273–282

    Google Scholar 

  29. Mioduchowski, A.; Thermann, K. 1973: Optimale Formen des dünnwandigen geschlossenen Querschnitts eines auf Biegung beanspruchten Balkens. ZAMM53(3), 193–198

    Google Scholar 

  30. Papkovitch, P.F. 1941: Theory of structural design of ships. Part 2, Gos. Soyuz. Izd. Sudostr. Promyshl., Leningrad (in Russian)

  31. Polynkin, A.A.; van Kaulen, F.; Toropov, V.V. 1995: Optimization of geometrically nonlinear thin-walled structures using the multipoint approximation method. Struct Optim9, 105–116

    Google Scholar 

  32. Rysz, M.; Życzkowski, M. 1989: Optimal design of a cylindrical shell under overall bending with axial force with respect to creep stability. Struct Optim1(1), 29–36

    Google Scholar 

  33. Shirshov, V.P. 1962: Local buckling of shells. In: Proc. II Vses. Konf. Teori Plastin i Obol., pp. 314–317 (in Russian)

  34. Taylor, J.E. 1967: The strongest column: energy approach. J Appl Mech34(2), 486–487

    Google Scholar 

  35. Wlassow, W.S. 1949: Allgemeine Schalentheorie und ihre Anwendung in der Technik. Berlin: Akademie-Verlag, (translated from Russian, Moskva-Leningrad 1949)

  36. Życzkowski, M. 1968: Optimale Formen des dünnwandigen geschlossenen Querschnittes eines Balkens bei Berücksichtigung von Stabilitätsbedingungen. ZAMM48(1), 455–462

    Google Scholar 

  37. Życzkowski, M. 1992: Recent advances in optimal structural design of shells. Eur J Mech A Solids11, Special issue, 5–24

    Google Scholar 

  38. Życzkowski, M.; Krużelecki, J. 1975: Optimal design of shells with respect to their stability. In: Sawczuk, A.; Mróz, Z. (eds.) IUTAM Symp. on Optimization in Structural Design(held in Warsaw 1973), pp. 229–247. Berlin Heidelberg New York: Springer

  39. Życzkowski, M.; Krużelecki, J.; Trzeciak, P. 2001: Optimal design of rotationally symmetric shells for buckling under thermal loadings. J Theor Appl Mech39(2), 443–455

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanics and Machine Design, Cracow University of Technology, ul. Jana Pawła II 37, 31-864 , Kraków, Poland

    M. Barski & J. Krużelecki

Authors
  1. M. Barski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Krużelecki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Krużelecki.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barski, M., Krużelecki, J. Optimal design of shells against buckling by means of the simulated annealing method. Struct Multidisc Optim 29, 61–72 (2005). https://doi.org/10.1007/s00158-004-0447-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-004-0447-3

Keywords

Search

Navigation