Advertisement

Structural optimization

, Volume 9, Issue 3–4, pp 200–206 | Cite as

Optimization of plastic shallow shells exhibiting nonstable behaviour

  • J. Lellep
  • J. Majak
Technical Papers
  • 36 Downloads

Abstract

An optimal design technique is suggested for axisymmetric shallow shells exhibiting nonstable behaviour in the post-yield point range. The material of the shells is ideally rigidplastic obeying the von Mises yield condition, which is satisfied in the average and the associated deformation law. Spherical shells pierced with a hole and subjected to uniformly distributed transverse pressure are studied. Different cases of the support conditions are considered. Making use of the methods of the optimal control theory the problem is transformed into a boundary value problem which is solved numerically.

Keywords

Civil Engineer Optimal Design Control Theory Support Condition Yield Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Budiansky, B. 1959: A reassessment of deformation theories of plasticity.J. Appl. Mech. 26, 259–264Google Scholar
  2. Duszek, M. 1975:Geometrically non-linear theory of plastic structures (in Polish). Warsaw: IPPTGoogle Scholar
  3. Erkhov, M. 1978:Theory of ideally plastic solids and structures (in Russian). Moscow: NaukaGoogle Scholar
  4. Garstecki, A.; Gawecki, A. 1978: Experimental study on optimal plastic rings in the range of large displacements.Int. J. Mech. Sci. 20, 823–832Google Scholar
  5. Gawecki, A.; Garstecki, A. 1979: Optimal plastic design of rings with geometric constraints (in Polish).Mech. Teoret. i Stosowana 17, 63–74Google Scholar
  6. Ilioushine, A. 1975:Plasticite. Paris: EyrollesGoogle Scholar
  7. Jones, N. 1969: Combined distributed loads on rigid-plastic circular plates with large deflections.Int. J. Solids & Struct. 5, 51–64Google Scholar
  8. Lellep, J. 1985: Parametrical optimization of plastic cylindrical shells in the post-yield range.Int. J. Eng. Sci. 23, 1289–1303Google Scholar
  9. Lellep, J. 1991:Optimization of plastic structures. Tartu: Tartu Univ. PressGoogle Scholar
  10. Lellep, J.; Hein, H. 1993: Optimization of rigid-plastic shallow shells of piece-wise constant thickness.Struct. Optim. 6, 134–141Google Scholar
  11. Lellep, J.; Lepik, Ü. 1984: Analytical methods in plastic structural design.Eng. Opt. 7, 209–239Google Scholar
  12. Lellep, J.; Majak, J. 1992: Minimum weight design of plastic cylindrical shells accounting for large deflections.Tartu Ülik. 939, 42–53Google Scholar
  13. Lellep, J.; Majak, J. 1993: Optimal design of plastic annular plates of von Mises material in the range of large deflections.Struct. Optim. 5, 197–203Google Scholar
  14. Lellep, J.; Majak, J. 1994: Optimal design of plastic shallow shells of von Mises material (in press)Google Scholar
  15. Mróz, Z.; Gawecki, A. 1975: Post-yield behaviour of optimal plastic structures. In: Sawczuk, A.; Mróz, Z. (eds.)Optimization in structural design, pp. 518–540. Berlin, Heidelberg, New York: SpringerGoogle Scholar
  16. Ponter, A.R.S.; Martin, J.B. 1972: Some extremal properties and energy theorems for inelastic materials and their relationship to the deformation theory of plasticity.J. Mech. Phys. Solids 20, 218–300Google Scholar
  17. Rozvany, G.I.N. 1989:Structural design via optimality criteria. Dordrecht: KluwerGoogle Scholar
  18. Save, M.; Guerlement, G.; Lamblin, G. 1989: On the safety of optimized structures.Struct. Optim. 1, 113–116Google Scholar
  19. Save, M.A.; Massonet, C.E. 1972:Plastic analysis and design of plates, shells and disks. Amsterdam: North-HollandGoogle Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • J. Lellep
    • 1
  • J. Majak
    • 1
  1. 1.Tartu UniversityTartuEstonia

Personalised recommendations