Structural optimization

, Volume 6, Issue 2, pp 134–141 | Cite as

Optimization of rigid-plastic shallow spherical shells of piecewise constant thickness

  • J. Lellep
  • H. Hein
Technical Papers
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Revised:

Abstract

An approximate method developed earlier for the investigation of large plastic deflections of circular and annular plates is accommodated for shallow spherical shells. The material of the shells is assumed to obey Tresca's yield condition and the associated deformation law. The minimum weight problem concerning shells operating in the post-yield range is posed under the conditions that (i) the thickness of the structure is piece-wise constant and (ii) the maximal deflections of the optimized shell and a reference shell of constant thickness, respectively, coincide. Necessary optimality conditions are derived with the aid of the variational methods of the optimal control theory. The set of equations obtained is solved numerically.

Keywords

Civil Engineer Control Theory Variational Method Yield Condition Approximate Method 
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References

  1. Budiansky, B. 1959: A reassessment of deformation theories of plasticity.J. Appl. Mech. 16, 259–264Google Scholar
  2. Duszek, M. 1969: Plastic analysis of shallow spherical shells at moderately large deflections. In: Niordson F.I. (ed.)Theory of thin shells, pp. 374–388. Berlin, Heidelberg, New York: SpringerGoogle Scholar
  3. Duszek, M. 1975:Geometrically non-linear theory of rigid-plastic structures (in Polish). Warsaw: IPPT PANGoogle Scholar
  4. Hodge, P.G. 1963:Limit analysis of rotationally symmetric plates and shells. New York: Prentice HallGoogle Scholar
  5. Ilioushine, A. 1957:Plasticité. Paris: EyrollesGoogle Scholar
  6. Jones, N.; Ich, N.T. 1972: The load carrying capacities of symmetrically loaded shallow shells.Int. J. Solids Struct. 8, 1339–1351Google Scholar
  7. Kislova, L. 1983: Large deflections of rigid-plastic shallow spherical shells hinged at the edge (in Russian).Issled. i rasczet stroit. konstr. M. TSNIISK, 25–31Google Scholar
  8. Kondo, K.; Pian, T.H.H. 1981: Large deformations of rigid-plastic shallow spherical shells.Int. J. Mech. Sci. 22, 69–76Google Scholar
  9. Krużelecki, J.; Życzkowski, M. 1985: Optimal structural design -a survey.SM Archives 10, 101–170Google Scholar
  10. Lellep, J. 1991:Optimization of plastic structures. Tartu: Tartu UniversityGoogle Scholar
  11. Lellep, J.; Hein, H. 1988: Large deflections of rigid-plastic shallow spherical shells (in Russian).Tartu Riikl. Ülik. Toim. 799, 37–51Google Scholar
  12. Lellep, J.; Hein, H. 1992: An approximate analysis of large plastic deformations of circular and annular plates.Tartu Ülik. Toim. 939, 54–69Google Scholar
  13. Lellep, J.; Lepik, Ü. 1984: Analytical methods in plastic structural design.Eng. Optim. 7, 209–239Google Scholar
  14. Rozvany, G.I.N. 1989:Structural design via optimality criteria. Dordrecht: KluwerGoogle Scholar
  15. Save, M.; Guerlement, G.; Lamblin, D. 1989: On the safety of optimized structures.Struct. Optim. 1, 113–116Google Scholar
  16. Save, M.; Prager, W. 1985:Structural optimization, Vol. 1, optimality criteria. New York: Plenum PressGoogle Scholar
  17. Sawczuk, A. 1982: On plastic shell theories at large strains and displacements.Int. J. Mech. Sci. 24, 231–244Google Scholar
  18. Shablii, O.N.; Koba, K.A. 1974: Finite deflections of annular axisymmetric shells of a rigid-plastic material with work-hardening (in Russian).Prikl. Mekh. (Soviet Appl. Mech.) 3, 9–16Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • J. Lellep
    • 1
  • H. Hein
    • 1
  1. 1.Department of Theoretical MechanicsTartu UniversityTartuEstonia

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