Limit and Shakedown Reliability Optimization Accounting for Nonlinear Geometric Effects

  • Andrzej Siemaszko
Part of the International Centre for Mechanical Sciences book series (CISM, volume 432)


In this chapter, the relation between deterministic, stochastic and design parameters is explained. Differences between deterministic and reliability-based optimisation are pointed out. A formulation of the system reliability optimization with the limit and shakedown failure criteria is presented. For discrete structures it allows to account for nonlinear geometric effects. An example of limit reliability optimization is presented.


Limit Load Limit State Function Joint Probability Density Function Failure Function Reliability Optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bjerager, P. (1988). Probability integration by directional simulation, J.Eng.Mech., ASCE 114: 1285–1302.CrossRefGoogle Scholar
  2. Cohn, M.Z., Ghosh, S.K. and Parimi, S.R. (1972). A unified approach to the theory of plastic structures. J.Eng.Mech.Div., ASCE 98, EMS, 1133–1158.Google Scholar
  3. Cyras, A.A. (1969). Linear programming and analysis of elastic plastic structures. Leningrad: Stroiizdat (in Russian).Google Scholar
  4. Dolinski, K. (1983). First order second-moment approximation in reliability of structural systems: critical review and alternative approach. Struct. Safety 1: 211–231.CrossRefGoogle Scholar
  5. Madsen, H.O., Krenk, S. and Lind, N.C. (1986). Methods of Structural Safety. Prentice-Hall.Google Scholar
  6. Maier, G. (1970). A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes. Meccanica 5: 54–66.CrossRefMATHGoogle Scholar
  7. Nguyen, D.H. (1983). Aspects of analysis and optimization of structures under proportional and variable loadings. Eng.Opt. 7: 35–57.CrossRefGoogle Scholar
  8. Santos, J.L.T., Siemaszko A., Gollwitzer, S. and Rackwitz R. (1995). Continuum sensitivity method for reliability-based structural design and optimization. Mech.Struct.&Mach. 23: 497–520.CrossRefGoogle Scholar
  9. Siemaszko, A. (1995). Limit, post-yield, shakedown and inadaptation analysis of inelastic discrete structures. In Mróz, Z., Weichert, D. and Dorosz, S., eds., Inelastic Behaviour of Structures under Variable Loads, Dordrecht: Kluwer Academic Publishers.Google Scholar
  10. Siemaszko, A. and Dolinski, K. (1996). Limit state reliability optimization accounting for geometric effects. Struct.Opt., 11: 80–87.CrossRefGoogle Scholar
  11. Siemaszko, A. and König, J.A. (1990). Plastic optimization accounting for nonlinear geometrical effects. GAMM’90 Conf., Hannover.Google Scholar
  12. Siemaszko, A. and Mr6z, Z. (1991). Sensitivity of plastic optimal structures to imperfections and nonlinear geometrical effects. Struct.Opt. 3: 99–105.CrossRefGoogle Scholar
  13. Siemaszko, A. and Mrôz, Z. (1991). Optimal plastic design of imperfect frame structures. Progress in Structural Engineering, D. Grierson, A. Franchi, P. Riva (eds.). Dordrecht: Kluwer Academic Publishers.Google Scholar
  14. Siemaszko, A. and Santos, J.L.T. (1993). Reliability-based structural optimization. Proc. Struct. Opt. 93 World Congress, Rio de Janeiro, I, 473–480.Google Scholar
  15. Thoft-Christensen, P. (1990). On reliability-based structural optimization. A.Der Kiureghian, P.ThoftChristensen (eds.), Proc. 3rd IFIP WG 7.5 Conf, Springer, 387–402.Google Scholar

Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Andrzej Siemaszko
    • 1
  1. 1.Institute of Fundamental Technological ResearchWarsawPoland

Personalised recommendations