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A New Second-Order Approximate Reliability Method Based on Hyper-Parabolic Failure Surfaces

  • G. Q. Cai
  • I. Elishakoff
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

The first-order and second-order methods for structural reliability analysis are reviewed with attendant new interpretation for the first-order method and a new approximate result for the second-order method. Exact and approximate solutions for the example case - reliability of a shaft subject to random bending moments and a random torque are obtained. The comparison of the approximate results with exact ones shows that the first-order approximation is only applicable to the case where the failure surface is “far” from the origin, while the suggested second-order approximation yields quite accurate results even when the failure surface is “close” to the origin.

Keywords

structural reliability exact solution first and second-order approximations 

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References

  1. 1.
    Ditlevsen, O., Generalized second moment reliability index. Journal of Structural Mechanics, 7 (1979) 435–451.CrossRefGoogle Scholar
  2. 2.
    Madsen, H. O., Krenk, S. and Lind, N. C., Methods of Structural Safety, Prentile-Hall Inc., Englewood Cliffs, NJ., 1986.Google Scholar
  3. 3.
    Ditlevsen, O., Principle of normal tail approximation. Journal of Engineering Mechanics Division, ASCE, 107 (1980) 1191–1206.Google Scholar
  4. 4.
    Hohenbichler, M. and Rackwitz, R., Non-normal dependent vectors in structural safety. Journal of Engineering Mechanics Division, ASCE, 107 (1980) 1227–1238.Google Scholar
  5. 5.
    Hasofer, A. M. and Lind, N. C., Exact and invariant second-moment code format. Journal of Engineering Mechanics Division, ASCE, 100 (1974) 111–121.Google Scholar
  6. 6.
    Elishakoff, I., Probabilistic Methods in the Theory of Structures, Wiley- Interscience, New York, 1983.MATHGoogle Scholar
  7. 7.
    Elishakoff, I. and Hasofer, A. M., On the accuracy of Hasofer-Lind reliability index. Proceedings of International Conference on Structural Safety and Reliability, Volume I, Kobe, Japan, 1985, pp. 229–239.Google Scholar
  8. 8.
    Elishakoff, I. and Hasofer, A. M., Exact versus approximate determination of structural reliability. Applied Scientific Research, 44 (1987) 303–312.MATHCrossRefGoogle Scholar
  9. 9.
    Shinozuka, M., Basic analysis of structural safety. Journal of Structural Engineering, ASCE, 109 (1980) 721–740.CrossRefGoogle Scholar
  10. 10.
    Schueller, G. I. and Strix, R., A critical appraisal of methods to determine failure probabilities. Structural Safety, 4 (1987) 293–309.CrossRefGoogle Scholar
  11. 11.
    Schueller, G. I., Bucher, C. G., Bourgund, U., and Ouypornprasert, W., On efficient computational schemes to calculate structural failure reliabilities. probabilistic Engineering Mechanics, 4 (1989) 10–18.CrossRefGoogle Scholar
  12. 12.
    Schueller, G. I. and Bayer, V., Computational procedures in structural reliability. Uncertainty Modeling and Analysis, ed. B. Ayyub, IEEE Computer Society Press, Los Alamitos, CA, 1993, pp. 552–559.Google Scholar
  13. 13.
    Fiessler, B., Neumann, H-J. and Rackwitz, R., Quadratic limit states in structural reliability. Journal of Engineering Mechanics Division, ASCE, 105 (1979) 661–676.Google Scholar
  14. 14.
    Breitung, K., An asymptotic formula for the failure probability. Reliability Theory of Structural Engineering Systems, ed. G. Mohr. Danish Engineering Academy, Civil Department, Lyngby, Denmark, 1982, pp. 19–45.Google Scholar
  15. 15.
    Breitung, K., Asymptotic approximation for multinomial integrals. Journal of Engineering Mechanics Division, ASCE, 110 (1984) 357–366.CrossRefGoogle Scholar
  16. 16.
    Tvedt, L., Two second-order approximations to the failure probability, Veritas Report R74–33, Det norse Veritas, Oslo, Norway, 1983.Google Scholar
  17. 17.
    Freudenthal, A. M., Safety and probability of structural failure. Transactions ASCE, 121 (1965) 1337–1375.Google Scholar
  18. 18.
    Murzewski, J., Niezawodnosc Konstrukcji Inzyniernich, Arkady Publishing House, Warszawa, Poland, 1989 (in Polish).Google Scholar
  19. 19.
    Levi, R., Calculs probabilistes de la security des constructions. Ann. Ponts et chaussees, 119 (1949) 493–539 (in French).Google Scholar
  20. 20.
    Rackwitz, R. and Fiessler, B., Structural reliability under combined random load sequences. Computers and Structures, 9 (1978) 489–494.MATHCrossRefGoogle Scholar
  21. 21.
    Bolotin, V. V., Application of the Methods of the Theory of Probability and the Theory of Reliability to Analysis of Structures, State Publishing House for Buildings, Moscow, 1971. (English translation: FTD-MT-24–771-73, Foreign Technology Division, Wright-Patterson AFB, Ohio, 1974).Google Scholar

Copyright information

© Springer-Verlag, Berlin Heidelberg 1994

Authors and Affiliations

  • G. Q. Cai
    • 1
  • I. Elishakoff
    • 2
  1. 1.Center for Applied Stochastics ResearchFlorida Atlantic UniversityBoca RatonUSA
  2. 2.Center for Applied Stochastics Research and Department of Mechanical EngineeringFlorida Atlantic UniversityBoca RatonUSA

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