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Non-probabilistic set-theoretic model for structural safety measure

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Summary

In this paper, a new non-probabilistic set-theoretic safety measure for structures is proposed. Based on the non-probabilistic set-theoretic stress–strength interference model, the ratio of the volume of the safe region to the total volume of the region associated with the variation of the basic interval variables is suggested as the measure of structural non-probabilistic safety. The compatibility between the presented non-probabilistic set-theoretic safety measure and the probabilistic reliability is demonstrated. Numerical examples are used to shed a light on the validity of the presented measure.

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References

  1. Wang G.Y. (2002). On the development of uncertain structural mechanics. Adv. Mech. 32(2): 205–211 (in Chinese)

    Google Scholar 

  2. Elishakoff I. (1998). Three versions of the finite element method based on concepts of either stochasticity, fuzziness or anti-optimization. Appl. Mech. Rev. 51(3): 209–218

    Article  Google Scholar 

  3. Ben-Haim Y. and Elishakoff I. (1990). Convex Models of Uncertainty in Applied Mechanics. Elsevier, Amsterdam

    MATH  Google Scholar 

  4. Elishakoff I. (1994). A new safety factor based on convex modeling. In: Ayyub, B.M. and Gupta, M.M. (eds) Uncertainty Modeling and Analysis: Theory and Applications, pp 145–171. North-Holland, Amsterdam

    Google Scholar 

  5. Ben-Haim Y. (1994). A non-probabilistic concept of reliability. Struct. Saf. 14: 227–245

    Article  Google Scholar 

  6. Elishakoff I. (1995). Discussion on: A non-probabilistic concept of reliability. Struct. Saf. 17(3): 195–199

    Article  Google Scholar 

  7. Good I.J. (1995). Reliability always depends on probability of course. J. Stat. Comput. Simul. 52: 192–193

    Google Scholar 

  8. Good I.J. (1996). Reply to Prof. Y. Ben-Haim. J. Stat. Comput. Simul. 55: 265–266

    Article  Google Scholar 

  9. Cai K.Y., Wen C.Y. and Zhang M.L. (1991). Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context. Fuzzy Sets Syst. 42(2): 145–172

    Article  MATH  MathSciNet  Google Scholar 

  10. Chowdhury S.G. and Misra K.B. (1992). Evalutation of fuzzy reliability of a non-series parallel network. Microelectron. Reliab. 32: 1–4

    Article  Google Scholar 

  11. Vinot P., Cogan S. and Lallement G. (2003). Approche non-probabiliste de fiabilité basée sur les modèles convexes. Mec. Ind. 4(1): 45–50

    Google Scholar 

  12. Wang X.J. and Qiu Z.P. (2003). Robust reliability of structural vibration. J. Beijing Univ. Aeronaut. Astronaut 29(11): 1006–1010 (in Chinese)

    MathSciNet  Google Scholar 

  13. Qiu Z.P., Chen S.Q. and Wang X.J. (2004). Criterion of the non-probabilistic robust reliability for structures. Chin. J. Comput. Mech. 21(1): 1–6 (in Chinese)

    Google Scholar 

  14. Qiu Z.P., Müller P.C. and Frommer A. (2004). The new non-probabilistic criterion of failure for dynamical systems based on convex models. Math. Comput. Model. 40(1–2): 201–215

    Article  MATH  Google Scholar 

  15. Guo S.X., Lu Z.Z. and Feng Y.S. (2001). A non-probabilistic model of structural reliability based on interval analysis. Chin. J. Comput. Mech. 18(1): 56–60 (in Chinese)

    Google Scholar 

  16. Moore R.E. (1979). Methods and Applications of Interval Analysis. SIAM, Philadelphia

    MATH  Google Scholar 

  17. Alefeld G. and Herzberger J. (1983). Introduction to Interval Computations. Academic, New York

    MATH  Google Scholar 

  18. Qiu Z.P. and Wang X.J. (2005). Parameter perturbation method for dynamic responses of structures with uncertain-but-bounded parameters based on interval analysis. Int. J. Solids Struct. 42(18–19): 4985–4970

    MathSciNet  Google Scholar 

  19. Qiu Z.P., Wang X.J. and Friswell M.I. (2005). Eigenvalue bounds of structures with uncertain-but-bounded parameters. J. Sound Vibr. 282: 297–312

    Article  MathSciNet  Google Scholar 

  20. Elishakoff I. (2004). Safety Factors and Reliablity: Friends or Foes? Kluwer, Dordercht

    Google Scholar 

  21. Elishakoff I. and Ferracuti B. (2006). Four alternative definitions of the fuzzy safety factor. J. Aerospace Engng. 19(4): 281–287

    Article  Google Scholar 

  22. Elishakoff I. and Ferracuti B. (2006). Fuzzy sets based interpretation of the safety factor. Fuzzy Sets Syst. 157(18): 2495–2512

    Article  MATH  MathSciNet  Google Scholar 

  23. Freudenthal A.M. (1938). Allowable stresses and safety of structures. J. Assoc. Engng. Israel 1: 149–153 (in Hebrew)

    Google Scholar 

  24. Freudenthal A.M. (1956). Safety and probability of structural failure. Trans. ASCE 121: 1337–1375

    Google Scholar 

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Correspondence to Xiaojun Wang.

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Wang, X., Qiu, Z. & Elishakoff, I. Non-probabilistic set-theoretic model for structural safety measure. Acta Mech 198, 51–64 (2008). https://doi.org/10.1007/s00707-007-0518-9

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  • DOI: https://doi.org/10.1007/s00707-007-0518-9

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