Abstract
The emphasis of this paper is on developing suitable intervening variables and constraint approximations for structural reliability analysis. Traditionally, these procedures are used in structural optimization, whereas this research work adopts these concepts to safety index and failure probability computations. The use of these concepts enables the development of an efficient and stable iteration algorithm for identifying the most probable failure points (MPPs) of the limit state functions. An approximate second-order failure probability is calculated at this MPP with no extra computations of the limit state function and gradients. The efficiency and accuracy of the proposed algorithm are demonstrated by several examples with highly nonlinear, complex, explicit/implicit performance functions.
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References
Breitung, K. 1984: Asymptotic approximations for multinormal integrals.J. Eng. Mech., ASCE 110, pp. 357–366
Cai, G.Q.; Elishakoff, I. 1994: Refined second-order reliability analysis.J. Struct. Safety 14, No. 4, 267–276
Hasofer, A.M.; Lind, N.C. 1974: Exact and invariant secondmoment code format.J. Engng. Mech. Div. 100, No. EM1, ASCE, 111–121
Koyluoglu, K.U.; Nielsen, S.R.K. 1994: New approximations for SORM integrals.J. Struct. Safety 13, No. 4, 235–246
Lin, H.; Khalessi, M. 1993: Identification of the most-probablepoint in original space applications to structural reliability.Proc. 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Material Conf. (held in La Jolla), Paper No. AIAA-93-1623, pp. 2791–2800
Liu, Pei-Ling; Der Kiureghian, A. 1986: Optimization algorithms for structural reliability analysis.Report No. UCB/SESM-86/09, Department of Civil Engineering, University of California, Berkeley
Madsen, H.O.; Krenk, S.; Lind, N.C. 1986:Methods of structural safety. Prentice-Hall, Englewood Cliffs, New Jersey
Melchers, R.E. 1987:Structural reliability analysis and prediction. London: Ellis Horwood
Rackwitz, R.; Fiessler, B. 1978: Structural reliability under combined load sequences.Comp. & Struct. 9, 489–494
Reddy, M.V.; Grandhi,R.V.; Hopkins, D.A. 1994: Reliability based structural optimization: a simplified safety index approach.Comp. & Struct. 53, No. 6, 1407–1418
Sweeting, T.J.; Finn, A.F. 1992: A Monte Carlo method based on first- and second-order reliability approximations.J. Struct. Safety 11, Nos. 3+4, 203–212
Tichy, M. 1994: First-order third-moment reliability method.J. Struct. Safety 16, No. 3, 189–200
Todd, J. 1962:Survey of numerical analysis. New York: McGraw Hill
Tvedt, L. 1984: Two second order approximations to the failure probability.Section on Structural Reliability, A/S Vertas Research, Hovik, Norway
Wang, L.P.; Grandhi, R.V. 1994: Efficient safety index calculation for structural reliability analysis.Comp. & Struct. 52, 103–111
Wang, L.P.; Grandhi, R.V.; Hopkins, D.A. 1994: Structural reliability optimization using an efficient safety index calculation procedure.Proc. 35th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Material Conf. (held at Hilton Head, SC), pp. 858–863
Wu, Y.T.; Millwater, H.R.; Cruse, T.A. 1990: Advanced probabilistic structural analysis method for implicit performance function.AIAA J. 1, 1663–1705
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Wang, L., Grandhi, R.V. Intervening variables and constraint approximations in safety index and failure probability calculations. Structural Optimization 10, 2–8 (1995). https://doi.org/10.1007/BF01743688
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DOI: https://doi.org/10.1007/BF01743688