A new reliability analysis method for uncertain structures with random and interval variables

Au, F.T.K., Cheng, Y.S., Tham, L.G., Zeng, G.W.: Robust design of structures using convex models. Comput. Struct. 81, 2611–2619 (2003)

Bayarri, M.J., Berjer, J.O., Higdon, D., Kennedy, M.C., Kottas, A., Paulo, R., Sacks, J., Cafeo, J.A., Cavendish, J., Lin, C.H., Tu, J.: A framework for validation of computer models. In: Foundations for Verification and Validation in the 21st Century Workshop. John Hopkins University/Applied Physics Laboratory, Laurel (2000)

Ben-Haim, Y., Elishakoff, I.: Convex Models of Uncertainties in Applied Mechanics. Elsevier Science Publisher, Amsterdam (1990)

Breitung, K.W.: Asymptotic approximation for multinormal integrals. ASCE J. Eng. Mech. 110(3), 357–366 (1984)

Breitung, K.W.: Asymptotic Approximations for Probability Integrals. Springer, Berlin (1994)

Cheng, Y.S., Zhong, Y.X., Zeng, G.W.: Structural robust design based on hybrid probabilistic and non-probabilistic models. Chin. J. Comput. Mech. 22(4), 501–505 (2005)

Ditlevsen, O., Madsen, H.O.: Structural Reliability Methods. Wiley, Chichester (1996)

Du, X.P.: Interval reliability analysis. In: ASME 2007 Design Engineering Technical Conference and Computers and Information in Engineering Conference (DETC2007), Las Vegas, NV, USA (2007)

Du, X.P.: Saddle point approximation for sequential optimization and reliability analysis. ASME J. Mech. Des. 130, 0110011–0110022 (2008)

Du, X.P., Sudjianto, A., Huang, B.Q.: Reliability-based design with the mixture of random and interval variables. In: ASME 2003 Design Engineering Technical Conference and Computers and Information in Engineering Conference (DETC2003), Chicago, IL, USA (2005)

Elishakoff, I., Colombi, P.: Combination of probabilistic and convex models of uncertainty when limited knowledge is present on acoustic excitation parameters. Comput. Methods Appl. Mech. Eng. 104, 187–209 (1993)

Elishakoff, I., Colombi, P.: Ideas of probability and convexity combined for analyzing parameter uncertainty. In: Schueller, G.I., Shinozuka, M., Yao, J. (eds.) Proceedings of the 6th International Conference on Structural Safety and Reliability, pp. 109–113. Balkema Publishers, Rotterdam (1994)

Elishakoff, I., Cai, G.Q., Starnes, J.H.: Non-linear buckling of a column with initial imperfections via stochastic and non-stochastic convex models. Int. J. Nonlinear Mech. 29, 71–82 (1994)

Guo, J., Du, X.P.: Reliability sensitivity analysis with random and interval variables. Int. J. Numer. Methods Eng. 78, 1585–1617 (2009)

Guo, S.X., Lu, Z.Z.: Hybrid probabilistic and non-probabilistic model of structural reliability. J. Mech. Strength 24(4), 524–526 (2002)

Guo, X., Bai, W., Zhang, W.S.: Extremal structural response analysis of truss structures under load uncertainty via SDP relaxation. Struct. Saf. 87, 246–253 (2009)

Hasofer, A.M., Lind, N.C.: Exact and invariant second-moment code format. ASME J. Eng. Mech. Div. 100, 111–121 (1974)

Jiang, C., Han, X., Li, W.X., Liu, J.: A hybrid reliability approach based on probability and interval for uncertain structures. ASME J. Mech. Des. (in press)

Jiang, C., Han, X., Liu, G.R.: Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval. Comput. Methods Appl. Mech. Eng. 196, 4791–4890 (2007)

Kang, Z., Luo, Y.J.: Reliability-based structural optimization with probability and convex set hybrid models. Struct. Multidiscip. Optim. 42(1), 89–102 (2010)

Liang, J.H., Mourelators, Z.P., Tu, J.: A single-loop method for reliability-based design optimization. In: Proceedings of DETC’04 ASME 2004 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Salt Lake City, UT, USA (2004)

Luo, Y.J., Kang, Z., Alex, L.: Structural reliability assessment based on probability and convex set mixed model. Comput. Struct. 87, 1408–1415 (2009)

Madsen, H.O.: First order vs. second order reliability analysis of series structures. Struct. Saf. 2, 207–214 (1985)

Madsen, H.O., Krenk, S., Lind, N.C.: Methods of Structural Safety. Prentice-Hall, Englewood Cliffs (1986)

Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)

Qiu, Z.P., Yang, D., Elishakoff, I.: Probabilistic interval reliability of structural systems. Int. J. Solids Struct. 45, 2850–2860 (2008)

Rackwitz, R., Fiessler, B.: Structural reliability under combined random load sequences. Comput. Struct. 9(5), 489–494 (1978)

Rubinstein, R.Y., Kroese, D.P.: Simulation and the Monte-Carlo Method, 2nd edn. Wiley, New York (2007)

Thoft-Christensen, P., Murotsu, Y.: Application of Structural Systems Reliability Theory. Springer, Berlin (1986)

Yuan, Y.X., Sun, W.Y.: Optimization Theories and Methods. Scientific Press, Beijing (2005)

Zhang, Y., der Kiureghian, A.: Two improved algorithms for reliability analysis. Reliability and optimization of structural systems, In: Proceedings of the Sixth IFIP WG7.5 Working Conference on Reliability and Optimization of Structural Systems, Assisi, Italy (1995)

Zhu, L.P., Elishakoff, I.: Hybrid probabilistic and convex modeling of excitation and response of periodic structures. Math. Probl. Eng. 2, 143–163 (1996)