The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters

Ang, 1984, vol. 2 Cheong, 1995, Estimation of the minimum pressure coefficient due to gusts, Struct Saf, 17, 1, 10.1016/0167-4730(94)00036-P Rychlik, 1997, Modelling and statistical analysis of ocean-wave data using transformed Gaussian process, Mar Struct, 10, 13, 10.1016/S0951-8339(96)00017-2 Fisher, 1928, Limiting forms of the frequency distribution of the largest and smallest member of a sample, Proc Cambridge Phil Soc, 24, 180, 10.1017/S0305004100015681 Gumbel, 1958 Powell, 1958, On the fatigue failure of structures due to vibration excited by random pressure fields, J Acoust Soc Am, 30, 1130, 10.1121/1.1909481 Grigoriu, 1984, Crossings of non-Gaussian translation process, J Eng Mech, 110, 610, 10.1061/(ASCE)0733-9399(1984)110:4(610) Grigoriu, 1998, Simulation of stationary non-Gaussian translation processes, J Eng Mech, 124, 121, 10.1061/(ASCE)0733-9399(1998)124:2(121) Tognarelli, 1997, Equivalent statistical quadratization and cubicization for nonlinear system, J Eng Mech, 123, 512, 10.1061/(ASCE)0733-9399(1997)123:5(512) Crandall, 1970, First-crossing probability of the linear oscillator, J Sound Vib, 12, 285, 10.1016/0022-460X(70)90073-8 Kawano, 1999, Dynamic response and reliability analysis of large offshore structures, Comput Methods Appl Mech Eng, 168, 255, 10.1016/S0045-7825(98)00144-3 Chen, 1997, Study on dynamic reliability analysis of the structures with multi-degree-of-freedom, Comput Struct, 62, 877, 10.1016/S0045-7949(96)00319-7 Rice, 1944, Mathematical analysis of random noise, Bell Sys Tech J, 23, 282, 10.1002/j.1538-7305.1944.tb00874.x Lin, 1995 Kleiber, 1992 Ghanem, 1991 Li, 1996 Cramer, 1966, On the intersections between the trajectories of a normal stationary stochastic process and a high level, Arkiv fur Matematik, 6, 337, 10.1007/BF02590962 Vanmarcke, 1972, Properties of spectral moments with applications to random vibration, J Eng Mech Div, ASCE, 98, 425, 10.1061/JMCEA3.0001593 Spencer, 1988, Reliability of uncertain linear and nonlinear systems, J Eng Mech, 114, 135, 10.1061/(ASCE)0733-9399(1988)114:1(135) Li, 2004, Probability density evolution method for dynamic response analysis of structures with uncertain parameters, Comput Mech, 34, 400, 10.1007/s00466-004-0583-8 Li, 2006, The probability density evolution method for dynamic response analysis of non-linear stochastic structures, Int J Numer Methods Eng, 65, 882, 10.1002/nme.1479 Chen, 2005, Dynamic response and reliability analysis of nonlinear stochastic structures, Probabilist Eng Mech, 20, 33, 10.1016/j.probengmech.2004.05.006 Dostupov, 1957, The equation for the integral of a system of ordinary differential equations containing random parameters, Automatika i Telemekhanika, 18, 620 Loeve, 1977 Vanmacke, 1983 Soong, 1973 Li, 2005, The mapping-based dimension-reduction algorithm for probability density evolution analysis of stochastic structural responses (in Chinese), Chinese J Theor Appl Mech, 37, 460 Li J, Chen JB. Stochastic seismic response analysis and reliability evaluation of hysteretic structures. In: Lü ZT et al., editors, Innovation and sustainability of structures. Proceedings of the international symposium on innovation and sustainability of structures in civil engineering, November 20–22, 2005, Nanjing, PR China. Invited paper, 218–230, Southeast University Press. Chapra, 1998 Anderson, 1995 Elishakoff, 1998, Three versions of the finite element method based on concepts of either stochasticity, fuzziness, or anti-optimization, Appl Mech Rev, 51, 209, 10.1115/1.3098998 Bouc R. Forced vibration of mechanical systems with hysteresis. In: Proceedings of the 4th conference on nonlinear oscillations, Prague, Czechoslovakia; 1967, p. 315. Wen, 1976, Method for random vibration of hysteretic systems, J Eng Mech, 102, 249 Chung, 1994, A new family of explicit time integration methods for linear and nonlinear structural dynamics, Int J Numer Methods Eng, 37, 3961, 10.1002/nme.1620372303 Liu, 1986, Probability finite elements for nonlinear structural dynamics, Comput Methods Appl Mech Eng, 56, 61, 10.1016/0045-7825(86)90136-2