The nonlinear gaussian spectrum of log-normal stochastic processes and variables

Journal of Applied Mechanics, Transactions ASME

Volumn 66, Issue 4, 1999, Pages 964-973

  Ghanem, R ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

POLYNOMIALS; RANDOM PROCESSES; SPECTRUM ANALYSIS;

LOGNORMAL PROCESSES; NONLINEAR GAUSSIAN SPECTRUM;

MECHANICS;

EID: 0033293545     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.2791806     Document Type: Article

References (24)

1. Benjamin, J., and Cornell, C.A., 1970, Probability Statistics, and Decision for Civil Engineers, McGraw-Hill, New York.
2. Chambers, J.M., and Hastie, T.J., 1992, Statistical Models in S Wadsworth and Brooks/Cole Advanced Books and Software, Belmont, CA.
3. Gelhar, L., 1993, Stochastic Subsurface Hydrology, Prentice-Hall, Englewood Cliffs, NJ.
4. Ghanem, R., 1998a, “Hybrid Stochastic Finite Elements: Coupling of Spectral Expansions With Monte Carlo Simulations,” submitted lor review to ASME Journal of Applied Mechanics.
5. Ghanem, R., 1998b, “Probabilistic Characterization of Transport in Random Porous Media,” Computer Methods in Applied Mechanics and Engineering, Vol. 158, No. 3-4
6. Ghanem, R., and Spanos, P., 1991, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, New York.
7. Ghanem, R., and Spanos, P., 1991, “A Spectral Stochastic Finite Element Formulation for Reliability Analysis,” ASCE Journal of Engineering Mechanics, Vol. 117, No. 10, pp. 2351-2372.
8. Ghanem, R., and Spanos, P., 1993, “A Stochastic Galerkin Expansion for Nonlinear Random Vibration Analysis,” Probabilistic Engineering Mechanics, Vol. 8, pp. 255-264.
9. Ghanem, R., and Kruger, R., 1996, “Numerical Solution of Spectral Stochastic Finite Element Systems,” Computer Methods in Applied Mechanics and Engineering, Vol. 129, pp. 289-303.
10. Ghanem, R., and Brzkala, V., 1996, “Stochastic Finite Element Analysis for Random Layered Media,” ASCE Journal of Engineering Mechanics, Vol. 122, No. 4, pp. 361-369.
11. Ghanem, R., and Spanos, P.D., 1997, “Spectral Techniques for Stochastic Finite Elements,” Archives of Computational Methods in Engineering, Vol. 4, No. 1, pp. 63-100.
12. Gradshteyn, I.S., and Ryzhik, I.M., 1980, Tables of Integrals, Series, and Products, Academic Press, San Diego, CA.
13. Johnson, N.L., and Kotz, S., 1972, Distributions in Statistics: Continuous Multivariate Distributions, John Wiley and Sons, Inc., New York.
14. Kakutani, S., 1961, “Spectral Analysis of Stationary Gaussian Processes,” Proceedings, Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. II, J. Neyman ed., University of California, Berkeley, pp. 239-247.
15. Kallianpur, G., 1970, “The Role of Reproducing Kernel Hilbert Spaces in the Study of Gaussian Processes,” Advances in Probability Theory and Related Topics, Volume 2, Peter Ney, ed., Marcel Decker, Inc., New York, pp. 49-83.
16. Kallianpur, G., 1972, “Homogeneous Chaos Expansions,” Statistical Models in Turbulence, M. Rosenblatt and C. Van Atta, eds, Springer-Verlag, Berlin Heidelberg, pp. 230-254.
17. Li, R., and Ghanem, R., 1998, “Adaptive Polynomial Chaos Simulation Applied to Statistics of Extremes in Nonlinear Random Vibration,” Probabilistic Engineering Mechanics, Vol. 13, No. 2, pp. 125-136.
18. Shinozuka, M., and Deodatis, G., 1991, “Simulation of Stochastic Processes by Spectral Representation,” Applied Mechanics Reviews, Vol. 44, No. 4, pp. 191-204.
19. Spanos, P., and Ghanem, R., 1991, “Boundary Element Method Analysis for Random Vibration Problems,” ASCE Journal of Engineering Mechanics, Vol. 117, No. 2, pp. 409-423.
20. Spanos, P., and Zeldin, B., 1998, “Monte Carlo Treatment of Random Fields: A Broad Perspective,” Applied Mechanics Reviews, Vol. 51, pp. 219-237.
21. “Stale-of-the-Art Review on Computational Stochastic Mechanics,” 1997, Report prepared by the Subcommittee on Computational Stochastic Mechanics, IAS-SAR, Probabilistic Engineering Mechanics, Vol. 12, No. 4, pp. 197-321.
22. Wiener, N., 1938, “The Homogeneous Chaos,” Amer. J. Math, Vol. 60, pp. 897-936.
23. Winterslcin, S., 1988, “Nonlinear Vibration Models for Extremes and Fatigue,” ASME Journal of Engineering Mechanics, Vol. 114, No. 10, pp. 1772-1790.
24. Yang, J.N., and Manning, S.D., 1996, “A Simple Second Order Approximation for Stochastic Crack Growth Analysis,” Engineering Fracture Mechanics, Vol. 53, No. 5, pp. 677-686.