Evaluation of structural dynamic responses by stochastic finite element method

  • Li, Q.S. (Department of Building and Construction, City University of Hong Kong) ;
  • Fang, J.Q. (Department of Building and Construction, City University of Hong Kong) ;
  • Liu, D.K. (Department of Building and Construction, City University of Hong Kong)
  • Published : 1999.11.25


The uncertainties associated with structural parameters and dynamic loading are identified and discussed. Structural parametric uncertainties are treated as random variables and dynamic wind load is simulated as a random process. Dynamic wind-induced responses of structures with parametric uncertainties are investigated by using stochastic finite element method. The formulas for structural dynamic reliability analysis considering the randomness of structural resistance and loading are proposed. Two numerical examples of high-rise structures are presented to illustrate the proposed methodology. The calculated results demonstrate that the variation in structural parameters indeed influences the dynamic response and the first passage probability evaluation of structures.


  1. Davenport, A.G. (1962), "The response of slender line-like structures to a gusty wind" , Proc. l.C.E., 23, 449-472.
  2. Kareem, A. and Hseih, J. (1986), "Reliability analysis of concrete chimmeys under wind loadings", J. Wind Engrg. & Ind. Aerodyn., 25.
  3. Kareem, A. and Sun, W.J. (1990), Dynamic response of structures with uncertain damping", Engineering Structure, 12, 1-8.
  4. Kleiber, M. and Hien, T.D. (1992), "The stochastic finite element method", John Wiley & Sons.
  5. Li, Q.S. (1986), "Dynamic reliability of tall buildings and high-rise structures with distributed parameters under the action of wind load", Journal of Engineering Mechanics, 3(3).
  6. Li, Q.S. (1988), "Analysis of random response and dynamic reliability of structures subjected to wind load", Journal of Earthquake Engineering and Engineering Vibration, 3.
  7. Li, Q.S. (1990), "Analysis of fuzzy random response and reliability of earthquake-resistant structures" , Chinese Journal of Applied Mechanics, 7(3).
  8. Li, Q.S. (1995), "Calculation of free vibration of high-rise structures", Asian Journal of Structural Engineering, 1(1), 17-25.
  9. Li, Q.S., Cao, H. and Li, Z. (1993a), "Dynamic Response and Reliability Analysis of Random Structures", Journal of Applied Mathematics and Mechanics, 14(10), 983-991.
  10. Li, Q.S., Cao, H. and Li, G.O. (1993b), "Dynamic reliability of Wuhan T.V. Tower under the action of wind load", Proceedings of the Third Asia-Pacific Symposium on Wind Engineering, 1, Hong Kong, December, 391-196.
  11. Li, Q.S., Cao, H. and Li, G.O. (1994), "Analysis of free vibrations of tall buildings", ASCE, Journal of Engineering Mechanics, 120(9), 1861-1876.
  12. Li, Q.S., Cao, H. and Li, G.O. (1996), "Static and dynamic analysis of straight bars with variable cross-section", International Journal of Computers & Structures, 59(6), 1185-1191.
  13. Spanos, P.D. and Ghanem, R. (1989), "Stochastic finite element expansion for random media", ASCE, Journal of Engineering Mechanics, 115, 1035-1053.
  14. Simiu, E. (1976), "The probability distributions of extreme wind speeds" , J. Struc. Div., ASCE, 107(ST9).
  15. Rice, S.O. (1944), "Mathematical analysis of random noise", Bell System Tech. Journal, 23, 282-332.
  16. Vanmarcke, E.H. and Grigoriu, M. (1983), "Stochastic finite element analysis of simple beam", ASCE, Journal of Engineering Mechanics, 109, 1203-1214.
  17. Wang, G.Y. (1978), Vibration of building and structures" , Science and Technology Press.

Cited by

  1. Response variability due to randomness in Poisson’s ratio for plane-strain and plane-stress states vol.43, pp.5, 2006,
  2. Analytical Evaluation of Dynamic Responses of Time-varying Systems vol.15, pp.8, 2009,
  3. Real-time modeling prediction for excavation behavior vol.16, pp.6, 2003,
  4. Failure probability prediction of concrete components vol.33, pp.10, 2003,
  5. Seismic random vibration analysis of tall buildings vol.26, pp.12, 2004,
  6. Forced Vibrations of Single-Degree-of-Freedom Systems with Nonperiodically Time-Varying Parameters vol.128, pp.12, 2002,
  7. Eigenvalues of structures with uncertain elastic boundary restraints vol.68, pp.3, 2007,
  8. Reliability analysis of a long span steel arch bridge against wind-induced stability failure during construction vol.65, pp.3, 2009,