Collocation-based stochastic finite element analysis for random field problems

Probabilistic Engineering Mechanics

Volumn 22, Issue 2, 2007, Pages 194-205

  Huang, Shuping ^a   Mahadevan, Sankaran ^a   Rebba, Ramesh ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

Collocation; Galerkin; Karhunen Loeve expansion; Polynomial chaos; Response surface; Stochastic finite elements

Indexed keywords

CHAOS THEORY; FINITE ELEMENT METHOD; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; RANDOM PROCESSES; SAMPLING;

KARHUNEN-LOEVE EXPANSION; POLYNOMIAL CHAOS; RANDOM FIELD PROBLEMS; RESPONSE SURFACE; STOCHASTIC FINITE ELEMENTS;

STOCHASTIC CONTROL SYSTEMS;

EID: 33847414385     PISSN: 02668920     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.probengmech.2006.11.004     Document Type: Article

References (24)

1. Ghanem R., and Spanos P.D. Stochastic finite elements: A spectral approach (1991), Springer-Verlag
2. Ghanem R., and Kruger R. Numerical solution of spectral stochastic finite element systems. Computer Methods in Applied Mechanics and Engineering 129 (1996) 289-303
3. Ghanem R., and Spanos P.D. Spectral techniques for stochastic finite elements. Archives of Computational Methods in Engineering 4 1 (1997) 63-100
4. Ghanem R. Ingredients for a general purpose of stochastic finite element formulation. Computer Methods in Applied Mechanics and Engineering 168 1-4 (1999) 19-34
5. Ghiocel D., and Ghanem R. Stochastic finite element analysis of seismic soil-structure interaction. Journal of Engineering Mechanics ASCE 128 1 (2002) 66-77
6. Huang S.P., Quek S.T., and Phoon K.K. Convergence study of the truncated Karhunen-Loeve expansion for simulation of stochastic processes. International Journal for Numerical Methods in Engineering 52 (2001) 1029-1043
7. Iman R.L., and Conover W.J. A distribution free approach to introducing rank correlation among input variables. Communication on Statistics-Simulation and Computation 11 3 (1982) 311-334
8. Isukapalli S.S., Roy A., and Georgopoulos P.G. Stochastic response surface methods (SRSMs) for uncertainty propagation: Application to environmental and biological systems. Risk analysis 18 3 (1998) 351-363
9. Li C.C., and Der-Kiureghian A. Optimal discretization of random process. Journal of Engineering Mechanics ASCE 119 6 (1993) 1136-1154
10. Li R., and Ghanem R. Adaptive polynomial chaos simulation applied to statistics of extremes in nonlinear random vibration. Probabilistic Engineering Mechanics 13 2 (1998) 125-136
11. Liu W.K., Belytschko T., and Mani A. Random field finite elements. International Journal for Numerical methods in Engineering 23 (1986) 1831-1845
12. McKay M.D., Beckman R.J., and Conover W.J. A comparison of three methods for selecting values of input variables in analysis of output from a computer code. Technometrics 2 (1979) 239-245
13. Pellissetti M., and Ghanem R. Iterative solution of systems of linear equations arising in the context of the stochastic FEM. Journal of Advances in Engineering Software 31 (2000) 607-616
14. Phoon K.K., Huang S.P., and Quek S.T. Simulation of non-Gaussian processes using Karhunen-Loeve expansion. Computers & Structures 80 (2002) 1049-1060
15. Phoon K.K., Huang S.P., and Quek S.T. Implementation of Karhunen-Loeve expansion for simulation using a wavelet-Galerkin scheme. Probabilistic Engineering Mechanics 17 (2002) 293-303
16. Quek S.T., Huang S.P., and Phoon K.K. A unified procedure for simulating second-order stochastic processes. First M.I.T. conference on computational fluid and solid mechanics (2001), Massachusetts Institute of Technology
17. Tatang M.A., Pan W., Prinn R.G., and McRae G.J. An efficient method for parametric uncertainty analysis of numerical geophysical models. Journal of Geophysical Research 102 D18 (1997) 21925-21932
18. Yamazaki F., and Shinozuka M. Neumann expansion for stochastic finite element analysis. Journal of Engineering Mechanics ASCE 114 8 (1988) 1335-1354
19. Van Trees H.L. Detection, estimation and modulation theory, Part 1 (1968), John Wiley & Sons, New York
20. Vanmarcke E., and Grigoriu M. Stochastic finite element analysis of simple beams. Journal of Engineering Mechanics ASCE 109 (1983) 1203-1214
21. Villadsen J., and Michelsen M.L. Solution of differential equation models by polynomial approximation (1978), Prentice-Hall, Englewood Cliffs (NJ)
22. Xiu D., and Karniadakis G.E. Modeling uncertainty in flow simulations via generalized polynomial chaos. Journal of Computational Physics (2001)
23. Schoutens W. Stochastic processes and orthogonal polynomials (2000), Springer, New York
24. Huang S. Simulation of random processes using Karhunen-Loeve expansion. Ph.D. thesis. National University of Singapore, Singapore; 2001