An unsteady adaptive stochastic finite elements formulation for rigid-body fluid-structure interaction

Computers and Structures

Volumn 86, Issue 23-24, 2008, Pages 2123-2140

  Witteveen, Jeroen A S ^a   Bijl, Hester ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Fluid structure interaction; Random parameters; Stochastic finite elements; Unsteady problems

Indexed keywords

AIRFOILS; COMPUTATIONAL MECHANICS; DAMPING; DYNAMICAL SYSTEMS; FINITE ELEMENT METHOD; FLOW INTERACTIONS; FLUID DYNAMICS; FUNCTION EVALUATION; INTERPOLATION; MONTE CARLO METHODS; RANDOM PROCESSES; SCHRODINGER EQUATION; STOCHASTIC PROGRAMMING; TIME SERIES ANALYSIS; UNSTEADY FLOW;

ADAPTIVE; COMPUTATIONAL COSTS; DAMPER SYSTEMS; DUFFING EQUATIONS; MASS-SPRING; MONTE-CARLO SIMULATIONS; PARAMETRIZATION; RANDOM INPUTS; RANDOM PARAMETERS; REFERENCE VALUES; ROBUST ADAPTIVE; SHAPE FUNCTIONS; SMALL INPUTS; STOCHASTIC BEHAVIORS; STOCHASTIC FINITE ELEMENTS; STRUCTURE INTERACTIONS; TIME SERIES; TIME TO CAPTURES; UNSTEADY PROBLEMS;

FLUID STRUCTURE INTERACTION;

EID: 54849432733     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2008.06.009     Document Type: Article

References (36)

1. Babuška I.M., Tempone R., and Zouraris G.E. Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J Numer Anal 42 2 (2004) 800-825
2. Babuška I.M., Nobile F., and Tempone R. A stochastic collocation method for elliptic partial differential equations with random input data. SIAM J Numer Anal 45 3 (2007) 1005-1034
3. Bathe K.J., and Zhang H. Finite element developments for general fluid flows with structural interactions. Int J Numer Methods Eng 60 (2004) 213-232
4. de Boer A., van der Schoot M.S., and Bijl H. Mesh deformation based on radial basis function interpolation. Comput Struct 85 (2007) 784-795
5. Breitung K. Asymptotic approximations for probability integrals (1994), Springer, New York
6. Casciati F., and Faravelli L. Fragility analysis of complex structural systems (1990), Research Studies Press, Taunton
7. Casciati F., and Roberts B. Mathematical models for structural reliability analysis (1996), CRC Press, Boca Raton
8. Chorin A.J., and Marsden J.E. A mathematical introduction to fluid mechanics (1979), Springer-Verlag, New York
9. Deb M.K., Babuška I.M., and Oden J.T. Solution of stochastic partial differential equations using Galerkin finite element techniques. Comput Methods Appl Mech Eng 190 (2001) 6359-6372
10. Fung Y. An introduction to aeroelasticity (1969), Dover Publications, New York
11. Ghanem R.G., and Spanos P.D. Stochastic finite elements: a spectral approach (1991), Springer-Verlag, New York
12. Hammersley J.M., and Handscomb D.C. Monte Carlo methods, Methuen's monographs on applied probability and statistics (1964), Fletcher & Son Ltd., Norwich
13. Hosder S, Walters RW, Perez R. A non-intrusive polynomial chaos method for uncertainty propagation in CFD simulations. In: 44th AIAA aerospace sciences meeting and exhibit, Reno (NV), AIAA-2006-891; 2006.
14. Iman R.L., Helton J.C., and Campbell J.E. An approach to sensitivity analysis of computer models: Part 1. Introduction, input variable selection and preliminary variable assessment. J Qual Technol 13 3 (1981) 174-183
15. Lee BHK, Jiang LY, Wong YS. Flutter of an airfoil with a cubic nonlinear restoring force. In: 39th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Long Beach (CA), AIAA-1998-1725; 1998.
16. Le Maître O.P., Knio O.M., Najm H.N., and Ghanem R.G. Uncertainty propagation using Wiener-Haar expansions. J Comput Phys 197 (2004) 28-57
17. Le Maître O.P., Najm H.N., Ghanem R.G., and Knio O.M. Multi-resolution analysis of Wiener-type uncertainty propagation schemes. J Comput Phys 197 (2004) 502-531
18. Loeven GJA, Witteveen JAS, Bijl H. Probabilistic collocation: an efficient non-intrusive approach for arbitrarily distributed parametric uncertainties. In: 45th AIAA aerospace sciences meeting and exhibit, Reno (NV), AIAA-2007-317; 2007.
19. Madsen H., Krenk S., and Lind N.C. Methods of structural safety (1986), Prentice-Hall, Englewood Cliffs
20. Mathelin L., Hussaini M.Y., and Zang Th.A. Stochastic approaches to uncertainty quantification in CFD simulations. Numer Alg 38 1-3 (2005) 209-236
21. McKay M.D., Conover W.J., and Beckman R.J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21 (1979) 239-245
22. Millman D.R., and King P.I. Airfoil pitch-and-plunge bifurcation behavior with Fourier chaos expansions. J Aircraft 42 2 (2005) 376-384
23. Myers R.H. Response surface methodology (1971), Allyn and Bacon, Boston
24. Pettit C.L., and Beran P.S. Effects of parametric uncertainty on airfoil limit cycle oscillation. J Aircraft 40 5 (2003) 1004-1006
25. Pettit C.L., and Beran P.S. Spectral and multiresolution Wiener expansions of oscillatory stochastic processes. J Sound Vib 294 (2006) 752-779
26. Reagan M.T., Najm H.N., Ghanem R.G., and Knio O.M. Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection. Combust Flame 132 (2003) 545-555
27. Schenk C.A., and Schuller G.I. Uncertainty assessment of large finite element systems (2005), Springer, Berlin
28. Tatang MA. Direct incorporation of uncertainty in chemical and environmental engineering systems. PhD thesis, Cambridge: MIT; 1995.
29. Wan X.L., and Karniadakis G.E. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. J Comput Phys 209 2 (2005) 617-642
30. Wan X.L., and Karniadakis G.E. Long-term behavior of polynomial chaos in stochastic flow simulations. Comput Methods Appl Mech 195 (2006) 5582-5596
31. Wiener N. The homogeneous chaos. Am J Math 60 (1938) 897-936
32. Wiener N. Nonlinear problems in random theory (1958), MIT Technology Press and John Wiley and Sons, New York
33. Witteveen J.A.S., Sarkar S., and Bijl H. Modeling physical uncertainties in dynamic stall induced fluid-structure interaction of turbine blades using arbitrary polynomial chaos. Comput Struct 85 (2007) 866-878
34. Witteveen J.A.S., Loeven G.J.A., Sarkar S., and Bijl H. Probabilistic collocation for period-1 limit cycle oscillations. J Sound Vib 311 1-2 (2008) 421-439
35. Witteveen JAS, Loeven GJA, Bijl H. An adaptive stochastic finite elements approach based on Newton-Cotes quadrature in simplex elements, submitted for publication.
36. Xiu D.B., and Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24 2 (2002) 619-644