Efficient stochastic structural analysis using Guyan reduction

Advances in Engineering Software

Volumn 42, Issue 4, 2011, Pages 187-196

  Panayirci, H M ^a   Pradlwarter, H J ^a   Schueller G I ^a  

^a UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

Computational efficiency; Guyan reduction; Polynomial chaos expansion; Stochastic finite elements; Stochastic structural analysis; Uncertainty quantification

Indexed keywords

CHAOS THEORY; COMPUTATIONAL MECHANICS; FINITE ELEMENT METHOD; POLYNOMIALS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; STRUCTURAL ANALYSIS; UNCERTAINTY ANALYSIS;

GUYAN REDUCTION; POLYNOMIAL CHAOS EXPANSION; STOCHASTIC FINITE ELEMENTS; STOCHASTIC STRUCTURAL ANALYSIS; UNCERTAINTY QUANTIFICATION;

COMPUTATIONAL EFFICIENCY;

EID: 79953214019     PISSN: 09659978     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advengsoft.2011.02.004     Document Type: Article

References (36)

1. MSC. Nastran, Version 2008, MSC. Software Corporation, Santa Ana, CA, USA; 2008.
2. MSC. Patran, Version 2008, MSC. Software Corporation, Santa Ana, CA, USA; 2008.
3. N.-Z. Chen, and C. Guedes Soares Spectral stochastic finite element analysis for laminated composite plates Comput Methods Appl Mech Eng 197 51-52 2008 4830 4839
4. D. Chung, M. Gutiérrez, L. Graham-Brady, and F. Lingen Efficient numerical strategies for spectral stochastic finite element models Int J Numer Methods Eng 64 10 2005 1334 1349 (Pubitemid 41569107)
5. B. Debusschere, H. Najm, A. Matta, O. Knio, R. Ghanem, and O.L. Maitre Protein labeling reactions in electrochemical microchannel flow: numerical simulation and uncertainty propagation Phys Fluids 15 8 2003 2238 2250 (Pubitemid 37096643)
6. C. Desceliers, R. Ghanem, and C. Soize Polynomial chaos representation of a stochastic preconditioner Int J Numer Methods Eng 64 5 2005 618 634 (Pubitemid 41398955)
7. A. Doostan, R. Ghanem, and J. Red-Horse Stochastic model reduction for chaos representations Comput Methods Appl Mech Eng 196 37-40 2007 3951 3966 (Pubitemid 47029549)
8. H.C. Elman, O.G. Ernst, D.P. O'Leary, and M. Stewart Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering Comput Methods Appl Mech Eng 194 9-11 2005 1037 1055 (Pubitemid 40133560)
9. R. Ghanem, and R. Kruger Numerical solution of spectral stochastic finite element systems Comput Methods Appl Mech Eng 129 3 1996 289 303 (Pubitemid 126395806)
10. R. Ghanem, S. Masri, M. Pellissetti, and R. Wolfe Identification and prediction of stochastic dynamical systems in a polynomial chaos basis Comput Methods Appl Mech Eng 194 12-16 2005 1641 1654 (Pubitemid 40262946)
11. R. Ghanem, and P. Spanos Stochastic finite elements: a spectral approach 1991 Springer New York
12. R.G. Ghanem, and A. Doostan On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data J Comput Phys 217 1 2006 63 81 (Pubitemid 44137076)
13. D. Ghosh, P. Avery, and C. Farhat A FETI-preconditioned conjugate gradient method for large-scale stochastic finite element problems Int J Numer Methods Eng 80 6-7 2009 914 931
14. M. Guedri, N. Bouhaddi, and R. Majed Reduction of the stochastic finite element models using a robust dynamic condensation method J Sound Vib 297 1-2 2006 123 145 (Pubitemid 44107356)
15. R. Guyan Reduction of stiffness and mass matrices AIAA J 3 2 1965 380
16. S. Huang, S. Mahadevan, and R. Rebba Collocation-based stochastic finite element analysis for random field problems Probabilist Eng Mech 22 2 2007 194 205 (Pubitemid 46341514)
17. A. Keese, and H. Matthies Hierarchical parallelisation for the solution of stochastic finite element equations Comput Struct 83 14 2005 1033 1047 (Pubitemid 40423305)
18. B. Nair, and A. Keane Stochastic reduced basis methods AIAA J 40 8 2002 1653 1664 (Pubitemid 34945951)
19. M. Ngah, and A. Young Application of the spectral stochastic finite element method for performance prediction of composite structures Compos Struct 78 3 2007 447 456 (Pubitemid 44849307)
20. F. Nobile, R. Tempone, and C.G. Webster An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data SIAM J Numer Anal 46 5 2008 2411 2442
21. F. Nobile, R. Tempone, and C.G. Webster A sparse grid stochastic collocation method for partial differential equations with random input data SIAM J Numer Anal 46 5 2008 2309 2345
22. H.M. Panayirci, and M.F. Pellissetti Efficient component-wise and solver-based intrusive SFEM analysis of complex structures Finite Elements Anal Des 46 5 2010 449 459
23. M. Pellissetti, and R. Ghanem Iterative solution of systems of linear equations arising in the context of stochastic finite elements Adv Eng Softw 31 8-9 2000 607 616
24. M.F. Pellissetti, and G.I. Schuëller On general purpose software in structural reliability Struct Safety 28 1-2 2006 3 16 (Pubitemid 41600803)
25. M.F. Pellissetti, and G.I. Schuëller Scalable uncertainty and reliability analysis by integration of advanced monte carlo simulation and generic finite element solvers Comput Struct 87 13-14 2009 930 947
26. C.E. Powell, and H.C. Elman Block-diagonal preconditioning for spectral stochastic finite-element systems IMA J Numer Anal 2008 drn014
27. S. Sachdeva, P. Nair, and A. Keane Hybridization of stochastic reduced basis methods with polynomial chaos expansions Probabilist Eng Mech 21 2 2006 182 192
28. A. Sarkar, N. Benabbou, and R. Ghanem Domain decomposition of stochastic pdes: theoretical formulations Int J Numer Methods Eng 77 5 2009 689 701
29. G.I. Schuëller, and H.J. Pradlwarter Computational stochastic structural analysis (COSSAN) - a software tool Struct Safety 28 1-2 2006 68 82 (Pubitemid 41600806)
30. G.I. Schuëller, A state-of-the-art report on computational stochastic mechanics Probabilistic engineering mechanics 12 4 1997 197 321 (Pubitemid 127668995)
31. B. Sudret Global sensitivity analysis using polynomial chaos expansions Reliab Eng Syst Safety 93 7 2008 964 979 (Pubitemid 351313888)
32. Sudret B, Der Kiureghian A. Stochastic finite element methods and reliability a state-of-the-art report. Tech. rep., Department of Civil and Environmental Engineering University of California, Berkeley; 2000.
33. C.V. Verhoosel, M.A. Gutiérrez, and S.J. Hulshoff Iterative solution of the random eigenvalue problem with application to spectral stochastic finite element systems Int J Numer Methods Eng 68 4 2006 401 424 (Pubitemid 44592927)
34. D. Wei, Z. Cui, and J. Chen Uncertainty quantification using polynomial chaos expansion with points of monomial cubature rules Comput Struct 86 23-24 2008 2102 2108
35. D. Xiu, and J. Hesthaven High-order collocation methods for differential equations with random inputs SIAM J Sci Comput 27 3 2005 1118 1139
36. D. Xiu, and G. Karniadakis Modeling uncertainty in flow simulations via generalized polynomial chaos J Comput Phys 187 1 2003 137 167 (Pubitemid 36515575)