Open Access
Issue
Mechanics & Industry
Volume 16, Number 4, 2015
Article Number 404
Number of page(s) 10
DOI https://doi.org/10.1051/meca/2015010
Published online 27 April 2015
  1. H.G. Matthies, C.E. Brenner, C.G. Bucher, C. Guedes Soares, Uncertainties in probabilistic numerical analysis of structures solids-Stochastic finite elements, Struct. Safety 19 (1997) 283–336 [CrossRef] [Google Scholar]
  2. G.I. Schuëller, A state-of-the-art report on computational stochastic mechanics, Probab. Eng. Mech. 12 (1997) 197–321 [CrossRef] [Google Scholar]
  3. M. Grigoriu, Stochastic mechanics, Int. J. Solids Struct. 37 (2000) 197–214 [CrossRef] [Google Scholar]
  4. G.S. Fishman, Monte Carlo: Concepts, Algorithms and Applications, Springer-Verlag, 1996 [Google Scholar]
  5. M. Kleiber, T.D. Hien, The stochastic finite element method: basic perturbation technique computer implementation, John Wiley & Sons, Engl, 1992 [Google Scholar]
  6. R.G. Ghanem, P.D. Spanos, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, 1991 [Google Scholar]
  7. K. Willcox, J. Peraire, Balanced model reduction via the proper orthogonal decomposition, AIAA J. 40 (2002) 2323–2330 [CrossRef] [Google Scholar]
  8. F. Chinesta, P. Ladevèze, E. Cueto, A short review on model order reduction based on proper generalized decomposition, Arch. Comput. Methods Eng. 18 (2011) 395–404 [CrossRef] [Google Scholar]
  9. D. Moens, M. Hanss, Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: Recent advances, Finite Elements in Analysis and Design 47 (2011) 4–16 [CrossRef] [Google Scholar]
  10. O. Dessombz, F. Thouverez, J.-P. Laîné, L. Jézéquel, Analysis of mechanical systems using interval computations applied to finite element methods, J. Sound Vib. 239 (2001) 949–968 [CrossRef] [Google Scholar]
  11. R.L. Muhanna, R.L. Mullen, Uncertainty in mechanics problems–Interval-based approach, J. Eng. Mech. 127 (2001) 557–566 [CrossRef] [Google Scholar]
  12. J.-P. Merlet, Interval analysis for certified numerical solution of problems in robotics, Int. J. Appl. Math. Comput. Sci. 19 (2009) 399–412 [Google Scholar]
  13. F. Massa, K. Ruffin, T. Tison, B. Lallem, A complete method for efficient fuzzy modal analysis, J. Sound Vib. 309 (2008) 63–85 [CrossRef] [Google Scholar]
  14. G. Quaranta, Finite element analysis with uncertain probabilities, Comput. Methods Appl. Mech. Eng. 200 (2011) 114–129 [CrossRef] [Google Scholar]
  15. Y. Ben-Haim, Information-gap Decision Theory: Decisions Under Severe Uncertainty, 2nd edition, Academic Press, 2006 [Google Scholar]
  16. G.J. Klir, Uncertainty information: foundations of generalized information theory, John Wiley & Sons, 2005 [Google Scholar]
  17. H. Bae, R.V. Grhi, R.A. Canfield, An approximation approach for uncertainty quantification using evidence theory, Reliab. Eng. Syst. Safety 86 (2004) 215–225 [CrossRef] [Google Scholar]
  18. C. Soize, A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probab. Eng. Mech. 15 (2000) 277–294 [CrossRef] [Google Scholar]
  19. C. Soize, Maximum entropy approach for modeling random uncertainties in transient elastodynamics, J. Acoust. Soc. Am. 109 (2001) 1979–1996 [CrossRef] [PubMed] [Google Scholar]
  20. P. Ladevèze, G. Puel, T. Romeuf, Lack of knowledge in structural model validation, Comput. Methods Appl. Mech. Eng. 195 (2006) 4697–4710 [CrossRef] [Google Scholar]
  21. F. Louf, P. Enjalbert, P. Ladevèze, T. Romeuf, On lack-of-knowledge theory in structural mechanics, C. R. Mécanique 338 (2010) 424–433 [CrossRef] [Google Scholar]
  22. M. Papadrakakis, A. Kotsopulos, Parallel solution methods for stochastic finite element analysis using Monte Carlo simulation, Comput. Methods Appl. Mech. Eng. 168 (1999) 305–320 [CrossRef] [Google Scholar]
  23. G.I. Schuëller, C.G. Bucher, U. Bourgund, W. Ouypornprasert, On efficient computational schemes to calculate structural failure probabilities, Probab. Eng. Mech. 4 (1989) 10–18 [CrossRef] [Google Scholar]
  24. R.E. Caflisch, Monte Carlo and quasi-Monte Carlo methods, Acta Numerica 7 (1998) 1–49 [CrossRef] [Google Scholar]
  25. G. Blatman, B. Sudret, M. Berveiller, Quasi random numbers in stochastic finite element analysis, Mech. Ind. 8 (2007) 289–298 [Google Scholar]
  26. J.C. Helton, F.J. Davis, Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems, Reliab. Eng. Syst. Safety 81 (2003) 23–69 [CrossRef] [Google Scholar]
  27. O. Ditlevsen, H.O. Madsen, Structural Reliability Methods, John Wiley & Sons, 1996, Vol. 178 [Google Scholar]
  28. B. Huang, X. Du, Probabilistic uncertainty analysis by mean-value first order saddlepoint approximation, Reliab. Eng. Syst. Safety 93 (2008) 325–336 [CrossRef] [Google Scholar]
  29. B. Sudret, A. Der Kiureghian, Stochastic finite element methods reliability: a state-of-the-art report, Department of Civil Environmental Engineering, University of California, 2000 [Google Scholar]
  30. G. Stefanou, The stochastic finite element method: past, present and future, Comput. Methods Appl. Mech. Eng. 198 (2009) 1031–1051 [CrossRef] [Google Scholar]
  31. C.-C. Li, A. Der Kiureghian, Optimal discretization of random fields, J. Eng. Mech. 119 (1993) 1136–1154 [CrossRef] [Google Scholar]
  32. B. Van den Nieuwenhof, J.-P. Coyette, Modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties, Comput. Methods Appl. Mech. Eng. 192 (2003) 3705–3729 [CrossRef] [Google Scholar]
  33. M. Shinozuka, G. Deodatis, Response variability of stochastic finite element systems, J. Eng. Mech. 114 (1988) 499–519 [CrossRef] [Google Scholar]
  34. F. Yamazaki, M. Shinozuka, G. Dasgupta, Neumann expansion for stochastic finite element analysis, J. Eng. Mech. 114 (1988) 1335–1354 [CrossRef] [Google Scholar]
  35. M. Papadrakakis, V. Papadopoulos, Robust efficient methods for stochastic finite element analysis using Monte Carlo simulation, Comput. Methods Appl. Mech. Eng. 134 (1996) 325–340 [CrossRef] [Google Scholar]
  36. D. Xiu, G.E. Karniadakis, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput. 24 (2002) 619–644 [CrossRef] [MathSciNet] [Google Scholar]
  37. G. Blatman, B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, J. Comput. Phys. 230 (2011) 2345–2367 [CrossRef] [Google Scholar]
  38. A. Doostan, R.G. Ghanem, J. Red-Horse, Stochastic model reduction for chaos representations, Comput. Methods Appl. Mech. Eng. 196 (2007) 3951–3966 [CrossRef] [Google Scholar]
  39. D. Ryckelynck, A priori hyperreduction method: an adaptive approach, J. Comput. Phys. 202 (2005) 346–366 [CrossRef] [Google Scholar]
  40. G. Rozza, D.B.P. Huynh, A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations, Archives Comput. Methods Eng. 15 (2008) 229–275 [CrossRef] [MathSciNet] [Google Scholar]
  41. E. Balmès, Efficient sensitivity analysis based on finite element model reduction, In Proc. IMAC XVII, SEM, Santa Barbara, CA, 1998, pp. 1168–1174 [Google Scholar]
  42. A. Nouy, A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations, Comput. Methods Appl. Mech. Eng. 199 (2010) 1603–1626 [CrossRef] [MathSciNet] [Google Scholar]
  43. F. Chinesta, A. Ammar, A. Leygue, R. Keunings, An overview of the proper generalized decomposition with applications in computational rheology, J. Non-Newtonian Fluid Mech. 166 (2011) 578–592 [CrossRef] [Google Scholar]
  44. A. Nouy, O.P. Le Maître, Generalized spectral decomposition for stochastic nonlinear problems, J. Comput. Phys. 228 (2009) 202–235 [CrossRef] [Google Scholar]
  45. F. Louf, L. Champaney, Fast validation of stochastic structural models using a PGD reduction scheme, Finite Elements in Analysis and Design 70–71 (2013) 44–56 [CrossRef] [Google Scholar]
  46. F. Chinesta, A. Ammar, E. Cueto, Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models, Archives Comput. Methods Eng. 17 (2010) 327–350 [CrossRef] [MathSciNet] [Google Scholar]
  47. C. Soize, random matrix theory for modeling uncertainties in computational mechanics, Comput. Methods Appl. Mech. Eng. 194 (2005) 1333–1366 [CrossRef] [Google Scholar]
  48. C. Soize, Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions, Int. J. Numer. Methods Eng. 81 (2010) 939–970 [Google Scholar]
  49. P. Ladevèze, G. Puel, T. Romeuf, On a strategy for the reduction of the lack of knowledge (LOK) in model validation, Reliab. Eng. Syst. Safety 91 (2006) 1452–1460 [CrossRef] [Google Scholar]
  50. S. Audebert, SICODYN international benchmark on dynamic analysis of structure assemblies: variability and numerical-experimental correlation on an industrial pump, Mécanique & Industries 11 (2010) 439–451 [CrossRef] [EDP Sciences] [Google Scholar]
  51. S. Audebert, A. Mikchevitch, I. Zentner, SICODYN international benchmark on dynamic analysis of structure assemblies: variability numerical-experimental correlation on an industrial pump (part 2), Mechanics & Industry 15 (2014) 1–17 [CrossRef] [EDP Sciences] [Google Scholar]
  52. A. Batou, C. Soize, S. Audebert, Model identification in computational stochastic dynamics using experimental modal data, Mech. Syst. Signal Process. 50-51 (2015) 307–322 [CrossRef] [Google Scholar]

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