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]
  2. G.I. Schuëller, A state-of-the-art report on computational stochastic mechanics, Probab. Eng. Mech. 12 (1997) 197–321 [CrossRef]
  3. M. Grigoriu, Stochastic mechanics, Int. J. Solids Struct. 37 (2000) 197–214 [CrossRef]
  4. G.S. Fishman, Monte Carlo: Concepts, Algorithms and Applications, Springer-Verlag, 1996
  5. M. Kleiber, T.D. Hien, The stochastic finite element method: basic perturbation technique computer implementation, John Wiley & Sons, Engl, 1992
  6. R.G. Ghanem, P.D. Spanos, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, 1991
  7. K. Willcox, J. Peraire, Balanced model reduction via the proper orthogonal decomposition, AIAA J. 40 (2002) 2323–2330 [CrossRef]
  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]
  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]
  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]
  11. R.L. Muhanna, R.L. Mullen, Uncertainty in mechanics problems–Interval-based approach, J. Eng. Mech. 127 (2001) 557–566 [CrossRef]
  12. J.-P. Merlet, Interval analysis for certified numerical solution of problems in robotics, Int. J. Appl. Math. Comput. Sci. 19 (2009) 399–412
  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]
  14. G. Quaranta, Finite element analysis with uncertain probabilities, Comput. Methods Appl. Mech. Eng. 200 (2011) 114–129 [CrossRef]
  15. Y. Ben-Haim, Information-gap Decision Theory: Decisions Under Severe Uncertainty, 2nd edition, Academic Press, 2006
  16. G.J. Klir, Uncertainty information: foundations of generalized information theory, John Wiley & Sons, 2005
  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]
  18. C. Soize, A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probab. Eng. Mech. 15 (2000) 277–294 [CrossRef]
  19. C. Soize, Maximum entropy approach for modeling random uncertainties in transient elastodynamics, J. Acoust. Soc. Am. 109 (2001) 1979–1996 [CrossRef] [PubMed]
  20. P. Ladevèze, G. Puel, T. Romeuf, Lack of knowledge in structural model validation, Comput. Methods Appl. Mech. Eng. 195 (2006) 4697–4710 [CrossRef]
  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]
  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]
  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]
  24. R.E. Caflisch, Monte Carlo and quasi-Monte Carlo methods, Acta Numerica 7 (1998) 1–49 [CrossRef]
  25. G. Blatman, B. Sudret, M. Berveiller, Quasi random numbers in stochastic finite element analysis, Mech. Ind. 8 (2007) 289–298
  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]
  27. O. Ditlevsen, H.O. Madsen, Structural Reliability Methods, John Wiley & Sons, 1996, Vol. 178
  28. B. Huang, X. Du, Probabilistic uncertainty analysis by mean-value first order saddlepoint approximation, Reliab. Eng. Syst. Safety 93 (2008) 325–336 [CrossRef]
  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
  30. G. Stefanou, The stochastic finite element method: past, present and future, Comput. Methods Appl. Mech. Eng. 198 (2009) 1031–1051 [CrossRef]
  31. C.-C. Li, A. Der Kiureghian, Optimal discretization of random fields, J. Eng. Mech. 119 (1993) 1136–1154 [CrossRef]
  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]
  33. M. Shinozuka, G. Deodatis, Response variability of stochastic finite element systems, J. Eng. Mech. 114 (1988) 499–519 [CrossRef]
  34. F. Yamazaki, M. Shinozuka, G. Dasgupta, Neumann expansion for stochastic finite element analysis, J. Eng. Mech. 114 (1988) 1335–1354 [CrossRef]
  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]
  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]
  37. G. Blatman, B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, J. Comput. Phys. 230 (2011) 2345–2367 [CrossRef]
  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]
  39. D. Ryckelynck, A priori hyperreduction method: an adaptive approach, J. Comput. Phys. 202 (2005) 346–366 [CrossRef]
  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]
  41. E. Balmès, Efficient sensitivity analysis based on finite element model reduction, In Proc. IMAC XVII, SEM, Santa Barbara, CA, 1998, pp. 1168–1174
  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]
  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]
  44. A. Nouy, O.P. Le Maître, Generalized spectral decomposition for stochastic nonlinear problems, J. Comput. Phys. 228 (2009) 202–235 [CrossRef]
  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]
  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]
  47. C. Soize, random matrix theory for modeling uncertainties in computational mechanics, Comput. Methods Appl. Mech. Eng. 194 (2005) 1333–1366 [CrossRef]
  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
  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]
  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]
  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]
  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]

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