44
Views
0
CrossRef citations to date
0
Altmetric
Articles

Error control in FORM reliability analysis

Pages 231-241 | Published online: 03 Sep 2012

References

  • Babuška , I. and Rheinboldt , W. 1978 . A posteriori estimates for the finite element method . International Journal for Numerical Methods in Engineering , 12 : 1597 – 1615 .
  • Deb, M., Babuška, I., & Oden J. (2001). Solution of stochastics partial differential equations using Galerkin finite element techniques. Computer Methods in Applied Mechanics and Engineering, 190, 6359–6372.
  • Der Kiureghian , A. and Dakessian , T. 1998 . Multiple design points in first and second-order reliability . Structural Safety , 20 : 37 – 49 .
  • Diez , P. and Calderon , G. 2007 . Remeshing criteria and proper error representations for goal oriented h-adaptivity . Computer Methods in Applied Mechanics and Engineering , 196 : 719 – 733 .
  • Ditlevsen , O. and Madsen , H. 1996 . Structural reliability methods , New York , NY : Wiley .
  • Gallimard , L. 2006 . Evaluation of the local quality of the Von Mises’s stress and L2-norm of the stress . Engineering Computations , 23 ( 7/8 ) : 876 – 897 .
  • Gallimard , L. 2009 . A constitutive relation error estimator based on traction-free recovery of the equilibrated stress . International Journal for Numerical Methods in Engineering , 78 : 460 – 482 .
  • Gallimard , L. 2011a . Error bounds for the reliability index in finite element reliability analysis . International Journal for Numerical Methods in Engineering , 87 : 781 – 794 .
  • Gallimard, L. (2011b). Estimation de l’erreur due á la méthode des éléments finis dans une analyse de fiabilité de type FORM, Actes du 10 ieme Colloque National en Calcul des Structures, Giens, 9–13 mai.
  • Gallimard , L. and Panetier , J. 2006 . Error estimation of stress intensity factors for mixed-mode crack . International Journal for Numerical Methods in Engineering , 68 : 299 – 316 .
  • Hasofer, A., & Lind, N. (1974). An exact and invariant first order reliability format. Journal of Engineering Mechanics – ASCE, 100, 111–121.
  • Haukaas , T. and Der Kiureghian , A. 2006 . Strategies for finding the design point in non-linear finite element reliability analysis . Probabilistic Engineering Mechanics , 21 : 133 – 147 .
  • Kelly , D. and Isles , J. 1989 . Procedures for residual equilibration and local error estimation in the finite element method . Communications in Applied Numerical Methods , 5 : 497 – 505 .
  • Ladevèze, P., & Florentin, E. (2006). Verification of stochastic models in uncertain environments using the constitutive relation error method. Computer Methods in Applied Mechanics and Engineering, 196, 225–234.
  • Ladevèze , P. and Leguillon , D. 1983 . Error estimate procedure in the finite element method and application . SIAM Journal on Numerical Analysis , 20 ( 3 ) : 485 – 509 .
  • Ladevèze , P. , Rougeot , P. , Blanchard , P. and Moreau , J. 1999 . Local error estimators for finite element analysis . Computer Methods in Applied Mechanics and Engineering , 176 : 231 – 246 .
  • Lemaire , M. 2005 . Fiabilité des structures , Paris : Hermes .
  • Melchers , R. 1989 . Importance sampling in structural systems . Structural Safety , 6 : 3 – 10 .
  • Mitteau , J. 1999 . Error evaluation for the computation of failure probability in static structural reliability problems . Probabilistic Engineering Mechanics , 14 : 119 – 135 .
  • Peraire, J., & Patera, A. (1998). Bounds for linear-functional outputs of coercive partial differential equations: local indicators and adaptive refinement. In P. Ladevèze & J. Oden (Eds.), Advances in adaptive computational methods (pp. 199–216). Cachan: Elsevier.
  • Prudhomme , S. and Oden , J. 1999 . On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors . Computer Methods in Applied Mechanics and Engineering , 176 : 313 – 331 .
  • Tada , H. , Paris , P. and Irwin , G. 2000 . The stress analysis of crack handbook , New York , NY : ASME Press .
  • Zhang Y., & Der Kiureghian, A. (1995). Two improved algorithms for reliability analysis. Reliability and Optimization of Structural Systems. In R. Rackwitz, G. Augusti and A. Borri (Eds.) Proceedings 6th IFIP WG7.5 working conference on reliability and optimization of structural systems. (pp. 297–304). Chapman & Hall.
  • Zienkiewicz , O. and Zhu , J. 1987 . A simple error estimator and adaptive procedure for practical engineering analysis . International Journal for Numerical Methods in Engineering , 24 : 337 – 357 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.