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RELIABILITY ASSESSMENT USING A COMBINATION OF POLYNOMIAL CHAOS AND SIMULATIONS: APPLICATION TO NONLINEAR FRACTURE MECHANICS

Riahi, H.; Bressolette, Ph.; Chateauneuf, A.; ., ;

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This paper presents a probabilistic approach based on polynomial chaos expansion, in order to provide accurate explicit approximation of the structural response to be considered in the limit state function. The main difficulties in this approach are related to the calculation of the expansion coefficients which are defined by multi-dimensional integrals. As an alternative to the quadrature methods, Monte-Carlo simulations based on low discrepancy Halton sequence have been used for this issue. The accuracy and the efficiency of the proposed approach have been approved through analytical models. It is shown that the use of low discrepancy sequence provides more rapidly converging estimates. The proposed approach has been applied to assess the integrity of a cracked pipe.

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Palavras-chave: Polynomial chaos expansion, Quasi-Monte Carlo, Sensitivity analysis, Reliability, Nonlinear fracture mechanics.,

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DOI: 10.5151/meceng-wccm2012-18746

Referências bibliográficas
  • [1] Madsen HO, Krenk S, Lind NC. Methods of structural safety. Prentice-Hall, Englewood Cliffs: New Jersey; 1986.
  • [2] Schuëller GI, Stix R. A critical appraisal of methods to determine failure probability. Struc Safe. 1987;4:293-309.
  • [3] Faravelli L. Surface-response approach for reliability analysis. J Eng Mech, ASCE, 1989; 115(12): 2763-81.
  • [4] Busher CG, Bourgund U. A fast and efficient response surface approach for structural reliability problems. Struc Safe. 1987;4:293-309.
  • [5] Maymon G. Probability of failure without a closed-form failure function. Comput Struct. 1993;49(2):301-13.
  • [6] Rajashekhar MR, Ellingwood BR. A new look at the response surface approach for reliability analysis. Struc Safe. 1993;12(3):205-20.
  • [7] Wong SM, Hobbs RE, Onof C. An adaptive response surface method for reliability analysis of structures with multiple loading sequences. Struc Safe. 2005;27:287-308.
  • [8] D. Xiu, GE Karniadakis. The Weiner-Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput. 24 (2): 619-644, 2002.
  • [9] J.H. Halton. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer. Math. 1960;2:84-90.
  • [10] H. Dai, W. Wang. Application of low-discrepancy sampling method in structural reliability analysis. Struct. Saf. 2009;31:55-64.
  • [11] M. Rosenblatt. Remarks on a multiformation. Ann Math Statist. 23: 470-472, 1952.
  • [12] A. Nataf. Détermination des distributions dont les marges sont données. Comptes Rendus de l’Académie des Sciences. 225: 42-43, 1962.
  • [13] I.M. Sobol. On quasi-Monte Carlo integrations. Math Compt Simul. 47: 103-112, 1998.
  • [14] C. Schlier. Errors trends in quasi-Monte Carlo integration. Comp Phys Com. 193: 93- 105, 2004.
  • [15] S. Kucherenko, M. Rodriguez-Fernandez, C. Pantelides, N. Shah. Monte Carlo evaluation of derivative-based sensitivity measures. Reliab. Eng. Syst. Saf. 2009;94:1135- 1148.
  • [16] R. Caflisch, W. Morokoff, A. Owen. Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension. J Comput Fin. 1997;1(1):27-46.
  • [17] B. Sudret, G. Blatman, M. Berveiller. Quasi-random numbers in stochastic finite element analysis-application to global sensitivity analysis. In proc. 10th Int. Conf. On Applications of stat. and Prob. in Civil Engineering (ICASP10), Tokyo (2007).
  • [18] M. Pendola, A. Mohamed, M. Lemaire, P. Hornet. Combination of finite element and reliability methods in nonlinear fracture mechanics. Reliability Engineering Andamp; System Safety. 70, (2000), 15-27.
  • [19] T.L. Anderson. Fracture mechanics: fundamentals and applications. Second ed. Boca Raton, Florida: CRC Press Inc.; 1995.
  • [20] H. Riahi, Ph. Bressolette, A. Chateauneuf. Random fatigue crack growth in mixed mode by stochastic collocation method. Eng Frac Mech. 77(16) :3292-3309, 2010.
  • [21] CEA / LAMS – Scalay. Cast3m, Commissariat à l’Energie Atomique, 2010
Como citar:

Riahi, H.; Bressolette, Ph.; Chateauneuf, A.; ., ; "RELIABILITY ASSESSMENT USING A COMBINATION OF POLYNOMIAL CHAOS AND SIMULATIONS: APPLICATION TO NONLINEAR FRACTURE MECHANICS", p. 2195-2208 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18746

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