Table of Contents Author Guidelines Submit a Manuscript
Shock and Vibration
Volume 2015 (2015), Article ID 574846, 12 pages
http://dx.doi.org/10.1155/2015/574846
Research Article

Reliability Analysis of Damaged Beam Spectral Element with Parameter Uncertainties

Department of Computational Mechanics, University of Campinas (UNICAMP), 13083-970 Campinas, SP, Brazil

Received 12 December 2014; Accepted 24 May 2015

Academic Editor: Gang Li

Copyright © 2015 M. R. Machado and J. M. C. Dos Santos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. H. Lyon and R. G. DeJong, Theory and Application of Statistical Energy Analysis, Butterworth-Heinemann, Boston, Mass, USA, 1995.
  2. J. F. Doyle, Wave Propagation in Structures, Springer, New York, NY, USA, 1989.
  3. J. F. Doyle, Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, Mechanical Engineering Series, Springer, New York, NY, USA, 2nd edition, 1997.
  4. U. Lee, Spectral Element Method in Structural Dynamics, BInha University Press, 2004.
  5. S. Gopalakrishnan, A. Chakraborty, and D. R. Mahapatra, Spectral Finite Element Method, Springer, New York, NY, USA, 2007.
  6. M. Krawczuk, “Application of spectral beam finite element with a crack and iterative search technique for damage detection,” Finite Elements in Analysis and Design, vol. 38, no. 6, pp. 537–548, 2002. View at Publisher · View at Google Scholar
  7. M. Krawczuk, J. Grabowska, and M. Palacz, “Longitudinal wave propagation. Part I—comparison of rod theories,” Journal of Sound and Vibration, vol. 295, no. 3–5, pp. 461–478, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. W. M. Ostachowicz, “Damage detection of structures using spectral finite element method,” Computers & Structures, vol. 86, no. 3-5, pp. 454–462, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. Z. Su and L. Ye, Identification of Damage Using Lamb Waves, Springer, New York, NY, USA, 2009.
  10. E. R. O. Santos, J. R. F. Arruda, and J. M. C. Dos Santos, “Modeling of coupled structural systems by an energy spectral element method,” Journal of Sound and Vibration, vol. 316, no. 1–5, pp. 1–24, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. A. K. Pandey, M. Biswas, and M. M. Samman, “Damage detection from changes in curvature mode shapes,” Journal of Sound and Vibration, vol. 145, no. 2, pp. 321–332, 1991. View at Google Scholar · View at Scopus
  12. A. K. Pandey and M. Biswas, “Damage detection in structures using changes in flexibility,” Journal of Sound and Vibration, vol. 169, no. 1, pp. 3–17, 1994. View at Publisher · View at Google Scholar · View at Scopus
  13. A. D. Dimarogonas, “Vibration of cracked structures: a state of the art review,” Engineering Fracture Mechanics, vol. 55, no. 5, pp. 831–857, 1996. View at Publisher · View at Google Scholar · View at Scopus
  14. S. Adhikari and M. I. Friswell, “Distributed parameter model updating using the Karhunen-Loève expansion,” Mechanical Systems and Signal Processing, vol. 24, no. 2, pp. 326–339, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. V. Ajith and S. Gopalakrishnan, “Spectral element approach to wave propagation in uncertain beam structures,” Journal of Mechanics of Materials and Structures, vol. 5, no. 4, pp. 637–659, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. A. T. Fabro, T. G. Ritto, R. Sampaio, and J. R. F. Arruda, “Stochastic analysis of a cracked rod modeled via the spectral element method,” Mechanics Research Communications, vol. 37, no. 3, pp. 326–331, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. C. T. Ng, M. Veidt, and H. F. Lam, “Probabilistic damage characterisation in beams using guided waves,” Procedia Engineering, vol. 14, pp. 490–497, 2011. View at Publisher · View at Google Scholar
  18. E. B. Flynn, M. D. Todd, P. D. Wilcox, B. W. Drinkwater, and A. J. Croxford, “Maximum-likelihood estimation of damage location in guided-wave structural health monitoring,” Proceedings of the Royal Society A, vol. 3, pp. 1–22, 2011. View at Publisher · View at Google Scholar
  19. M. Machado and J. DosSantos, “Stochastic analysis ofwave propagation in a cracked rod via spectral element and polinomial chaos expansion,” in Proceedings of the Innovations in Wave Modelling (Innowave ’12), Nottingham,UK, 2012.
  20. M. R. Machado and J. M. C. dos Santos, “Damage detection in an energy flow model including parameter uncertainty,” in Topics in Modal Analysis, Volume 7: Proceedings of the 31st IMAC, A Conference on Structural Dynamics, 2013, Conference Proceedings of the Society for Experimental Mechanics Series, pp. 131–140, Springer, New York, NY, USA, 2014. View at Publisher · View at Google Scholar
  21. M. Machado, S. Adhikari, and J. DosSantos, “Damage characterization in structures with random properties,” in Proceedings of the 2nd International Symposium on Uncertainty Quantification and Stochastic Modeling, Rouen, France, 2014.
  22. A. Haldar and S. Mahadevan, Reliability Assessment Using Stochastic Finite Element Analysis, John Wiley & Sons, New York, NY, USA, 2000.
  23. S. Mahadevan and A. Haldar, Probability, Reliability and Statistical Methods in Engineering Design, John Wiley & Sons, 2000.
  24. A. der Kiureghian, “The geometry of random vibrations and solutions by form and sorm,” Probabilistic Engineering Mechanics, vol. 15, no. 1, pp. 81–90, 2000. View at Publisher · View at Google Scholar · View at Scopus
  25. A. M. Hasofer and N. C. Lind, “Exact and invariant second moment code format,” Journal of Engineering Mechanics Division, vol. 100, no. 1, pp. 111–121, 1974. View at Google Scholar · View at Scopus
  26. I. M. Sobol', A Primer for the Monte Carlo Method, CRC Press, 1994. View at MathSciNet
  27. L. Faravelli, “Response-surface approach for reliability analysis,” Journal of Engineering Mechanics, vol. 115, no. 12, pp. 2763–2781, 1989. View at Google Scholar · View at Scopus
  28. C. G. Bucher and U. Bourgund, “A fast and efficient response surface approach for structural reliability problems,” Structural Safety, vol. 7, no. 1, pp. 57–66, 1990. View at Publisher · View at Google Scholar · View at Scopus
  29. M. R. Rajashekhar and B. R. Ellingwood, “A new look at the response surface approach for reliability analysis,” Structural Safety, vol. 12, no. 3, pp. 205–220, 1993. View at Google Scholar · View at Scopus
  30. K. Breitung and L. Faravelli, “Log-likelihood maximization and response surface in reliability assessment,” Nonlinear Dynamics, vol. 5, no. 3, pp. 273–285, 1994. View at Publisher · View at Google Scholar · View at Scopus
  31. X. L. Guan and R. E. Melchers, “Effect of response surface parameter variation on structural reliability estimates,” Structural Safety, vol. 23, no. 4, pp. 429–444, 2001. View at Publisher · View at Google Scholar · View at Scopus
  32. K. Breitung and L. Faravelli, “Response surface methods and asymptotic approximations,” in Mathematical Models for Structural Reliability Analysis, CRC Press, Boca Raton, Fla, USA, 1996. View at Google Scholar
  33. R. E. Melchers, Structural Reliability Analysis and Prediction, John Wiley & Sons, New York, NY, USA, 2nd edition, 1999.
  34. S. T. Choi, R. V. Grandhi, and R. A. Canfield, Reliability-based Structural Design, Springer, 2007.
  35. E. D. Leonel, A. T. Beck, and W. S. Venturini, “On the performance of response surface and direct coupling approaches in solution of random crack propagation problems,” Structural Safety, vol. 33, no. 4-5, pp. 261–274, 2011. View at Publisher · View at Google Scholar · View at Scopus
  36. M. Pendola, A. Mohamed, M. Lemaire, and P. Hornet, “Combination of finite element and reliability methods in nonlinear fracture mechanics,” Reliability Engineering and System Safety, vol. 70, no. 1, pp. 15–27, 2000. View at Google Scholar · View at Scopus
  37. W.-X. Ren and H.-B. Chen, “Finite element model updating in structural dynamics by using the response surface method,” Engineering Structures, vol. 32, no. 8, pp. 2455–2465, 2010. View at Publisher · View at Google Scholar · View at Scopus
  38. H. Tada, P. Paris, and G. R. Irwin, Stress Analysis of Cracks Handbook, Del Research Corporatoin, 1973.
  39. R. Rackwitz and B. Fiessler, “Note on discrete safety checking when using non-normal stochastic models for basic variables,” Tech. Rep., MIT, Cambridge, Mass, USA, 1976. View at Google Scholar
  40. M. L. Shooman, Probabilistic Reliability: An Engineering Approach, McGraw-Hill, 1968.
  41. A. Khuri and J. A. Cornell, Response Surface: Designs and Analyses, Marcel Dekker, New York, NY, USA, 1996.
  42. E. D. Leonel, A. Chateauneuf, and W. S. Venturini, “Probabilistic crack growth analyses using a boundary element model: applications in linear elastic fracture and fatigue problems,” Engineering Analysis with Boundary Elements, vol. 36, no. 6, pp. 944–959, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus