Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 524562, 10 pages
http://dx.doi.org/10.1155/2013/524562
Research Article

Homotopy Iteration Algorithm for Crack Parameters Identification with Composite Element Method

Department of Applied Mechanics, Sun Yat-sen University, Guangzhou, Guangdong 510006, China

Received 19 July 2013; Revised 12 October 2013; Accepted 12 October 2013

Academic Editor: Timon Rabczuk

Copyright © 2013 Ling Huang et al. 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. M. I. Friswell and J. E. Mottershead, Finite Element Model Updating in Structural Dynamics, Kluwer Academic, Dodrecht, The Netherlands, 1995.
  2. A. G. Peano, “Hierarchies of conforming finite elements for plane elasticity and plate bending,” Computers and Mathematics with Applications, vol. 2, no. 3-4, pp. 211–224, 1976. View at Google Scholar · View at Scopus
  3. P. Zeng, “Composite element method for vibration analysis of structure,” Journal of Sound and Vibration, vol. 218, no. 4, pp. 619–696, 1998. View at Google Scholar
  4. Z. R. Lu and S. S. Law, “Discussions on ‘composite element method for vibration analysis of structure’,” Journal of Sound and Vibration, vol. 305, no. 1-2, pp. 357–361, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Cattarius and D. J. Inman, “Time domain analysis for damage detection in smart structures,” Mechanical Systems and Signal Processing, vol. 11, no. 3, pp. 409–423, 1997. View at Google Scholar · View at Scopus
  6. Z. R. Lu and J. K. Liu, “Identification of both structural damages in bridge deck and vehicular parameters using measured dynamic responses,” Computers and Structures, vol. 89, no. 13-14, pp. 1397–1405, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. Z. R. Lu and S. S. Law, “Dynamic condition assessment of a cracked beam with the composite element model,” Mechanical Systems and Signal Processing, vol. 23, no. 2, pp. 415–431, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. X. B. Lu, J. K. Liu, and Z. R. Lu, “A two-step approach for crack identification in beam,” Journal of Sound and Vibration, vol. 332, no. 2, pp. 282–293, 2013. View at Google Scholar
  9. B. C. Eaves, F. J. Gould, H. O. Peitgen, and M. J. Todd, Homotopy Methods and Global Convergence, Plenum Press, New York, NY, USA, 1983.
  10. J. H. He, “Homotopy perturbation method: a new nonlinear analytical technique,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 73–79, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. S. J. Liao, “On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1274–1303, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. C. Alexander and J. A. Yorke, “The homotopy continuation method: numerically implementable topological procedures,” Transactions of the American Mathematical Society, vol. 242, pp. 271–284, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. K. Sinha, M. I. Friswell, and S. Edwards, “Simplified models for the location of cracks in beam structures using measured vibration data,” Journal of Sound and Vibration, vol. 251, no. 1, pp. 13–38, 2002. View at Publisher · View at Google Scholar · View at Scopus
  14. K. J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice Hall, Upper Saddle River, NJ, USA, 1982.