166
Views
11
CrossRef citations to date
0
Altmetric
Original Articles

An efficient numerical algorithm for crack reconstruction in elastic media by the circular US scanning

&
Pages 361-379 | Received 02 Sep 2009, Accepted 04 Nov 2009, Published online: 05 Mar 2010

References

  • Krautkrämer, J, and Krautkrämer, H, 1983. Ultrasonic Testing of Materials. Berlin: Springer-Verlag; 1983.
  • Colton, D, and Kress, R, 1983. Integral Equation Methods in Scattering Theory. New York: John Wiley & Sons; 1983.
  • Colton, D, and Kress, R, 1992. Inverse Acoustic and Electromagnetic Scattering Theory. Berlin: Springer-Verlag; 1992.
  • Potthast, R, 2001. Point Sources and Multipoles in Inverse Scattering Theory. London: Chapman & Hall; 2001.
  • Friedman, A, and Vogelius, M, 1989. Determining cracks by boundary measurements, Indiana Univ. Math. J. 38 (1989), pp. 527–556.
  • Andrieux, S, and Abda, AB, 1996. Identification of planar cracks by complete overdetermined data: Inversion formulae, Inverse Probl. 12 (1996), pp. 553–563.
  • Bannour, T, Abda, AB, and Jaoua, M, 1997. A semi-explicit algorithm for the reconstruction of 3D planar cracks, Inverse Probl. 13 (1997), pp. 899–917.
  • Abda, AB, Kallel, M, Leblond, J, and Marmorat, J-P, 2002. Line segment crack recovery from incomplete boundary data, Inverse Probl. 18 (2002), pp. 1057–1077.
  • Alessandrini, G, Beretta, E, and Vessella, S, 1996. Determining linear cracks by boundary measurements: Lipschitz stability, SIAM J. Math. Anal. 27 (1996), pp. 361–375.
  • Crouch, SL, and Starfield, AM, 1983. Boundary Element Methods in Solid Mechanics. London: George Allen & Unwin; 1983.
  • Yin, HP, and Ehrlacher, A, 1993. Variational approach of displacement discontinuity method and application to crack problems, Int. J. Fract. 63 (1993), pp. 135–153.
  • Li, H, Liu, CL, Mizuta, Y, and Kayupov, MA, 2001. Crack edge element of three-dimensional displacement discontinuity method with boundary division into triangular leaf elements, Commun. Numer. Methods Eng. 17 (2001), pp. 365–378.
  • Abramowitz, M, and Stegun, IA, 1968. Handbook of Mathematical Functions, . New York: Dover; 1968.
  • Tikhonov, AN, and Arsenin, VY, 1977. Solutions of Ill-posed Problems. Washington, DC: Winston; 1977.
  • Kantorovich, LV, and Akilov, GP, 1982. Functional Analysis. Oxford: Pergamon Press; 1982.
  • Gill, PE, Murray, W, and Wright, MH, 1981. Practical Optimization. London: Academic Press; 1981.
  • Corana, M, Marchesi, M, Martini, C, and Ridella, S, 1987. Minimizing multimodal functions of continuous variables with the simulated annealing algorithm, ACM Trans. Math. Software 13 (1987), pp. 262–280.

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.