Table of Contents
International Journal of Computational Mathematics
Volume 2014 (2014), Article ID 358617, 9 pages
http://dx.doi.org/10.1155/2014/358617
Research Article

Plane Elastostatic Solution in an Infinite Functionally Graded Layer Weakened by a Crack Lying in the Middle of the Layer

1Department of Mathematics, Hooghly Engineering & Technology College, Hooghly, West Bengal 712 103, India
2Department of Mathematics, Gobardanga Hindu College, 24 Parganas (North), West Bengal 743 273, India
3Makhla Debiswari Vidyaniketan, Hooghly, West Bengal 712 245, India
4Department of Applied Mathematics, University of Calcutta, 92 A. P. C. Road, Kolkata 700 009, India

Received 17 June 2014; Revised 6 November 2014; Accepted 14 November 2014; Published 25 November 2014

Academic Editor: Sheung-Hung Poon

Copyright © 2014 R. Patra 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. I. Reynolds and J. Nathan, Functionally Graded Materials, Nova Science, New York, NY, USA, 2012.
  2. Y. Miyamoto, Functionally Graded Materials: Design, Processing, and Applications, Chapman & Hall, 1999.
  3. P. K. Chaudhuri and S. Ray, “Sudden twisting of a penny-shaped crack in a nonho mogeneous elastic medium,” Journal of Mathematical and Physical Sciences, vol. 29, no. 5, pp. 207–221, 1995. View at Google Scholar
  4. M. Ozturk and F. Erdogan, “The axisymmetric crack problem in a nonhomogeneous medium,” Journal of Applied Mechanics, vol. 60, no. 2, pp. 406–413, 1993. View at Publisher · View at Google Scholar · View at Scopus
  5. Z. Yong and M. T. Hanson, “Circular crack system in an infinite elastic medium under arbitrary normal loads,” Journal of Applied Mechanics, vol. 61, no. 3, pp. 582–588, 1994. View at Publisher · View at Google Scholar · View at Scopus
  6. V. I. Fabrikant, B. S. Rubin, and E. N. Karapetian, “External circular crack under normal load: a complete solution,” Journal of Applied Mechanics, vol. 61, no. 4, pp. 809–814, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. V. I. Fabrikant, “Interaction of an arbitrary force with a flexible punch or with an external circular crack,” International Journal of Engineering Science, vol. 34, no. 15, pp. 1753–1765, 1996. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Dag and F. Erdogan, “A surface crack in a graded medium under general loading conditions,” Journal of Applied Mechanics, vol. 69, no. 5, pp. 580–588, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. H. H. Sherief and N. M. El-Maghraby, “An internal penny-shaped crack in an infinite thermoelastic solid,” Journal of Thermal Stresses, vol. 26, no. 4, pp. 333–352, 2003. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Birinci, F. Birinci, F. L. Cakiroglu, and R. Erdol, “An internal crack problem for an infinite elastic layer,” Archive of Applied Mechanics, vol. 80, no. 9, pp. 997–1005, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. S. P. Barik, M. Kanoria, and P. K. Chaudhuri, “Stress distribution in the neighbourhood of an external crack in a transversely isotropic medium,” Indian Journal of Theoretical Physics, vol. 55, no. 1, pp. 85–96, 2007. View at Google Scholar
  12. S. P. Barik, M. Kanoria, and P. K. Chaudhuri, “Steady state thermoelastic problem in an in fi nite Functionally graded solid with a crack,” International Journal of Applied Mathematics and Mechanics, vol. 19, pp. 44–66, 2010. View at Google Scholar
  13. W. Q. Chen, H. J. Ding, and D. S. Ling, “Thermoelastic field of a transversely isotropic elastic medium containing a penny-shaped crack: exact fundamental solution,” International Journal of Solids and Structures, vol. 41, no. 1, pp. 69–83, 2004. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. G. Zhao, X. W. Zhang, and Y. Y. Bai, “Investigation of two Griffith cracks subject to uniform tension by using the non-local theory,” International Journal of Engineering Science, vol. 37, no. 13, pp. 1709–1722, 1999. View at Publisher · View at Google Scholar
  15. S. J. Matysiak and V. J. Pauk, “On crack problem in an elastic ponderable layer,” International Journal of Fracture, vol. 96, no. 4, pp. 371–380, 1999. View at Google Scholar · View at Scopus
  16. D.-S. Lee, “The problem of internal cracks in an infinite strip having a circular hole,” Acta Mechanica, vol. 169, no. 1–4, pp. 101–110, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. G. D. Gupta and F. Erdogan, “The problem of edge cracks in an infinite strip,” Journal of Applied Mechanics, vol. 41, no. 4, pp. 1001–1006, 1974. View at Publisher · View at Google Scholar · View at Scopus
  18. M. S. Matbuly, “Analytical solution for an interfacial crack subjected to dynamic anti-plane shear loading,” Acta Mechanica, vol. 184, no. 1–4, pp. 77–85, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. F. Erdogan and G. D. Gupta, “On the numerical solution of singular integral equations,” Quarterly of Applied Mathematics, vol. 29, pp. 525–534, 1972. View at Google Scholar · View at MathSciNet
  20. S. Krenk, “A note on the use of the interpolation polynomial for solution of singular integral equations,” Quarterly of Applied Mathematics, vol. 32, pp. 479–485, 1975. View at Google Scholar