Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 726402, 25 pages
http://dx.doi.org/10.5402/2011/726402
Research Article

Divergent Integrals in Elastostatics: General Considerations

Materials Department, Centro de Investigacion Cientifica de Yucatan A.C., Calle 43, No. 130, Colonia Chuburná de Hidalgo, 97200 Mérida, YUC, Mexico

Received 4 April 2011; Accepted 31 May 2011

Academic Editors: S.-W. Chyuan and E. A. Navarro

Copyright © 2011 V. V. Zozulya. 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. J. Balas, J. Sladek, and V. Sladek, Stress Analysis by Boundary Element Methods, Elsevier, Amsterdam, The Netherlands, 1989.
  2. P. K. Banerjee, Boundary Element Method in Engineering Science, McGraw Hill, New York, NY, USA, 1994.
  3. S. W. Chyuan, Y. S. Liao, and J. T. Chen, “An efficient method for solving electrostatic problems,” Computing in Science & Engineering, vol. 5, no. 3, pp. 52–58, 2003. View at Publisher · View at Google Scholar · View at Scopus
  4. A. N. Guz and V. V. Zozulya, Brittle Fracture of Constructive Materials under Dynamic Loading, Naukova Dumka, Kiev, Ukraine, 1993.
  5. S. Mukherjee and Y. X. Mukherjee, Boundary Methods: Elements, Contours, and Nodes, vol. 187 of Mechanical Engineering, CRC/Taylor & Francis, Boca Raton, Fla, USA, 2005. View at Publisher · View at Google Scholar
  6. J. T. Chen and H. K. Hong, “Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series,” Applied Mechanics Reviews, vol. 52, no. 1, pp. 17–32, 1999. View at Google Scholar · View at Scopus
  7. H. K. Hong and J. T. Chen, “Derivations of integral equations in elasticity,” Journal of Engineering Mechanics Division, vol. 114, no. 6, pp. 1028–1044, 1988. View at Google Scholar
  8. M. Tanaka, V. Sladek, and J. Sladek, “Regularization techniques applied to boundary element methods,” Applied Mechanics Reviews, vol. 47, no. 10, pp. 457–499, 1994. View at Google Scholar
  9. A. N. Guz and V. V. Zozulya, “Fracture dynamics with allowance for crack edge contact interaction,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 2, no. 3, pp. 173–233, 2001. View at Publisher · View at Google Scholar
  10. A. N. Guz and V. V. Zozulya, “Elastodynamic unilateral contact problems with friction for bodies with cracks,” International Applied Mechanics, vol. 38, no. 8, pp. 3–45, 2002. View at Publisher · View at Google Scholar
  11. V. V. Zozulya, “Integrals of Hadamard type in dynamic problems of crack theory,” Doklady Akademii Nauk Ukrainskoj SSR Serija A, no. 2, pp. 19–22, 1991 (Russian). View at Google Scholar
  12. V. V. Zozulya, “Regularization of the divergent integrals. I. General consideration,” Electronic Journal of Boundary Elements, vol. 4, no. 2, pp. 49–57, 2006. View at Google Scholar
  13. V. V. Zozulya, “Regularization of the divergent integrals. II. Application in fracture mechanics,” Electronic Journal of Boundary Elements, vol. 4, no. 2, pp. 58–66, 2006. View at Google Scholar
  14. V. V. Zozulya, “The regularization of the divergent integrals in 2-D elastostatics,” Electronic Journal of Boundary Elements, vol. 7, no. 2, pp. 50–88, 2009. View at Google Scholar
  15. V. V. Zozulya, “Regularization of hypersingular integrals in 3-D fracture mechanics: triangular BE, and piecewise-constant and piecewise-linear approximations,” Engineering Analysis with Boundary Elements, vol. 34, no. 2, pp. 105–113, 2010. View at Publisher · View at Google Scholar
  16. V. V. Zozulya, “Divergent integrals in elastostatics: regularization in 3-D case,” Computer Modeling in Engineering & Sciences, vol. 70, no. 3, pp. 253–349, 2010. View at Google Scholar
  17. V. V. Zozulya and P. I. Gonzalez-Chi, “Weakly singular, singular and hypersingular integrals in 3-D elasticity and fracture mechanics,” Journal of the Chinese Institute of Engineers, vol. 22, no. 6, pp. 763–775, 1999. View at Publisher · View at Google Scholar
  18. V. V. Zozulya and A. N. Lukin, “On the solution of three-dimensional problems of fracture mechanics by the method of boundary integral equations,” International Applied Mechanics, vol. 34, no. 6, pp. 45–53, 1998. View at Google Scholar
  19. V. V. Zozulya and V. A. Men'shikov, “Solution of three-dimensional problems of the dynamic theory of elasticity for bodies with cracks using hypersingular integrals,” International Applied Mechanics, vol. 36, no. 1, pp. 74–81, 2000. View at Google Scholar · View at Scopus
  20. L. Gaul, M. Kögl, and M. Wagner, Boundary Element Methods for Engineers and Scientists, Springer, Berlin, Germany, 2003. View at Zentralblatt MATH
  21. S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, vol. 7 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 1963.
  22. V. A. Trenogin, Functional Analysis, Fizmatlit, Moscow, Russia, 2002.
  23. J. Nečas and I. Hlaváček, Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, vol. 3 of Studies in Applied Mechanics, Elsevier Scientific, Amsterdam, The Netherlands, 1980.