Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2006, Article ID 17936, 24 pages
http://dx.doi.org/10.1155/JAM/2006/17936

A one-dimensional spot welding model

1Department of Mathematics and Statistics, Oakland University, Rochester 48309-4478, MI, USA
2Department of Mechanical Engineering, Oakland University, Rochester 48309-4478, MI, USA

Received 3 July 2006; Revised 3 November 2006; Accepted 22 November 2006

Copyright © 2006 K. T. Andrews 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. D. J. Browne, H. W. Chandler, J. T. Evans, and I. Wen, “Computer simulation of resistance spot welding in aluminum—part 1,” Welding Journal, vol. 74, no. 10, pp. 339–344, 1995. View at Google Scholar
  2. J. Crank, Free and Moving Boundary Problems, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1984. View at Zentralblatt MATH · View at MathSciNet
  3. C. M. Elliott and J. R. Ockendon, Weak and Variational Methods for Moving Boundary Problems, vol. 59 of Research Notes in Mathematics, Pitman, Massachusetts, 1982. View at Zentralblatt MATH · View at MathSciNet
  4. E. Feulvarch, V. Robin, and J. M. Bergheau, “Resistance spot welding simulation: a general finite element formulation of electro thermal contact conditions,” Journal of Materials Processing Technology, vol. 153-154, pp. 436–441, 2004. View at Publisher · View at Google Scholar
  5. R. M. Furzeland, “A comparative study of numerical methods for moving boundary problems,” Journal of the Institute of Mathematics and Its Applications, vol. 26, no. 4, pp. 411–429, 1980. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. R. F. Gariepy, M. Shillor, and X. Xu, “Existence of generalized weak solutions to a model for in situ vitrification,” European Journal of Applied Mathematics, vol. 9, no. 6, pp. 543–559, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. E. Gould, “An examination of Nugget development during spot welding using both experimental and analytical techniques,” Welding Journal, vol. 66, no. 1, pp. 1–10, 1987. View at Google Scholar
  8. S. D. Howison, J. F. Rodrigues, and M. Shillor, “Stationary solutions to the thermistor problem,” Journal of Mathematical Analysis and Applications, vol. 174, no. 2, pp. 573–588, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. A. Khan, K. Broach, and A. Kabir, “Numerical thermal model of resistance spot welding in aluminum,” Journal of Thermophysics and Heat Transfer, vol. 14, no. 1, pp. 88–95, 2000. View at Google Scholar
  10. J. A. Khan, L. Xu, and Y.-J. Chao, “Prediction of nugget development during resistance spot welding using coupled thermal-electrical-mechanical model,” Science and Technology of Welding and Joining, vol. 4, no. 4, pp. 201–207, 1999. View at Publisher · View at Google Scholar
  11. A. A. Lacey and M. Shillor, “The existence and stability of regions with superheating in the classical two-phase one-dimensional Stefan problem with heat sources,” IMA Journal of Applied Mathematics, vol. 30, no. 2, pp. 215–230, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. A. A. Lacey and A. B. Tayler, “A mushy region in a Stefan problem,” IMA Journal of Applied Mathematics, vol. 30, no. 3, pp. 303–313, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. A. Mackenzie and M. L. Robertson, “The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method,” Journal of Computational Physics, vol. 161, no. 2, pp. 537–557, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. P. Shi, M. Shillor, and X. Xu, “Existence of a solution to the Stefan problem with Joule's heating,” Journal of Differential Equations, vol. 105, no. 2, pp. 239–263, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. X. Sun and M. A. Khaleel, “Resistance spot welding of aluminum alloy to steel with transition material—part 2: finite element analysis of nugget growth,” Welding Journal, vol. 83, no. 7, pp. 197–202, 2004. View at Google Scholar
  16. A. B. Tayler, Mathematical Models in Applied Mechanics, Oxford Applied Mathematics and Computing Science Series, The Clarendon Press, Oxford University Press, New York, 1986. View at Zentralblatt MATH · View at MathSciNet
  17. L. Wei, D. Cerjanec, and G. A. Grzadzinski, “A comparative study of single-phase AC and multiphase DC resistance spot welding,” Journal of Manufacturing Science and Engineering, vol. 127, no. 8, pp. 583–589, 2005. View at Publisher · View at Google Scholar
  18. X. Xu and M. Shillor, “The Stefan problem with convection and Joule's heating,” Advances in Differential Equations, vol. 2, no. 4, pp. 667–691, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. L. S. Yao and J. Prusa, “Melting and freezing,” in Advances in Heat transfer, vol. 19, pp. 1–95, 1989. View at Google Scholar
  20. “Technology for efficient and accurate spot welding,” Technology and Products Section, JETRO, November 1995, 24–25.