Share This Article:

Finite Element Analysis of the Ramberg-Osgood Bar

Abstract Full-Text HTML Download Download as PDF (Size:295KB) PP. 211-216
DOI: 10.4236/ajcm.2013.33030    5,248 Downloads   7,609 Views   Citations

ABSTRACT

In this work, we present a priori error estimates of finite element approximations of the solution for the equilibrium equation of an axially loaded Ramberg-Osgood bar. The existence and uniqueness of the solution to the associated nonlinear two point boundary value problem is established and used as a foundation for the finite element analysis.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

D. Wei and M. Elgindi, "Finite Element Analysis of the Ramberg-Osgood Bar," American Journal of Computational Mathematics, Vol. 3 No. 3, 2013, pp. 211-216. doi: 10.4236/ajcm.2013.33030.

References

[1] W. R. Osgood and W. Ramberg, “Description of Stress-Strain Curves by Three Parameters,” NACA Technical Note 902, National Bureau of Standards, Washington DC, 1943.
[2] L. A. James, “Ramberg-Osgood Strain-Harding Characterization of an ASTM A302-B Steel,” Journal of Pressure Vessel Technology, Vol. 117, No. 4, 1995, pp. 341-345. doi:10.1115/1.2842133
[3] K. J. R. Rasmussen, “Full-Range Stress-Strain Curves for Stainless Steel Alloys,” Research Report R811, University of Sydney, Department of Civil Engineering, 2001.
[4] V. N. Shlyannikov, “Elastic-Plastic Mixed-Mode Fracture Criteria and Parameters, Lecture Notes Applied Mechanics, Vol. 7,” Springer, Berlin, 2002.
[5] P. Dong and L. DeCan, “Computational Assessment of Build Strategies for a Titanium Mid-Ship Section,” 11th International Conference on Fast Sea Transportation, FAST, Honolulu, 26-29 September 2011, pp. 540-546.
[6] P. Dong, “Computational Weld Modeling: A Enabler for Solving Complex Problems with Simple Solutions, Keynote Lecture,” Proceedings of the 5th IIW International Congress, Sydney, 7-9 March 2007, pp. 79-84.
[7] E. Zeidler, “Nonlinear Functional Analysis and Its Applications, Variational Methods and Optimization, Vol. III,” Springer Verlag, New York, 1986. doi:10.1007/978-1-4612-4838-5
[8] R. A. Adams, “Sobolev Spaces, Pure and Applied Mathematics, Vol. 65,” Academic Press, Inc., New York, San Francisco, London, 1975.
[9] V. G. Maz’Ja, “Sobolev Spaces,” Springer-Verlag, New York, 1985.
[10] F. E. Browder, “Variational Methods for Non-Linear Elliptic Eigenvalue Problems,” Bulletin of the American Mathematical Society, Vol. 71, 1965, pp. 176-183. doi:10.1090/S0002-9904-1965-11275-7
[11] R. Temam, “Mathematical Problems in Plasticity,” Gauthier-Villars, Paris, 1985.
[12] G. Strang and G. J. Fix, “An Analysis of the Finite Element Method,” Prentice-Hall, Inc., Englewood Cliffs, 1973.
[13] P. G. Ciarlet, “The Finite Element Method for Elliptic Problems,” North-Holland, Amsterdam, 1978.
[14] J. T. Oden And G. F. Carey, “Finite Elements,” Prentice-Hall, Englewood Cliffs, 1984.
[15] S. C. Brenner and L. R. Scott, “The Mathematical Theory of Finite Element Methods, Texts in Applied Mathematics, v. 15,” 3rd Edition, Springer Verlag, New York, 2008. doi:10.1007/978-0-387-75934-0

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.