Transient response of an impulsively loaded plastic string on a plastic foundation
Authors:
M. Mihăilescu-Suliciu, I. Suliciu, T. Wierzbicki and M. S. Hoo Fatt
Journal:
Quart. Appl. Math. 54 (1996), 327-343
MSC:
Primary 73E50; Secondary 73K03
DOI:
https://doi.org/10.1090/qam/1388020
MathSciNet review:
MR1388020
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Abstract: The problem of an impulsive loading of a long rigid-plastic string resting on a rigid-plastic foundation is studied. A closed form solution is obtained by disregarding the longitudinal motion and considering an arbitrarily large transversal motion. Expressions for the final shape of the string are derived in terms of the magnitude of the applied impulse. It is found that the stress and the foundation reaction force are not uniquely determined, while the shape of the string is.
N. Cristescu, Dynamic Plasticity, North-Holland, 1967
M. S. Hoo Fatt and T. Wierzbicki, Damage of plastic cylinders under localized pressure loading, Internat. J. Mech. Sci. 33, 999–1016 (1991)
M. S. Hoo Fatt, Deformation and rupture of cylindrical shells under dynamic loading, Ph.D. thesis, Massachusetts Institute of Technology, 1992
M. Mihǎilescu and I. Suliciu, Riemann and Goursat step data problems for extensible strings, J. Math. Anal. Appl. 52, 10–24 (1975)
M. Mihăilescu and I. Suliciu, Riemann and Goursat step data problems for extensible strings with non-convex stress-strain relation, Rev. Roumaine Math. Pures Appl. 20, 551–559 (1975)
J. B. Keller, Large amplitude motion of a string, Amer. J. Phys. 27, 584–586 (1959)
T. Wierzbicki and M. S. Hoo Fatt, Impact response of a string-on-plastic foundation, Internat. J. Impact Engrg. 12, 21–36 (1992)
N. Jones, On the dynamic inelastic failure of beams, Structural Failure (T. Wierzbicki and N. Jones, eds.), John Wiley & Sons, New York, 1989, pp. 133–159
M. S. Hoo Fatt and T. Wierzbicki, Impact damage of long plastic cylinders, Proceedings of the First International Conference of Offshore Engineering, vol. IV, Edinburgh, Scotland, 11–16 August, 1991, pp. 172–182
I. Suliciu, On modeling phase transition by means of rate type constitutive equations. Shock wave structure, Internat. J. Engrg. Sci. 28, 829–841 (1990)
T. Wierzbicki and M. S. Hoo Fatt, Damage assessment of cylinders due to impact and explosive loading, Internat. J. Impact Engrg. 13, 215–241 (1993)
N. Cristescu, Dynamic Plasticity, North-Holland, 1967
M. S. Hoo Fatt and T. Wierzbicki, Damage of plastic cylinders under localized pressure loading, Internat. J. Mech. Sci. 33, 999–1016 (1991)
M. S. Hoo Fatt, Deformation and rupture of cylindrical shells under dynamic loading, Ph.D. thesis, Massachusetts Institute of Technology, 1992
M. Mihǎilescu and I. Suliciu, Riemann and Goursat step data problems for extensible strings, J. Math. Anal. Appl. 52, 10–24 (1975)
M. Mihăilescu and I. Suliciu, Riemann and Goursat step data problems for extensible strings with non-convex stress-strain relation, Rev. Roumaine Math. Pures Appl. 20, 551–559 (1975)
J. B. Keller, Large amplitude motion of a string, Amer. J. Phys. 27, 584–586 (1959)
T. Wierzbicki and M. S. Hoo Fatt, Impact response of a string-on-plastic foundation, Internat. J. Impact Engrg. 12, 21–36 (1992)
N. Jones, On the dynamic inelastic failure of beams, Structural Failure (T. Wierzbicki and N. Jones, eds.), John Wiley & Sons, New York, 1989, pp. 133–159
M. S. Hoo Fatt and T. Wierzbicki, Impact damage of long plastic cylinders, Proceedings of the First International Conference of Offshore Engineering, vol. IV, Edinburgh, Scotland, 11–16 August, 1991, pp. 172–182
I. Suliciu, On modeling phase transition by means of rate type constitutive equations. Shock wave structure, Internat. J. Engrg. Sci. 28, 829–841 (1990)
T. Wierzbicki and M. S. Hoo Fatt, Damage assessment of cylinders due to impact and explosive loading, Internat. J. Impact Engrg. 13, 215–241 (1993)
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Article copyright:
© Copyright 1996
American Mathematical Society
