Localization theory for long continuous structures is extended to the buckling of a thin elastic strut supported by a bilinear elastoplastic medium. It is demonstrated that the form of localization has much in common with the buckling of struts on linear and nonlinear elastic foundations in that the localized response, which is of the greatest practical significance, is accompanied by a myriad of associated less significant solutions including periodic ones. Special shooting techniques are developed to deal with the problem of finding the localized solutions from amongst all competing possibilities.
Issue Section:
Technical Papers
1.
Baker, G., and Hunt, G. W., 1994, “Energy Computations of Softening Phenomena,” Fracture and Damage of Quasi-Brittle Materials: Proceedings of the U.S.-Europe Workshop. Prague, Z. P. Bazˇant, Z. Bittnar, M. Jirasek, and J. Mazars, eds., Sept., E & FN Spon, London, pp. 387–394.
2.
Bazˇant, Z. P., and Cedolin, L., 1991, Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories, Oxford University Press, New York.
3.
Blackmore, A., and Hunt, G. W., 1996, “The Dynamical Phase-Space Analogy as a Tool for the Analysis of Upheaval Buckling,” to be published.
4.
Champneys
A. R.
Toland
J. F.
1993
, “Bifurcation of a Plethora of Large Amplitude Homoclinic Orbits for Hamiltonian Systems
,” Nonlinearity
, Vol. 6
, pp. 665
–721
.5.
He´non
M.
1982
, “On the Numerical Computation of Poincare´ Maps
,” Physica D
, Vol. 5
, pp. 412
–414
.6.
Hete´nyi, M., 1946, Beams on Elastic Foundation, The University of Michigan Press, Ann Arbor, MI.
7.
Hunt
G. W.
Wadee
M. K.
1991
, “Comparative Lagrangian Formulations for Localized Buckling
,” Proceedings of the Royal Society of London
, Vol. A434
, pp. 485
–502
.8.
Hunt, G. W., Bolt, H. M., and Thompson, J. M. T., 1989, “Structural Localization Phenomena and the Dynamical Phase-Space Analogy,” Proceedings of the Royal Society of London, Vol. A425, pp. 245–267.
9.
Hunt
G. W.
Wadee
M. K.
Shiacolas
N.
1993
, “Localized Elasticæ for the Strut on the Linear Foundation
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 60
, pp. 1033
–1038
.10.
Hunt, G. W., Mu¨hlhaus, H-B., and Whiting, A. I. M., 1996a, “Evolution of Localized Folding for a Thin Elastic Layer in a Softening Visco-Elastic Medium,” PAGEOP to be published.
11.
Hunt, G. W., Lawther, R., and Provideˆncia, P., 1996b, “Finite Element Modelling of Spatially-Chaotic Structures,” to be published.
12.
Sanz-Serna
J. M.
1988
, “Runge-Kutta Schemes for Hamiltonian Systems
,” BIT
, Vol. 28
, pp. 877
–883
.13.
Thompson, J. M. T., and Hunt, G. W., 1973, A General Theory of Elastic Stability, Wiley, London.
14.
Tvergaard
V.
Needleman
A.
1980
, “On the Localization of Buckle Patterns
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 47
, pp. 613
–619
.
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