Localized Elasticae for the Strut on the Linear Foundation

[+] Author and Article Information
G. W. Hunt, M. K. Wadee, N. Shiacolas

Department of Civil Engineering, Imperial College of Science, Technology, and Medicine, London SW7 2BU, U.K.

J. Appl. Mech 60(4), 1033-1038 (Dec 01, 1993) (6 pages) doi:10.1115/1.2900971 History: Received March 26, 1992; Revised October 26, 1992; Online March 31, 2008


Localized solutions, for the classical problem of the nonlinear strut (elastica) on the linear elastic foundation, are predicted from double-scale analysis, and confirmed from nonlinear volume-preserving Runge-Kutta runs. The dynamical phase-space analogy introduces a spatial Lagrangian function, valid over the initial post-buckling range, with kinetic and potential energy components. The indefinite quadratic form of the spatial kinetic energy admits unbounded solutions, corresponding to escape from a potential well. Numerical experimentation demonstrates that there is a fractal edge to the escape boundary, resulting in spatial chaos.

Copyright © 1993 by The American Society of Mechanical Engineers
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