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IMA Journal of Applied Mathematics Advance Access originally published online on December 17, 2004
IMA Journal of Applied Mathematics 2005 70(1):162-172; doi:10.1093/imamat/hxh051
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IMA Journal of Applied Mathematics Vol. 70 No. 1 © Institute of Mathematics and its Applications 2005; all rights reserved.

Stability of localized solutions under rigid loading in a heuristic buckling model*

M. Khurram Wadee §

Department of Engineering, School of Engineering, Computer Science and Mathematics, University of Exeter, North Park Road, Exeter, Devon EX4 4QF, UK

The stability of static localized buckling solutions which bifurcate from the critical load for a strut on an elastic foundation is analysed under conditions of rigid loading (i.e. with prescribed end shortening) using a non-periodic modal analysis. The characteristic of such deflection patterns is in marked contrast with stability under the more straightforward case of dead loading (behaviour under prescribed load). The model presented incorporates initial destabilization and subsequent restabilization of the response at the lowest order.

Keywords: elastic potential energy; homoclinic solutions; nonlinear structural mechanics; Rayleigh–Ritz analysis.

* Dedicated to Ray W. Ogden on the occasion of his 60th birthday

§ Email: m.k.wadee{at}ex.ac.uk


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