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Characterization of limiting homoclinic behaviour in a one-dimensional elastic buckling model
Localization of buckle patterns in a long one-dimensional structure is studied when the nonlinearity present ensures subcritical behaviour but subsequently restabilizes the response. Previous works have shown that with a weak restabilizing component localized soliton-like solutions are possible but as the degree of restabilization increases towards a critical threshold value so the localized forms give way to a thoroughly periodic response. Multiple-scale asymptotic analysis is used to describe the evolution of the solution structure through this stage, which is shown to be governed by a pair of second-order amplitude equations containing quintic nonlinearity. These equations are investigated both numerically and asymptotically and their solutions are compared with direct computations using the full governing forms. The agreement between the approaches is found to be very encouraging and suggests that further insight into the processes at work may be obtained by application of more refined analytical techniques.
History
Publication title
Journal of The Mechanics and Physics of SolidsVolume
48Issue
11Pagination
2297-2313ISSN
0022-5096Department/School
School of Natural SciencesPublisher
Pergamon-Elsevier Science LtdPlace of publication
The Boulevard, Langford Lane, Kidlington, Oxford, England, Ox5 1GbRepository Status
- Restricted