Asymptotics of cellular buckling close to the Maxwell load

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We study the deformation of an elastic strut on a nonlinear Winkler foundation subjected to an axial compressive load P. Using multi–scale analysis and numerical methods we describe the localized, cellular, post–buckled state of the system when P is removed from the critical load P = 2. The solutions, and their modulation frequencies, differ significantly from those predicted by weakly nonlinear analysis very close to P = 2. In particular, when P approaches the Maxwell load PM , the localized solutions approach a large–amplitude heteroclinic connection between an unbuckled solution and a periodic solution. An asymptotic description of PM in terms of the system parameters is given. The agreement between the numerical calculations and the asymptotic approximations is striking.
Original languageEnglish
Pages (from-to)2935-2964
Number of pages30
JournalProceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
Issue number2016
Publication statusPublished - 2001


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