Asymptotics of cellular buckling close to the Maxwell load

C. J. Budd, G. W. Hunt, R. Kuske

Research output: Contribution to journal › Article

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Abstract

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.
LanguageEnglish
Pages2935-2964
Number of pages30
JournalProceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
Volume457
Issue number2016
DOIs
StatusPublished - 2001

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buckling
Buckling
Heteroclinic Connection
Critical Load
Multiscale Analysis
Frequency Modulation
P Systems
Struts
Asymptotic Approximation
Nonlinear analysis
Frequency modulation
Nonlinear Analysis
Numerical Calculation
struts
Numerical methods
Periodic Solution
Numerical Methods
frequency modulation
approximation

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Asymptotics of cellular buckling close to the Maxwell load. / Budd, C. J.; Hunt, G. W.; Kuske, R.

In: Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, Vol. 457, No. 2016, 2001, p. 2935-2964.

Research output: Contribution to journal › Article

Budd, CJ, Hunt, GW & Kuske, R 2001, 'Asymptotics of cellular buckling close to the Maxwell load' Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, vol. 457, no. 2016, pp. 2935-2964. DOI: 10.1098/rspa.2001.0843
Budd CJ, Hunt GW, Kuske R. Asymptotics of cellular buckling close to the Maxwell load. Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences. 2001;457(2016):2935-2964. Available from, DOI: 10.1098/rspa.2001.0843
Budd, C. J. ; Hunt, G. W. ; Kuske, R./ Asymptotics of cellular buckling close to the Maxwell load. In: Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences. 2001 ; Vol. 457, No. 2016. pp. 2935-2964
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