### Abstract

Language | English |
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Pages | 2935-2964 |

Number of pages | 30 |

Journal | Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences |

Volume | 457 |

Issue number | 2016 |

DOIs | |

Status | Published - 2001 |

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

Research output: Contribution to journal › Article

*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

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TY - JOUR

T1 - Asymptotics of cellular buckling close to the Maxwell load

AU - Budd,C. J.

AU - Hunt,G. W.

AU - Kuske,R.

N1 - ID number: ISI:000172976900008

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://dx.doi.org/10.1098/rspa.2001.0843

U2 - 10.1098/rspa.2001.0843

DO - 10.1098/rspa.2001.0843

M3 - Article

VL - 457

SP - 2935

EP - 2964

JO - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

T2 - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

SN - 1364-503X

IS - 2016

ER -