Asymptotics of cellular buckling close to the Maxwell load

Research output: Contribution to journalArticle

  • 41 Citations

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

Fingerprint

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

Cite this

@article{fe073e4032fc475aa9276c9200dc7715,
title = "Asymptotics of cellular buckling close to the Maxwell load",
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.",
author = "Budd, {C. J.} and Hunt, {G. W.} and R. Kuske",
note = "ID number: ISI:000172976900008",
year = "2001",
doi = "10.1098/rspa.2001.0843",
language = "English",
volume = "457",
pages = "2935--2964",
journal = "Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences",
issn = "1364-503X",
publisher = "Royal Society of London",
number = "2016",

}

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 -