Homoclinic and heteroclinic solutions of upheaval buckling

Giles W Hunt, A Blackmore

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

Upheaval of a heavy flexible strut from a rigid bed is viewed as an initial–value problem and spatial kinetic and potential energy functions are consequently defined. Upheaval from a perfectly flat state is characterized by the simultaneous vanishing of both functions at the boundaries. Smooth (flat to flat) connection without contact over a step in the bed is thus deemed impossible. A linear non–homogeneous fourth–order ordinary differential equation governs in regions of separation, but not when contact with the bed is maintained. This piecewise property is enough to ensure that several kinds of homoclinic and heteroclinic solutions exist for prop and step imperfections. Application is to subsea pipelines and examples of competing solutions for a realistically proportioned finite–length experimental pipe are included.
Original languageEnglish
Pages (from-to)2185-2195
Number of pages11
JournalPhilosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences
Volume355
Issue number1732
DOIs
Publication statusPublished - 1997

Fingerprint

Heteroclinic Solutions
Potential energy functions
Homoclinic Solutions
Initial value problems
Struts
buckling
Buckling
Ordinary differential equations
Kinetic energy
beds
Pipelines
Pipe
Contact
Flat Connection
Defects
Imperfections
Potential Function
Energy Function
Initial Value Problem
Fourth Order

Cite this

Homoclinic and heteroclinic solutions of upheaval buckling. / Hunt, Giles W; Blackmore, A.

In: Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences, Vol. 355, No. 1732, 1997, p. 2185-2195.

Research output: Contribution to journalArticle

@article{e898df8baee84a30be55f8e34018cb2c,
title = "Homoclinic and heteroclinic solutions of upheaval buckling",
abstract = "Upheaval of a heavy flexible strut from a rigid bed is viewed as an initial–value problem and spatial kinetic and potential energy functions are consequently defined. Upheaval from a perfectly flat state is characterized by the simultaneous vanishing of both functions at the boundaries. Smooth (flat to flat) connection without contact over a step in the bed is thus deemed impossible. A linear non–homogeneous fourth–order ordinary differential equation governs in regions of separation, but not when contact with the bed is maintained. This piecewise property is enough to ensure that several kinds of homoclinic and heteroclinic solutions exist for prop and step imperfections. Application is to subsea pipelines and examples of competing solutions for a realistically proportioned finite–length experimental pipe are included.",
author = "Hunt, {Giles W} and A Blackmore",
year = "1997",
doi = "10.1098/rsta.1997.0117",
language = "English",
volume = "355",
pages = "2185--2195",
journal = "Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences",
issn = "1364-503X",
publisher = "Royal Society of London",
number = "1732",

}

TY - JOUR

T1 - Homoclinic and heteroclinic solutions of upheaval buckling

AU - Hunt, Giles W

AU - Blackmore, A

PY - 1997

Y1 - 1997

N2 - Upheaval of a heavy flexible strut from a rigid bed is viewed as an initial–value problem and spatial kinetic and potential energy functions are consequently defined. Upheaval from a perfectly flat state is characterized by the simultaneous vanishing of both functions at the boundaries. Smooth (flat to flat) connection without contact over a step in the bed is thus deemed impossible. A linear non–homogeneous fourth–order ordinary differential equation governs in regions of separation, but not when contact with the bed is maintained. This piecewise property is enough to ensure that several kinds of homoclinic and heteroclinic solutions exist for prop and step imperfections. Application is to subsea pipelines and examples of competing solutions for a realistically proportioned finite–length experimental pipe are included.

AB - Upheaval of a heavy flexible strut from a rigid bed is viewed as an initial–value problem and spatial kinetic and potential energy functions are consequently defined. Upheaval from a perfectly flat state is characterized by the simultaneous vanishing of both functions at the boundaries. Smooth (flat to flat) connection without contact over a step in the bed is thus deemed impossible. A linear non–homogeneous fourth–order ordinary differential equation governs in regions of separation, but not when contact with the bed is maintained. This piecewise property is enough to ensure that several kinds of homoclinic and heteroclinic solutions exist for prop and step imperfections. Application is to subsea pipelines and examples of competing solutions for a realistically proportioned finite–length experimental pipe are included.

UR - http://dx.doi.org/10.1098/rsta.1997.0117

U2 - 10.1098/rsta.1997.0117

DO - 10.1098/rsta.1997.0117

M3 - Article

VL - 355

SP - 2185

EP - 2195

JO - 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 - 1732

ER -