Homoclinic and heteroclinic solutions of upheaval buckling

Giles W Hunt, A Blackmore

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19 Citations (SciVal)


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
Issue number1732
Publication statusPublished - 1997


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