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.
|Number of pages||11|
|Journal||Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences|
|Publication status||Published - 1997|
Hunt, G. W., & Blackmore, A. (1997). Homoclinic and heteroclinic solutions of upheaval buckling. Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences, 355(1732), 2185-2195. https://doi.org/10.1098/rsta.1997.0117