Deflections and buckling of a bent elastica in contact with a flat surface

A straight elastica is bent until its ends are vertical and a _xed distance apart\ and then it is pushed onto a ~at rigid surface[ The weight of the strip and friction between the strip and the surface are neglected[ Planar equilibrium states of the strip are investigated\ using either a shooting method or an integral formulation[ Both symmetric and asymmetric con_gurations are possible[ There may be a single point of contact\ a ~at region of contact\ or two points of contact with a buckled section between them[ Also\ if the ends are pushed down su.ciently far\ one or two loops may form when the upper portion of the strip makes contact with the lower portion on the surface[ If the two ends are held together "vertically# and then pushed down\ asymmetric con_gurations may occur in which there is a region of contact between the upper and lower portions of the strip near their ends[ The properties of these various equilibrium shapes are investigated