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

Abstract

A straight elastica is bent until its ends are vertical and a fixed distance apart, and then it is pushed onto a flat 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 configurations are possible. There may be a single point of contact, a flat region of contact, or two points of contact with a buckled section between them. Also, if the ends are pushed down sufficiently 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 configurations 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.