Large deformations of a heavy cantilever

Abstract

A cantilever of uniform cross-section and density is held at an angle α \alpha at one end. The shape of the cantilever depends heavily on α \alpha and a nondimensional parameter K K which represents the relative importance of density and length so that of flexural rigidity. Perturbations on the elastica equations for small and large K K show good agreement with exact numerical integration. It is found that whenever K K reaches a critical value, bifurcations of the solutions occur. This nonuniqueness can be observed by the flipping phenomena as α \alpha is increased.