摘要
In this paper a mathematical model is discussed describing the deformation of a cantilever by its own weight. We assume that a cantilever of uniform cross-section and density is held fixed at an angle $\\\\\\\\\\\\\\\\alpha $ at one end and is free at the other end. The shape of the cantilever depends heavily on $\\\\\\\\\\\\\\\\alpha $ and a nondimensional parameter K which represents the relative importance of density and length to that of flexural rigidity. We analyze the bifurcation phenomena for the vertical case, $\\\\\\\\\\\\\\\\alpha = \\\\\\\\\\\\\\\\pi $. Several numerical results are presented and discussed.