Finite Element Solutions for the Elastica

The finite deflection analysis of flexible bars subjected to vertical loads as well as the prediction of the buckling load and post-buckling response in the case of horizontal loading has attract the attention of numerous researchers. Publications related to large deflections of slender beams are referenced in and the monograph contains several applications as well as additional references to previous work. In the present note an efficient finite element procedure is developed for the problem of the elastica including variable loading and foundation stiffness. The effectiveness of the procedure is demonstrated by considering a number of example problems. Because of the generality of the finite element method extensions to more general problems than those presented here can easily be accomplished.