Large deformation in-plane analysis of elastic beams

A large deformation theory for in-plane beam problems, analogous to Budiansky's non-linear shell theory, is formulated. The formulation results in objective equations. A finite element representation of displacements, using cubic interpolating functions, is combined with the virtual work form of these equations, in order to obtain numerical solutions. The capability of the formulation is demonstrated by computing the displacements associated with a thin cantilever strip, subjected to pure moment, until it forms a complete circle. A solution of the elastica problem illustrates a potential of the formulation in solving ‘post-buckling’ problems.