Extended variational formulations and F.E. models for non-linear beams under non-conservative loading

For nonconservative mechanical systems, classical variational principles do not hold true; hence the principle of incremental virtual work is usually taken as a convenient foundation for finite element solution methods [2,8,9]. Recent results on the so-called ‘inverse problem’ of calculus of variations, however, lead to ‘extended’ variational formulations, which can be provided even for nonconservative systems. In the present paper, this approach is used for the particular case of a nonlinear beam subjected to a co-planar follower static loading. Suitable finite element models are deduced from the ‘extended’ variational principle, and their numerical performance is assessed by means of some meaningful examples.