Improving stability by change of representation in time-stepping analysis of non-linear beams dynamics

In this paper we propose a change in the representation of the discrete motion equations in structural non-linear dynamics to obtain an improvement in the stability of time numerical integrations. In particular, natural local state variables are indicated for a finite element approach to beam problems. The results, relative to Newmark approximations for the variations in the displacement and velocity vectors, show a significant increase in the range of stability of the time integration process and a reduction in the number of Newton iterations required in the time integration steps. The proposed method, further, preserves energy as well as the linear and angular momentum of the dynamical system.