A Nonlinear Beam Element Formulation in the Framework of an Energy Preserving Time Integration Scheme for Constrained Multibody Systems Dynamics

Abstract

A nonlinear large rotations beam element is presented within the framework of an energy conserving algorithm which was presented in previous works [Lens E, Cardona A, Ge´radin M. Energy preserving time integration for constrained multibody systems. Multibody System Dyn 2004;11:41?61; Lens E. Energy preserving/decaying time integration schemes for multibody systems dynamics. PhD thesis, Universidad Nacional del Litoral, Argentina; 2006]. Flexibility is dealt with easily in energy conserving algorithms only for finite element models with displacement degrees of freedom. However, beam models which have rotation degrees of freedom are more cumbersome to be handled. The beam model which we introduce in this paper has simplifications that lead to quite compact expressions of its different terms. This kind of algorithms has many advantages, both theoretical and practical, because of its unconditional stability which is guaranteed even in the nonlinear regime.