An Energy-Conserving and Filtering Method for Stiff Nonlinear Multibody Dynamics

Abstract

The conservation of energy is necessary for accuracy oflong-term simulations, and also guarantees energystability, which is sought to alleviate any stabilityrestrictions on the time integration step size. We discusssome issues regarding the integration of stiff nonlineardynamics with traditional dissipative and energy andmomentum conserving methods and we introduce a new 2-stagemethod which is an adaptation of the time integrationscheme presented in [1] for rigid multibody dynamics. Bycombining an energy conserving scheme with a substageacceleration filter, we devise an implicit method thatpreserves the energy map and is capable of integratingstiff flexible multibody systems that require numericaldissipation. In order to avoid the artificial stiffnessand the resulting instabilities caused by the enforcementof kinematic constraints, a joint coordinate formulationis adopted to model the rigid components of the system,while a total Lagrangian approach is adopted to model theflexible elements in the system. As the resulting model istypically characterized by a large number of degrees offreedom, we also demonstrate how the method may beextended to incorporate a form of domain decomposition.