An energy-conserving and filtering method for stiff nonlinear multibody dynamics

The conservation of energy is necessary for accuracy of long-term simulations, and also guarantees energy stability, which is sought to alleviate any stability restrictions on the time integration step size. We discuss some issues regarding the integration of stiff nonlinear dynamics with traditional dissipative and energy and momentum conserving methods and we introduce a new 2-stage method which is an adaptation of the time integration scheme presented in [1] for rigid multibody dynamics. By combining an energy conserving scheme with a substage acceleration filter, we devise an implicit method that preserves the energy map and is capable of integrating stiff flexible multibody systems that require numerical dissipation. In order to avoid the artificial stiffness and the resulting instabilities caused by the enforcement of kinematic constraints, a joint coordinate formulation is adopted to model the rigid components of the system, while a total Lagrangian approach is adopted to mode! the flexible elements in the system. As the resulting model is typically characterized by a large number of degrees of freedom, we also demonstrate how the method may be extended to incorporate a form of domain decomposition.