Conserving Properties in Constrained Dynamics of Flexible Multibody Systems

Abstract

The context of this work is the non-linear dynamics ofmultibody systems (MBS). The approach followed for parametrisation ofrigid bodies is the use of inertial coordinates, forming a dependent setof parameters. This approach mixes naturally with nodal coordinates in adisplacement-based finite element discretisation of flexible bodies,allowing an efficient simulation for MBS dynamics. An energy-momentumtime integration algorithm is developed within the context of MBSconstraints enforced through penalty methods. The approach follows theconcept of a discrete derivative for Hamiltonian systems proposed byGonzalez, achieving exact preservation of energy and momentum. Thealgorithm displays considerable stability, overcoming the traditionaldrawback of the penalty method, namely numerical ill-conditioning thatleads to stiff equation systems. Additionally, excellent performance isachieved in long-term simulations with rather large time-steps.