Conserving properties in constrained dynamics of flexible multibody systems

The context of this work is the non-linear dynamics of multibody systems (MBS). The approach followed for parametrisation of rigid bodies is the use of inertial coordinates, forming a dependent set of parameters. This approach mixes naturally with nodal coordinates in a displacement-based finite element discretisation of flexible bodies, allowing an efficient simulation for MBS dynamics. An energy-momentum time integration algorithm is developed within the context of MBS constraints enforced through penalty methods. The approach follows the concept of a discrete derivative for Hamiltonian systems proposed by Gonzalez, achieving exact preservation of energy and momentum. The algorithm displays considerable stability, overcoming the traditional drawback of the penalty method, namely numerical ill-conditioning that leads to stiff equation systems. Additionally, excellent performance is achieved in long-term simulations with rather large time-steps.