Reference : Lie group generalized-alpha time integration of constrained flexible multibody systems
Scientific journals : Article
Engineering, computing & technology : Mechanical engineering
Lie group generalized-alpha time integration of constrained flexible multibody systems
Bruls, Olivier mailto [Université de Liège - ULg > Département d'aérospatiale et mécanique > Laboratoire des Systèmes Multicorps et Mécatroniques >]
Cardona, Alberto mailto [Universidad Nacional del Litoral - Conicet > CIMEC-INTEC > > >]
Arnold, Martin mailto [Martin Luther University Halle-Wittenberg > NWFII - Institute of Mathematics > > >]
Mechanism & Machine Theory
Pergamon Press - An Imprint of Elsevier Science
Yes (verified by ORBi)
[en] differential-algebraic equations ; geometric integration ; mechanical system
[en] This paper studies a Lie group extension of the generalized-alpha time integration method for the simulation of flexible multibody systems. The equations of motion are formulated as an index-3 differential-algebraic equation (DAE) on a Lie group, with the advantage that rotation variables can be taken into account without the need of introducing any parameterization. The proposed integrator is designed to solve this equation directly on the Lie group without index reduction. The convergence of the method for DAEs is studied in detail and global second-order accuracy is proven for all solution components, i.e. for nodal translations, rotations and Lagrange multipliers. The convergence properties are confirmed by three benchmarks of rigid and flexible systems with large rotation amplitudes. The Lie group method is compared with a more classical updated Lagrangian method which is also formulated in a Lie group setting. The remarkable simplicity of the new algorithm opens interesting perspectives for real-time applications, model-based control and optimization of multibody systems.
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