An energy-momentum algorithm for flexible multibody systems with finite element techniques

A unified approach for the treatment of the non-linear dynamics of multibody systems (MBS) composed of both rigid and elastic bodies is proposed. Large displacements and rotations, large strains and non-linear elastic material response are considered for the elastic bodies. The proposed formulation exploits three key ingredients: the use of a dependent set of inertial coordinates of selected points of the system; the use of a basic constraint library enforced through the penalty method; the use of the energy-momentum method to integrate the equations. The proposed algorithm is set in the framework of a non-conventional finite element formulation, which combine naturally the displacement-based discretisation of the deformable bodies with rigid body mechanics. Two key performance features are achieved. The exact conservation of total momentum and total energy in conservative systems is ensured. The major drawback of the penalty method, namely numerical ill-conditioning that leads to stiff equation systems, is overcome.