Three-dimensional formulation of rigid-flexible multibody systems with flexible beam elements

Multibody systems generally contain solids with appreciable deformations and which decisively influence the dynamics of the system. These solids have to be modeled by means of special formulations for flexible solids. At the same time, other solids are of such a high stiffness that they may be considered rigid, which simplifies their modeling. For these reasons, for a rigid-flexible multibody system, two types of formulations coexist in the equations of the system. Among the different possibilities provided in the literature on the material, the formulation in natural coordinates and the formulation in absolute nodal coordinates are utilized in this paper to model the rigid and flexible solids, respectively. This paper contains a mixed formulation based on the possibility of sharing coordinates between a rigid solid and a flexible solid. The global mass matrix of the system is shown to be constant and, in addition, many of the constraint equations obtained upon utilizing these formulations are linear and can be eliminated.