Substructure synthesis methods for dynamic analysis of multi-body systems

The formulation for the dynamic analysis of flexible multi-body systems that undergo large rigid body motion, leads to geometrically non-linear inertia properties due to large rotations. These inertia non-linearities that represent the coupling between gross rigid body motion and small elastic deformation, are dependent on the assumed displacement field. As alternatives to the finite element methods, deformable body shape functions and shape vectors are commonly employed to describe elastic deformation of linear structures. In this paper, substructure shape functions and shape vectors are used to describe elastic deformation of non-linear inertia-variant multi-body systems. This leads to two different representations of inertia nonlinearities; one is based on a consistent mass formulation, while the other is a lumped mass technique. The multi-body systems considered are collections of interconnected rigid and flexible bodies. Open and closed loop systems are permitted.