Integration of elastic multibody systems by invariant conserving/dissipating algorithms. I. Formulation Original Research Article

This work presents a novel methodology for the dynamic analysis of general non-linear flexible multibody systems. In Part I we develop the 6-D compact representation of motion for those body models which motion may be described by a displacement field plus an independent rotation field. This approach explores the fundamental properties of rigid body motion, and in particular the coupled nature of linear and angular quantities in both kinematics and dynamics, inspiring a novel parameterization technique based on the exponential map. Using the proposed approach, we derive the governing equations for the case of multibody systems composed by rigid bodies and geometrically non-linear beams connected by holonomic constraints. These equations provide the starting point for the derivation of a class of numerical algorithms characterized by non-conventional conservation properties. In Part II of this work we develop the algorithms and illustrate their properties with the aid of some numerical applications.