M. Borri, C.L.
Bottasso, L. Trainelli
Integration
of Elastic Multibody Systems by Invariant Conserving/Dissipating Algorithms –
Part I : Formulation
Computer Methods in Applied Mechanics and Engineering, 190:
3669-3699 (2001).
Abstract
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 of motion. 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.