M. Borri, C.L.
Bottasso, L. Trainelli
Integration
of Elastic Multibody Systems by Invariant Conserving/Dissipating Algorithms –
Part II : Numerical Schemes and Applications
Computer Methods in Applied Mechanics and Engineering, 190:
3701-3733 (2001).
Abstract
This work presents a novel methodology for the dynamic
analysis of general non-linear multibody systems composed of rigid and
deformable bodies, the latter under the small strain assumption. In Part I we
developed the 6-D compact representation and parameterization of motion for
constrained bodies. Part II is devoted to the design of a class of modified
Runge-Kutta methods dedicated to non-linear dynamics. These are capable of
integrating on the configuration manifold and of preserving linear and angular
momenta. Within this class of methods, two second-order algorithms are designed
under the requirement of attaining non-linear unconditional stability: the
‘Energy Preserving’ and ‘Energy Decaying’ methods. These schemes respectively
display an algorithmic law of conservation and dissipation of the total
mechanical energy of the system, together with the vanishing of the algorithmic
work done by ideal, time-independent constraints. Their performances are
assessed with the aid of some representative numerical applications which
confirm the non-conventional properties predicted in the analysis.