M. Borri, C.L. Bottasso, L. Trainelli
A
Novel Momentum-Preserving Energy-Decaying Algorithm for Finite-Element Multibody Procedures
Computer Assisted Mechanics and Engineering Sciences, 9:
315-340 (2002).
also presented at Computational Aspects of Nonlinear
Structural Systems with Large Rigid Body Motion, NATO Advanced Research
Workshop, Pultusk, Poland, July 2-7, 2000.
Abstract
We present a new methodology for the integration of
general non-linear multibody systems within a
finite-element framework, with special attention to numerical robustness. The
outcome is a non-linearly unconditionally stable algorithm with dissipation
properties. This algorithm exactly
preserves the total linear and angular momenta of holonomically constrained multibody
systems, which implies the satisfaction of Newton's Third law of Action and
Reaction. Furthermore, the scheme
strictly dissipates the total mechanical energy of the system. This is accomplished by selective damping of
the unresolved high-frequency components of the response. We derive the governing equations relying on
the 6-D compact representation of motion and we employ a parameterization based
on the Cayley transform which ensures geometric
invariance of the resulting numerical schemes. We present some numerical tests
in order to illustrate the main features of the methodology, and to demonstrate
the properties predicted in the analysis.