A novel momentum-preserving energy-decaying algorithm for finit e-element multibody procedures

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.