Half-Explicit Runge-Kutta Lie Group Integrators for Flexible Multibody Systems

EasyChair Preprint 13407

Abstract

When modelling geometrically exact beams under constraints, two problems arise:The presence of nonlinear configuration spaces for describing large rotations and the presence of algebraic variables coupled with differential ones. To obtain an efficient numerical solution for the latter problem, half-explicit Runge-Kutta methods have been introduced in 1992 by Brasey and Hairer. The current work adapts these half-explicit Runge-Kutta methods to solve DAEs in nonlinear configuration spaces, of the Lie group form, so that the first problem is covered. The study aims at the analysis of the so called drift-off effect, which is a deviation from the constraints at position level when evaluating the numerical solution of the index-2 DAEs. Specifically, we adapt classical techniques for avoiding the drift-off effect to nonlinear configuration spaces. To conclude the study, numerical experiments on flexible structures modelled as Cosserat rods are performed.

Keyphrases: Drift-off effect, Half-explicit Runge-Kutta, Index-2 Baumgarte formulation, Lie groups time integration

@booklet{EasyChair:13407,
  author    = {Denise Tumiotto and Martin Arnold},
  title     = {Half-Explicit Runge-Kutta Lie Group Integrators for Flexible Multibody Systems},
  howpublished = {EasyChair Preprint 13407},
  year      = {EasyChair, 2024}}