Error analysis of generalized-alpha Lie group time integration methods for constrained mechanical systems

MARTIN ARNOLD; OLIVIER BRULS; ALBERTO CARDONA

NUMERISCHE MATHEMATIK

SPRINGER

Lugar: Berlin; Año: 2015 vol. 129 p. 149 - 179

0029-599X

Generalized-alpha methods are very popular in structural dynamics. They are methods of Newmark type and combine favourable stability properties with second order convergence for unconstrained second order systems in linear spaces. Recently, they were extended to constrained systems in flexible multibody dynamics that have a configuration space with Lie group structure. In the present paper, the convergence of these Lie group methods is analysed by a coupled one-step error recursion for differential and algebraic solution components. It is shown that spurious oscillations in the transient phase result from order reduction that may be avoided by a perturbation of starting values or by index reduction. Numerical tests for a benchmark problem from the literature illustrate the results of the theoretical investigations.