Article (Scientific journals)
Error analysis of generalized-alpha Lie group time integration methods for constrained mechanical systems
Arnold, Martin; Bruls, Olivier; Cardona, Alberto
2015In Numerische Mathematik, 129 (1), p. 149-179
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Keywords :
time integration; convergence analysis; Lie group methods; differential-algebraic equation
Abstract :
[en] 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.
Disciplines :
Mechanical engineering
Author, co-author :
Arnold, Martin
Bruls, Olivier  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire des Systèmes Multicorps et Mécatroniques
Cardona, Alberto
Language :
English
Title :
Error analysis of generalized-alpha Lie group time integration methods for constrained mechanical systems
Publication date :
2015
Journal title :
Numerische Mathematik
ISSN :
0029-599X
eISSN :
0945-3245
Publisher :
Springer-Verlag, Berlin, Germany
Volume :
129
Issue :
1
Pages :
149-179
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 18 May 2014

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