Klas Modin
SKF Engineering Research Centre MDC, RKs–2, Sweden
Dag Fritzson
SKF Engineering Research Centre MDC, RKs–2, Sweden
Claus Führer
Centre for Mathematical Sciences, Lund University, Sweden
Ladda ner artikel
Ingår i: The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007); 30-31 October; 2007; Göteborg (Särö)
Linköping Electronic Conference Proceedings 27:6, s. 49-65
Publicerad: 2007-12-21
ISBN:
ISSN: 1650-3686 (tryckt), 1650-3740 (online)
Numerical integration is considered for second order differential equations on the form where Ais significantly more expensive to evaluate than B; and B is stiff (highly oscillatory) in comparison with A. Examples of such problem are multibody problem with contact forces acting between bodies; and constraints formulated as penalty forces. Based on the splitting A+B of the acceleration field; a numerical integration algorithm; which is explicit in the A–part and implicit in the B–part; is suggested. Consistency and linear stability analysis of the proposed method is carried out. Numerical examples with the proposed method is carried out for two simple test problems; and for a complex multibody model of a rotating ball bearing. Comparison with conventional implicit methods is given for each example. The results indicate that the proposed method is more efficient; in terms of number of evaluations of A; at the same accuracy level.
[Hin] A. Hindmarsh. CVODE open-source software. www.llnl.gov/CASC/sundials/.
[HLW06] Ernst Hairer; Christian Lubich; and Gerhard Wanner. Geometric numerical integration; volume 31 of Springer Series in Computational Mathematics. Springer-Verlag; Berlin; second edition; 2006. Structure-preserving algorithms for ordinary differential equations.
[HS05] Ernst Hairer and Gustaf Söderlind. Explicit; time reversible; adaptive step size control. SIAM J. Sci. Comput.; 26(6):1838–1851 (electronic); 2005.
[MF06] Klas Modin and Claus Führer. Time-step adaptivity in variational integrators with application to contact problems. ZAMM Z. Angew. Math. Mech.; 86(10):785–794; 2006.
[MQ02] Robert I. McLachlan and G. ReinoutW. Quispel. Splitting methods. Acta Numer.; 11:341– 434; 2002.
[Nak06] I. Nakhimovski. Contributions to the Modeling and Simulation of Mechanical Systems with Detailed Contact Analyses. PhD thesis; Linköpings Universitet; Linköping; 2006.
[SF01] L-E Stacke and D. Fritzson. Dynamical behaviour of rolling bearings: simulations and experiments. Proc. Instn. Mech. Engrs.; 215:499–508; 2001.
[Söd02] Gustaf Söderlind. Automatic control and adaptive time-stepping. Numer. Algorithms; 31(1- 4):281–310; 2002. Numerical methods for ordinary differential equations (Auckland; 2001).
[Söd03] Gustaf Söderlind. Digital filters in adaptive time-stepping. ACM Trans. Math. Software; 29(1):1–26; 2003.
