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Simulation of multibody systems with the use of coupling techniques: a case study

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Abstract

Simulation coupling (or cosimulation) techniques provide a framework for the analysis of decomposed dynamical systems with the use of independent numerical procedures for decomposed subsystems. These methods are often seen as very promising because they enable the utilization of the existing software for subsystem analysis and usually are easy to parallelize, and run in a distributed environment. For example, in the domain of multibody systems dynamics, a general setup for “Gluing Algorithms” was proposed by Wang et al. It was intended to provide a basis for multilevel distributed simulation environments. The authors presented an example where Newton’s method was used to synchronize the responses of subsystem simulators.

In this paper, we discuss some properties of a simplified iterative coupling scheme, where subsystems’ responses are synchronized at discrete time points. We use a simple multibody model to investigate the influence of synchronization parameters on computations. We also try to provide explanation to the oscillatory behavior of the solutions obtained from this method.

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References

  1. Anderson, K.S., Duan, S.: Highly parallelizable low order dynamics simulation algorithm for multi-rigid-body systems. J. Guid. Control Dyn. 23(2), 355–364 (2000)

    Article  Google Scholar 

  2. Andrus, J.F.: Numerical solution of systems of ordinary differential equations separated into subsystems. SIAM J. Numer. Anal. 16(4), 605–611 (1979). doi: 10.1137/0716045. URL http://link.aip.org/link/?SNA/16/605/1

    Article  MATH  MathSciNet  Google Scholar 

  3. Arnold, M.: Multi-rate time integration for large scale multibody system models. In: IUTAM Symposium on Multiscale Problems in Multibody System Contacts, vol. 1, pp. 1–10 (2007)

  4. Bae, D.S., Haug, E.J.: A recursive formulation for constrained mechanical system dynamics: Part I: Open loop systems. Mech. Struct. Mach. 15(3), 383–393 (1987)

    Article  Google Scholar 

  5. Bae, D.S., Haug, E.J.: A recursive formulation for constrained mechanical system dynamics: Part II: Closed loop systems. Mech. Struct. Mach. 15(4), 481–506 (1987)

    Article  Google Scholar 

  6. Bae, D.S., Kuhl, J.G., Haug, E.J.: A recursive formulation for constrained mechanical system dynamics: Part III: Parallel processor implementation. Mech. Struct. Mach. 16(2), 249–269 (1988)

    Article  Google Scholar 

  7. Chawla, B.R., Gummel, H.K., Kozak, P.: MOTIS—an MOS timing simulator. IEEE Trans. Circuits Syst. cas-22(12), 901–910 (1975)

    Article  Google Scholar 

  8. Featherstone, R.: A divide-and-conquer articulated-body algorithm for parallel O(log (n)) calculation of rigid-body dynamics. Part 1: Basic algorithm. Int. J. Robot. Res. 18(9), 867–875 (1999)

    Article  Google Scholar 

  9. Featherstone, R.: A divide-and-conquer articulated-body algorithm for parallel O(log (n)) calculation of rigid-body dynamics. Part 2: Trees, loops, and accuracy. Int. J. Robot. Res. 18(9), 876–892 (1999)

    Article  Google Scholar 

  10. Gear, C.W., Wells, D.R.: Multirate linear multistep methods. BIT 24(4), 484–502 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  11. Gear, C.W., Gupta, G.K., Leimkuhler, B.: Automatic integration of Euler–Lagrange equations with constraints. J. Comput. Appl. Math. 12, 77–90 (1985)

    Article  MathSciNet  Google Scholar 

  12. Gu, B., Asada, H.H.: Co-simulation of algebraically coupled dynamic subsystems. In: Proceedings of the American Control Conference. Arlington, VA (2001)

  13. Gu, B., Asada, H.H.: Co-simulation of algebraically coupled dynamic subsystems without disclosure of proprietary subsystem models. ASME J. Dyn. Syst., Meas. Control 126(1), 1–13 (2004)

    Article  Google Scholar 

  14. Gu, B., Gordon, W., Asada, H.H.: Co-simulation of coupled dynamic subsystems: A differential-algebraic approach using singularly perturbed sliding manifolds. In: Proceedings of the American Control Conference. Chicago, Illinois (2000)

  15. Harchel, G.D., Sangiovanni-Vincentelli, A.L.: A survey of third-generation simulation techniques. In: Proceedings of the IEEE, vol. 69, pp. 1264–1280 (1981)

  16. Hippmann, G., Arnold, M., Schittenhelm, M.: Efficient simulation of bush and roller chain drives. In: Multibody Dynamics 2005, ECCOMAS Thematic Conference. Madrid, Spain (2005)

  17. Kim, S.S.: A subsystem synthesis method for efficient vehicle multibody dynamics. Multibody Syst. Dyn. 7, 189–207 (2002)

    Article  MATH  Google Scholar 

  18. Kübler, R., Schiehlen, W.: Modular simulation in multibody system dynamics. Multibody Syst. Syn. 4, 107–127 (2000)

    Article  MATH  Google Scholar 

  19. Kübler, R., Schiehlen, W.: Virtual assembly of multibody systems. Stab. Control: Theory Appl. 3(3), 223–233 (2000)

    Google Scholar 

  20. Leimkuhler, B.: Estimating waveform relaxation convergence. SIAM. J. Sci. Comput. 14, 872–889 (1993)

    MATH  MathSciNet  Google Scholar 

  21. Leimkuhler, B.: Relaxation techniques in multibody dynamics. Trans. Can. Soc. Mech. Eng. 17(4A), 459–471 (1993)

    MathSciNet  Google Scholar 

  22. Lelarasmee, E.: The waveform relaxation method for time domain analysis of large scale integrated circuits: Theory and applications. Ph.D. thesis (1982)

  23. Lelarasmee, E., Ruehli, A.E., Sangiovanni-Vincentelli, A.L.: The waveform relaxation method for time-domain analysis of large scale integrated circuits. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 1(3), 131–145 (1982)

    Article  Google Scholar 

  24. Schiehlen, W., Rükgauer, A., Schirle, T.: Force coupling versus differential algebraic description of constrained multibody systems. Multibody Syst. Dyn. 4, 317–340 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  25. The MathWorks, Inc.: MATLAB function reference

  26. Tseng, F.C.: Multibody dynamics simulation in network-distributed environments. Ph.D. thesis (2000)

  27. Tseng, F.C., Ma, Z.D., Hulbert, G.: Efficient numerical solution of constrained multibody dynamics systems. Comput. Methods Appl. Mech. Eng. 192, 439–472 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  28. Utkin, V., Guldner, J., Shi, J.: Sliding Mode Control in Electromechanical Systems. CRC Press, Boca Raton (1996)

    Google Scholar 

  29. Wang, J., Ma, Z.D., Hulbert, G.: A gluing algorithm for distributed simulation of multibody systems. Nonlinear Dyn. 34, 159–188 (2003)

    Article  MATH  Google Scholar 

  30. Wang, J., Ma, Z.D., Hulbert, G.: A distributed mechanical system simulation platform based on a “gluing algorithm”. J. Comput. Inf. Sci. Eng. 5, 71–76 (2005)

    Article  Google Scholar 

  31. Wang, J., Ma, Z.D., Hulbert, G.: Gluing for dynamic simulation of distributed mechanical systems. Adv. Comput. Multibody Syst. 5, 69–94 (2005)

    Google Scholar 

  32. Wells, D.R.: Multirate linear multistep methods for the solution of systems of ordinary differential equations. Ph.D. thesis, Champaign, IL, USA (1982)

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Authors and Affiliations

  1. The Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Nowowiejska 24, 00-665, Warsaw, Poland

    Paweł Tomulik & Janusz Fra̧czek

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  1. Paweł Tomulik
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  2. Janusz Fra̧czek
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Correspondence to Paweł Tomulik.

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Tomulik, P., Fra̧czek, J. Simulation of multibody systems with the use of coupling techniques: a case study. Multibody Syst Dyn 25, 145–165 (2011). https://doi.org/10.1007/s11044-010-9206-y

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