Multibody System Dynamics

, Volume 16, Issue 2, pp 179–190 | Cite as

A benchmarking system for MBS simulation software: Problem standardization and performance measurement

  • M. GonzálezEmail author
  • D. Dopico
  • U. Lugrís
  • J. Cuadrado


Despite the importance given to the computational efficiency of multibody system (MBS) simulation tools, there is a lack of standard benchmarks to measure the performance of these kinds of software applications. Benchmarking is done on an individual basis: different sets of problems are used, and the procedures and conditions considered to measure computational efficiency are also different. In this scenario, it becomes almost impossible to compare the performance of the different available simulation methods in an objective and quantitative way.

This work proposes a benchmarking system for MBS simulation tools. The structure of the benchmark problem collection is defined, and a group of five problems involving rigid bodies is proposed. For these problems, documentation and validated reference solutions in standard formats have been generated, and a procedure to measure the computational efficiency of a given simulation software is described.

Finally, the benchmarking system has been applied to evaluate the performance of two different simulation tools: ADAMS/Solver, a popular general-purpose commercial MBS simulation tool, and a custom Fortran code implementation of an Index-3 augmented Lagrangian formulation with projections combined with the implicit single-step trapezoidal rule as integration scheme. Results show that the proposed problems are able to reach the limits of the tested simulation methods, and therefore they can be considered good benchmark problems.


Multibody dynamics Simulation Benchmarking Efficiency Performance Accuracy 


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  1. 1.
    Haug, E.: High speed multibody dynamic simulation and its impact on man-machine systems. In: Schiehlen, W. (ed.) Advanced Multibody System Dynamics: Simulation and Software Tools, pp. 1–18. Kluwer Academic Publishers, Dordrecht, Netherlands (1993)Google Scholar
  2. 2.
    García de Jalón, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems – The Real-Time Challenge. Springer-Verlag, New York (1994)Google Scholar
  3. 3.
    Cuadrado, J., Cardenal, J., Morer, P.: Modeling and solution methods for efficient real-time simulation of multibody dynamics. Multibody Syst. Dyn. 1(3), 259–280 (1997)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Bae, D.S., Lee, J.K., Cho, H.J., Yae, H.: An explicit integration method for realtime simulation of multibody vehicle models. Comput Methods Appl. Mechanics Eng. 187(1–2), 337–350 (2000)CrossRefzbMATHGoogle Scholar
  5. 5.
    García Orden, J.C., Goicolea, J.M.: Conserving properties in constrained dynamics of flexible multibody systems. Multibody Syst. Dyn. 4(3), 225–244 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    Anderson, K.S., Critchley, J.H., Improved ‘order-N’ performance algorithm for the simulation of constrained multi-rigid-body dynamic systems. Multibody Syst. Dyn. 9(2), 185–212 (2003)CrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    Schiehlen, W. (ed.): Multibody Systems Handbook. Springer-Verlag, Dordrecht (1990)zbMATHGoogle Scholar
  8. 8.
    Kortum, W., Sharp, R.S.: A report on the state-of-affairs on application of multibody computer codes to vehicle system dynamics. Vehicle Syst. Dyn. 20(3–4), 177–184 (1991)Google Scholar
  9. 9.
    Kortum, W., Sharp, R.S.: Multibody Computer Codes in Vehicle System Dynamics. Swets and Zeitlinger Publishers (1993)Google Scholar
  10. 10.
    Anderson, R.J.: Iltis Benchmark Proposal. Department of Mechanical Engineering, Queen's University, Kingston, Ontario, Canada (1990)Google Scholar
  11. 11.
    Hiller, M., Frik, S.: Road vehicle benchmark 2 – five-link suspension. Vehicle Syst. Dyn. 22(suppl.issue), 254–262 (1993)CrossRefGoogle Scholar
  12. 12.
    Quirt, R.C., Anderson, R.J.: Comparisons of a linear with a nonlinear multibody simulation of an off-road vehicle. Vehicle Syst. Dyn. 20, 490–503 (1992)CrossRefGoogle Scholar
  13. 13.
    Langlois, R.G., Hanna, D.M., Anderson, R.J.: Implementing preview control on an off-road vehicle with active suspension. Vehicle Syst. Dyn. 20, 340–353 (1992)CrossRefGoogle Scholar
  14. 14.
    Schiehlen, W.: Prospects of the German multibody system research-project on vehicle dynamics simulation. Vehicle Syst. Dyn. 20, 537–550 (1992)CrossRefGoogle Scholar
  15. 15.
    Cuadrado, J., Cardenal, J., Morer, P., Bayo, E.: Intelligent simulation of multibody dynamics: space-state and descriptor methods in sequential and parallel computing environments. Multibody Syst. Dyn. 4(1), 55–73 (2000)CrossRefzbMATHGoogle Scholar
  16. 16.
    Schwab, A.L., Meijaard, J.P.: Dynamics of flexible multibody systems having rolling contact: application of the wheel element to the dynamics of road vehicles. Vehicle Syst. Dyn. 33, 338–349 (1999)Google Scholar
  17. 17.
    Schumann, A.R., Anderson, R.J.: Optimal control of an active anti roll suspension for an off-road utility vehicle using interconnected hydragas suspension units. Vehicle Syst. Dyn. 37, 145–156 (2002)CrossRefGoogle Scholar
  18. 18.
    von Schwerin, R.: Multibody System Simulation: Numerical Methods, Algorithms and Software. Springer-Verlag (1999)Google Scholar
  19. 19.
    Minaker, B., Anderson, R.J.: Modelling the dynamics of a vehicle with active geometry suspension. Vehicle Syst. Dyn. 33, 716–727 (1999)Google Scholar
  20. 20.
    Rodríguez, J.I.: Análisis Eficiente de Mecanismos 3D con Métodos Topológicos y Tecnología de Componentes en Internet. Ph.D. Dissertation, Universidad de Navarra, San Sebastián, Spain (2000)Google Scholar
  21. 21.
    Simeon, B.: On the numerical solution of a wheel suspension benchmark problem. J Comput Appl. Math. 66(1–2), 443–456 (1996)CrossRefMathSciNetzbMATHGoogle Scholar
  22. 22.
    Iwnicki, S.: Manchester benchmarks for rail vehicle simulation. Vehicle Syst. Dyn. 30(3–4), 295–313 (1998)CrossRefGoogle Scholar
  23. 23.
    Iwnicki, S.: The Manchester benchmarks for rail vehicle simulation. Vehicle Syst. Dyn. 31, 1 (1999)CrossRefGoogle Scholar
  24. 24.
    Rail Technology Unit, Manchester Metropolitan University, The Manchester Benchmarks for Rail Vehicle Simulation. (1998)
  25. 25.
    Bayo, E., Avello, A.: Singularity-free augmented lagrangian algorithms for constrained multibody dynamics. Nonlinear Dyn. 5(2), 209–231 (1994)Google Scholar
  26. 26.
    Jahnke, M., Popp, K., Dirr, B.: Approximate analysis of flexible parts in multibody systems using the finite element method. In: Schiehlen, W. (ed.) Advanced multibody system dynamics: Simulation and software tools, pp. 237–256. Kluwer Academic Publishers, Dordrecht, Netherlands (1993)Google Scholar
  27. 27.
    Simeon, B.: Numerical analysis of flexible multibody systems. Multibody Syst. Dyn. 6(4), 305–325 (2001)CrossRefzbMATHGoogle Scholar
  28. 28.
    Cuadrado, J., Gutierrez, R., Naya, M.A., Morer, P.: A comparison in terms of accuracy and efficiency between a MBS dynamic formulation with stress analysis and a non-linear FEA code. Int. J. Numerical Methods Eng. 51(9), 1033–1052 (2001)CrossRefzbMATHGoogle Scholar
  29. 29.
    Schaub, M., Simeon, B.: Automatic H-scaling for the efficient time integration of stiff mechanical systems. Multibody Syst. Dyn. 8(3), 329–345 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  30. 30.
    Bauchau, O.A., Theron, N.J.: Energy decaying scheme for non-linear beam models. Comput Methods Appl Mechanics Eng. 134(1–2), 37–56 (1996)CrossRefMathSciNetzbMATHGoogle Scholar
  31. 31.
    Bauchau, O.A., Bottasso, C.L.: On the design of energy preserving and decaying schemes for flexible, nonlinear multi-body systems. Comput. Methods Appl. Mechanics Eng. 169(1–2), 61–79 (1999)CrossRefMathSciNetzbMATHGoogle Scholar
  32. 32.
    Bottasso, C.L., Borri, M., Trainelli, L.: Integration of elastic multibody systems by invariant conserving/dissipating algorithms. II. Numerical schemes and applications. Comput. Methods. Appl. Mechanics Eng. 190(29–30), 3701–3733 (2001)CrossRefMathSciNetGoogle Scholar
  33. 33.
    MSC Software Corporation: ADAMS/Solver, (2004)
  34. 34.
    Gonzalez, M., Dopico, D., Cuadrado, J.: A new software environment for MBS simulation based on XML and integrated With CAD/CAE packages. Eleventh World Congress in Mechanism and Machine Science, Proceedings, vol. 2, pp. 642–646. Tianjin, China (2004)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • M. González
    • 1
    Email author
  • D. Dopico
    • 1
  • U. Lugrís
    • 1
  • J. Cuadrado
    • 1
  1. 1.Escuela Politécnica SuperiorUniversity of La CoruñaFerrolSpain

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