Skip to main content

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


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.

This is a preview of subscription content, access via your institution.


  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. 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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  7. Schiehlen, W. (ed.): Multibody Systems Handbook. Springer-Verlag, Dordrecht (1990)

    MATH  Google Scholar 

  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. Kortum, W., Sharp, R.S.: Multibody Computer Codes in Vehicle System Dynamics. Swets and Zeitlinger Publishers (1993)

  10. Anderson, R.J.: Iltis Benchmark Proposal. Department of Mechanical Engineering, Queen's University, Kingston, Ontario, Canada (1990)

    Google Scholar 

  11. Hiller, M., Frik, S.: Road vehicle benchmark 2 – five-link suspension. Vehicle Syst. Dyn. 22(suppl.issue), 254–262 (1993)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  14. Schiehlen, W.: Prospects of the German multibody system research-project on vehicle dynamics simulation. Vehicle Syst. Dyn. 20, 537–550 (1992)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  18. von Schwerin, R.: Multibody System Simulation: Numerical Methods, Algorithms and Software. Springer-Verlag (1999)

  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. 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)

  21. Simeon, B.: On the numerical solution of a wheel suspension benchmark problem. J Comput Appl. Math. 66(1–2), 443–456 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  22. Iwnicki, S.: Manchester benchmarks for rail vehicle simulation. Vehicle Syst. Dyn. 30(3–4), 295–313 (1998)

    Article  Google Scholar 

  23. Iwnicki, S.: The Manchester benchmarks for rail vehicle simulation. Vehicle Syst. Dyn. 31, 1 (1999)

    Article  Google Scholar 

  24. Rail Technology Unit, Manchester Metropolitan University, The Manchester Benchmarks for Rail Vehicle Simulation. (1998)

  25. Bayo, E., Avello, A.: Singularity-free augmented lagrangian algorithms for constrained multibody dynamics. Nonlinear Dyn. 5(2), 209–231 (1994)

    Google Scholar 

  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. Simeon, B.: Numerical analysis of flexible multibody systems. Multibody Syst. Dyn. 6(4), 305–325 (2001)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  33. MSC Software Corporation: ADAMS/Solver, (2004)

  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)

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to M. González.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

González, M., Dopico, D., Lugrís, U. et al. A benchmarking system for MBS simulation software: Problem standardization and performance measurement. Multibody Syst Dyn 16, 179–190 (2006).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Multibody dynamics
  • Simulation
  • Benchmarking
  • Efficiency
  • Performance
  • Accuracy