GPU-Based Parallel Computing for the Simulation of Complex Multibody Systems with Unilateral and Bilateral Constraints: An Overview

  • Alessandro Tasora
  • Dan Negrut
  • Mihai Anitescu
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 23)


This work reports on advances in large-scale multibody dynamics simulation facilitated by the use of the Graphics Processing Unit (GPU). A description of the GPU execution model along with its memory spaces is provided to illustrate its potential parallel scientific computing. The equations of motion associated with the dynamics of large system of rigid bodies are introduced and a solution method is presented. The solution method is designed to map well on the parallel hardware, which is demonstrated by an order of magnitude reductions in simulation time for large systems that concern the dynamics of granular material. One of the salient attributes of the solution method is its linear scaling with the dimension of the problem. This is due to efficient algorithms that handle in linear time both the collision detection and the solution of the nonlinear complementarity problem associated with the proposed approach. The current implementation supports the simulation of systems with more than one million bodies on commodity desktops. Efforts are under way to extend this number to hundreds of millions of bodies on small affordable clusters.


Graphic Processing Unit Collision Detection Global Memory Frictional Contact Multibody Dynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1].
    Pfeiffer F, Glocker C (1996) Multibody dynamics with unilateral contacts. Wiley, SingaporezbMATHCrossRefGoogle Scholar
  2. [2].
    Anitescu M (2006) Optimization-based simulation of nonsmooth dynamics. Math Programming 105(1): 113–143zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3].
    Anitescu M, Hart GD (2004) A constraint-stabilized time-stepping approach for rigid multibody dynamics with joints, contact and friction. Int J Numer Methods Eng 60(14): 2335–2371zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4].
    Anitescu M, Potra FA, Stewart DE (1999) Time-stepping for three-dimensional rigid body dynamics. Comput Methods Appl Mech Eng 177(3–4): 183–197zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5].
    Lotstedt P (1982) Mechanical systems of rigid bodies subject to unilateral constraints. SIAM J Appl Math 42(2): 281–296CrossRefMathSciNetGoogle Scholar
  6. [6].
    Marques M (1993) Differential inclusions in nonsmooth mechanical problems: shocks and dry friction. Birkhäuser, Boston, MAzbMATHGoogle Scholar
  7. [7].
    Moreau JJ (1983) Standard inelastic shocks and the dynamics of unilateral constraints: CISM Courses and Lectures. In: Piero GD, Macieri F (eds) Unilateral problems in structural analysis. Wiley, New York, p 173–221Google Scholar
  8. [8].
    Pang JS, Kumar V, Song P (2005) Convergence of time-stepping method for initial and boundary-value frictional compliant contact problems. SIAM J Numer Anal 43: 2200zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9].
    Pang, JS, Trinkle JC (1996) Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with Coulomb friction. Math Programming 73(2): 199–226.CrossRefMathSciNetGoogle Scholar
  10. [10].
    Song P, Kraus P, Kumar V, Dupont P (2001) Analysis of rigid-body dynamic models for simulation of systems with frictional contacts. J Appl Mech 68(1): 118–128zbMATHCrossRefGoogle Scholar
  11. [11].
    Glocker C, Pfeiffer F (1995) Multiple impacts with friction in rigid multibody systems. Nonlinear Dyn 7(4): 471–497CrossRefMathSciNetGoogle Scholar
  12. [12].
    Manferdelli JL (2007) The many-core inflection point for mass market computer systems. CTWatch Quart 3(1)Google Scholar
  13. [13].
    Negrut D (2008) High performance computing for engineering applications, Course Notes ME964 (September 9 Lecture):, University of Wisconsin
  14. [14].
    NVIDIA (2009) Compute unified device architecture programming guide 2.3:
  15. [15].
    Stewart DE, Trinkle JC (1996) An implicit time-stepping scheme for rigid-body dynamics with inelastic collisions and Coulomb friction. Int J Numer Methods Eng 39: 2673–2691zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16].
    Moreau J (1988) Unilateral contact and dry friction in finite freedom dynamics. Nonsmooth Mech Appl, 302: 1–82MathSciNetGoogle Scholar
  17. [17].
    Pfeiffer F, Foerg M, Ulbrich H (2006) Numerical aspects of non-smooth multibody dynamics. Comput Methods Appl Mech Eng 195(50–51): 6891–6908zbMATHCrossRefMathSciNetGoogle Scholar
  18. [18].
    Stewart DE (2000) Rigid-body dynamics with friction and impact. SIAM Rev 42(1): 3–39zbMATHCrossRefMathSciNetGoogle Scholar
  19. [19].
    Stewart DE (1998) Convergence of a time stepping scheme for rigid body dynamics and resolution of Painlevé’s problem. Arch Ration Mech Anal 145(3): 215–260zbMATHCrossRefMathSciNetGoogle Scholar
  20. [20].
    Tasora A, Anitescu M (2008) A fast NCP solver for large rigid-body problems with contacts, friction, and joints. Multibody dynamics: computational methods and applications. Springer, Berlin, p. 45Google Scholar
  21. [21].
    Anitescu M, Tasora A (2010) An iterative approach for cone complementarity problems for nonsmooth dynamics. Comput Optim Appl 47(2): 207–235zbMATHCrossRefGoogle Scholar
  22. [22].
    Harris M, Shubhabrata S, Owens JD (2008) Parallel Prefix Sum (Scan) with CUDA. In: Nguyen H (ed) GPU Gems 3, Addison-Wesley, New York, p. 851–876Google Scholar
  23. [23].
    Heyn T, Mazhar H, Negrut D (2009) On the simulation of tracked vehicles operating on granular terrain: a parallel multibody dynamics aproach (to be submitted). Multibody system dynamicsGoogle Scholar
  24. [24].
    Heyn T (2009) Simulation of tracked vehicles on granular terrain leveraging GPU computing. M.S. Thesis, in Mechanical Engineering, University of Wisconsin-Madison, MadisonGoogle Scholar
  25. [25].
    Mazhar H (2009) Million body simulation.
  26. [26].
    Gougar H, Ougouag A, Terry W (2004) Advanced core design and fuel management for pebble-bed reactors. Idaho National Engineering and Environmental Laboratory, INEEL/EXT-04-02245Google Scholar
  27. [27].
    Kadak A, Bazant M (2004) Pebble flow experiments for pebble bed reactors, 2nd International Topical Meeting on High Temperature Reactor Technology, Beijing, China, 22–24 Sept 2004Google Scholar
  28. [28].
    Tasora A, Anitescu M (2010) A convex complementarity approach for simulating large granular flows. J Comput Nonlinear Dynam 5(3): 031004CrossRefGoogle Scholar
  29. [29].
    Ougouag A, Ortensi J, Hiruta H (2009) Analysis of an earthquake-initiated-transient in a PBR. Tech. Rep. INL/CON-08-14876, Idaho National Laboratory (INL)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.University of ParmaParmaItaly
  2. 2.University of WisconsinMadisonUSA
  3. 3.Argonne National LaboratoryArgonneUSA

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