A GPU-based implementation of a cone convex complementarity approach for simulating rigid body dynamics with frictional contact

ASME International Mechanical Engineering Congress and Exposition, Proceedings

Volumn 11, Issue , 2009, Pages 107-117

  Tasora, Alessandro ^a   Negrut, Dan ^b   Anitescu, Mihai ^c  

^a UNIVERSITY OF PARMA   (Italy)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

^c ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMOBILE BODIES; FRICTION; GRANULAR MATERIALS; ITERATIVE METHODS; PROGRAM PROCESSORS; RIGID STRUCTURES;

COMPLEMENTARITY PROBLEMS; CONTACT DYNAMICS; FIXED-POINT ITERATIONS; FRICTIONAL CONTACT; GAUSS-SEIDEL; ITERATION ALGORITHMS; LARGE SYSTEM; NOVEL METHODS; RIGID BODY; RIGIDBODY DYNAMICS;

GRAPHICS PROCESSING UNIT;

EID: 69949113528     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/IMECE2008-66766     Document Type: Conference Paper

References (37)

1. J. Madsen, N. Pechdimaljian, and D. Negrut. Penalty versus complementarity-based frictional contact of rigid bodies: A CPU time comparison. Technical Report TR-2007-2105, Simulation-Based Engineering Lab, University of Wisconsin, Madison, 2007.
2. M. Anitescu and A. Tasora. An iterative approach for cone complementarity problems for nonsmooth dynamics. Computational Optimization and Applications, 2008, in press.
3. N. Kikuchi and J.T. Oden. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM, Philadelphia, PA, 1998.
4. Peter Wriggers. Computational Contact Mechanics. Springer-Verlag, Berlin, Heidelberg, second edition, 2006.
5. Bruce R. Donald and Dinesh K. Pai. On the motion of compliantly connected rigid bodies in contact: a system for analyzing designs for assembly. In Proceedings of the Conf on Robotics and Automation, pages 1756-1762. IEEE, 1990.
6. Peng Song, P. Kraus, Vijay Kumar, and P. Dupont. Analysis of rigid-body dynamic models for simulation of systems with frictional contacts. Journal of Applied Mechanics, 68(1):118-128, 2001. (Pubitemid 33716359)
7. Peng Song, Jong-Shi Pang, and Vijay Kumar. A semi-implicit time-stepping model for frictional compliant contact problems. International Journal of Numerical Methods in Engineering, 60(13):267-279, 2004.
8. Jong-Shi Pang, Vijay Kumar, and Peng Song. Convergence of time-stepping method for initial and boundary-value frictional compliant contact problems. SIAM J. Numer. Anal., 43(5):2200-2226, 2005.
9. Jong-Shi Pang and David Stewart. Differential variational inequalities. Mathematical Programming, 113(2):345-424, 2008.
10. Jean J. Moreau. Standard inelastic shocks and the dynamics of unilateral constraints. In G. Del Piero and F. Macieri, editors, Unilateral Problems in Structural Analysis, pages 173-221, New York, 1983. CISM Courses and Lectures no. 288, Springer-Verlag.
11. P. Lotstedt. Mechanical systems of rigid bodies subject to unilateral constraints. SIAM Journal of Applied Mathematics, 42(2):281-296, 1982. (Pubitemid 12521692)
12. M. D. P.Monteiro Marques. Differential Inclusions in Non-smooth Mechanical Problems: Shocks and Dry Friction, volume 9 of Progress in Nonlinear Differential Equations and Their Applications. Birkhäuser Verlag, Basel, Boston, Berlin, 1993.
13. David Baraff. Issues in computing contact forces for non-penetrating rigid bodies. Algorithmica, 10:292-352, 1993.
14. Jong-Shi Pang and Jeffrey C. Trinkle. Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with Coulomb friction. Math. Program., 73(2): 199-226, 1996.
15. Jeffrey Trinkle, Jong-Shi Pang, Sandra Sudarsky, and Grace Lo. On dynamic multi-rigid-body contact problems with Coulomb friction. Zeitschrift fur angewandte Mathematik und Mechanik, 77:267-279, 1997. (Pubitemid 127780388)
16. David E. Stewart and Jeffrey C. Trinkle. An implicit time-stepping scheme for rigid-body dynamics with inelastic collisions and Coulomb friction. International Journal for Numerical Methods in Engineering, 39:2673-2691, 1996. (Pubitemid 126648043)
17. Mihai Anitescu and Florian A. Potra. Formulating dynamic multi-rigid-body contact problems with friction as solvable linear complementarity problems. Nonlinear Dynamics, 14:231-247, 1997.
18. Mihai Anitescu, Florian A. Potra, and David Stewart. Time-stepping for three-dimensional rigid-body dynamics. Computer Methods in Applied Mechanics and Engineering, 177:183-197, 1999. (Pubitemid 30510495)
19. David E. Stewart. Rigid-body dynamics with friction and impact. SIAM Review, 42(1):3-39, 2000.
20. Richard W. Cottle and George B. Dantzig. Complementary pivot theory of mathematical programming. Linear Algebra and Its Applications, 1:103-125, 1968.
21. [21 ] David Baraff. Fast contact force computation for nonpenetrating rigid bodies. In Computer Graphics (Proceedings of SIGGRAPH), pages 23-34, 1994.
22. Mihai Anitescu and Gary D. Hart. A fixed-point iteration approach for multibody dynamics with contact and friction. Mathematical Programming, Series B, 101(1):3-32, 2004.
23. Alessandro Tasora, E. Manconi, and M. Silvestri. Un nuovo metodo del simplesso per il problema di complementarit lineare mista in sistemi multibody con vincoli unilateri. In Proceedings of AIMETA 05, Firenze, Italy, 2005.
24. Mihai Anitescu. Optimization-based simulation of non-smooth rigid multibody dynamics. Math. Program., 105(1):113-143, 2006.
25. NVIDIA. CUDA Programming Guide. Available online at http://developer. download.nvidia.com/compute/cuda/1-1/NVIDIA-CUDA-Programming-Guide-1.1.pdf, 2007.
26. A. A. Shabana. Dynamics of Multibody Systems. Cambridge University Press, third edition, 2005.
27. A. Tasora. High performance complementarity solver for non-smooth dynamics. In C. L. Bottasso, P. Masarati, and L. Trainelli, editors, Proceedings of the ECCOMAS Multi-body Dynamics Conference, Milano, Italy, 2007.
28. Young J. Kim, Ming C. Lin, and Dinesh Manocha. Deep: Dual-space expansion for estimating penetration depth between convex polytopes. In Proceedings of the 2002 International Conference on Robotics and Automation, volume 1, pages 921-926. Institute for Electrical and Electronics Engineering, 2002.
29. Mihai Anitescu, James F. Cremer, and Florian A. Potra. Formulating 3d contact dynamics problems. Mechanics of Structures and Machines, 24(4):405-437, 1996.
30. Mihai Anitescu and Gary D. Hart. A constraint-stabilized time-stepping approach for rigid multibody dynamics with joints, contact and friction. International Journal for Numerical Methods in Engineering, 60(14):2335-2371, 2004. (Pubitemid 39039874)
31. G. D. Hart. A constraint-stabilized time-stepping approach for piecewise smooth multibody dynamics. Ph.d in mathematics, University of Pittsburgh, 2007.
32. J. J. Moreau. Unilateral contact and dry friction in finite freedom dynamics. In J. J. Moreau and P. D. Panagiotopoulos, editors, Nonsmooth Mechanics and Applications, pages 1-82, Berlin, 1988. Springer-Verlag.
33. Dimitri P Bertsekas. Nonlinear Programming. Athena Scientific, Belmont, MA, 1995.
34. J. S. Pang and D. E. Stewart. Differential variational inequalities. Mathematical Programming, 113:1-80, 2008.
35. David E. Stewart. Convergence of a time-stepping scheme for rigid body dynamics and resolution of Painleve's problems. Archive Rational Mechanics and Analysis, 145(3):215-260, 1998.
36. C. H. Rycroft, G. S. Grest, J. W. Landry, and M. Z. Bazant. Analysis of granular flow in a pebble-bed nuclear reactor. Physical Review E, 74, 021306, 2006.
37. Physics Simulation Forum. Bullet Physics Library. Available online at http://www.bulletphysics.com/Bullet/wordpress/bullet, 2008.