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A Gluing Algorithm for Network-Distributed Multibody Dynamics Simulation

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Abstract

The improved performance and capacity of networks has made thecombined processing power of workstation clusters a potentiallypromising avenue for solving computationally intensive problems acrosssuch distributed environments. Moreover, networks provide an idealplatform to employ heterogeneous hardware and software to solvemultibody dynamics problems. One fundamental difficulty with distributedsimulation is the requirement to couple and synchronize the distributedsimulations. This paper focuses on the algorithms necessary to coupletogether separately developed multibody dynamics modules so that theycan perform integrated system simulation. To identify a useful couplingstrategy, candidate numerical algorithms in the literature are reviewedbriefly – namely, stiff time integration, local parameterization,waveform relaxation, stabilized constraint and perturbation. Anunobtrusive algorithm that may well serve this `gluing' role ispresented. Results from numerical experiments are presented and theperformance of the gluing algorithm is investigated.

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References

  1. Mousseau, C.W., Laursen, T.A., Lidberg, M. and Taylor, R.L., 'Vehicle dynamics simulations with coupled multibody and finite element models', Finite Elements in Analysis and Design 31(4), 295–315 (1999).

    Google Scholar 

  2. Hulbert, G.M., Michelena, N., Ma, Z.-D., Tseng, F.-C., Fellini, R., Scheffer, C., Choi, K.K., Tang, J., Ogarevic, V. and Hardee, E., 'A case study for network-distributed collaborative design and simulation: Extended life optimization for M1 Abrams tank road arm', Mechanics of Structures and Machines 27(4), 1999, 423–451.

    Google Scholar 

  3. Enslow, Jr., P.H., 'What is a distributed data processing system?', IEEE Computer 11(1), 1978, 13–21.

    Google Scholar 

  4. Singhal, M. and Casavant, T.L., 'Distributed computing systems', IEEE Computer 24(8), 1991, 12–15.

    Google Scholar 

  5. OMG, Object Management Group, The Common Object Request Broker: Architecture and Specification, Revision 2.0, Framingham, MA, 1995.

  6. IONA Technologies, ORBIX 2, Distributed Object Technology: Programming Guide, Version 2.1, 1996.

  7. Orlandea, N., Chace, M.A. and Calahan, D.A., 'A sparsity-oriented approach to the dynamic analysis and design of mechanical systems - Part I', Journal of Engineering for Industry 99(3), 1977, 773–779.

    Google Scholar 

  8. Orlandea, N., Calahan, D.A. and Chace, M.A., 'A sparsity-oriented approach to the dynamic analysis and design of mechanical systems - Part II', Journal of Engineering for Industry 99(3), 1977, 780–784.

    Google Scholar 

  9. Cardona, A. and Géradin, M., 'Time integration of the equations of motion in mechanism analysis', Computers and Structures 33(3), 1989, 801–820.

    Google Scholar 

  10. Farhat, C., Crivelli, L. and Géradin, M., 'Implicit time integration of a class of constrained hybrid formulations - Part I: Spectral stability theory', Computer Methods in Applied Mechanics and Engineering 125, 1995, 71–107.

    Google Scholar 

  11. Chung, J. and Hulbert, G.M., 'A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-α method', Journal of Applied Mechanics 60, 1993, 371–375.

    Google Scholar 

  12. Brenan, K.E., Campbell, S.L. and Petzold, L.R., Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Elsevier, New York, 1989.

    Google Scholar 

  13. Petzold, L.R., 'A description of DASSL: A differential/algebraic system solver', in Transactions of the Tenth IMACS World Congress on Systems Simulation and Scientific Computation, International Association for Mathematics & Computers in Simulation, 1982, Vol. 1, 430–432.

    Google Scholar 

  14. Kurdila, A., Papastavridis, J.G. and Kamat, M.P., 'Role of Maggi's equations in computational methods for constrained multibody systems', Journal of Guidance, Control and Dynamics 13(1), 1990, 113–120.

    Google Scholar 

  15. Walton, Jr., W.C. and Steeves, E.C., 'A new matrix theorem and its application for establishing independent coordinates for complex dynamical systems with constraints', NASA Technical Report, NASA TR R-326, 1969, 1–27.

  16. Wehage, R.A. and Haug, E.J., 'Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems', Journal of Mechanical Design 104, 1982, 247–255.

    Google Scholar 

  17. Kim, S.S. and Vanderploeg, M.J., 'QR decomposition for state space representation of constrained mechanical dynamic systems', Journal of Mechanisms, Transmissions, and Automation in Design 108, 1986, 183–188.

    Google Scholar 

  18. Singh, R.P. and Likins, P.W., 'Singular value decomposition for constrained dynamical systems', Journal of Applied Mechanics 52, 1985, 943–948.

    Google Scholar 

  19. Kane, T.R. and Levinson, D.A., Dynamics: Theory and Applications, McGraw-Hill, New York, 1985.

    Google Scholar 

  20. Yen, J., 'Constrained equations of motion in multibody dynamics as ODEs on manifolds', SIAM Journal on Numerical Analysis 30(2), 1993, 553–568.

    Google Scholar 

  21. Yen, J., Haug, E.J. and Tak, T.O., 'Numerical methods for constrained equations of motion in mechanical system dynamics', Mechanics of Structures and Machines 19(1), 1991, 41–76.

    Google Scholar 

  22. Papastavridis, J.G., 'Maggi's equations of motion and the determination of constraint reactions', Journal of Guidance, Control and Dynamics 13(2), 1990, 213–220.

    Google Scholar 

  23. Lelarasmee, E., Ruehli, A.E. and Sangiovanni-Vincentelli, A.L., 'The waveform relaxation method for time-domain analysis of large scale integrated circuits', IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems CAD-13, 1982, 131–145.

    Google Scholar 

  24. Leimkuhler, B., 'Relaxation techniques in multibody dynamics', Transactions of the CSME 17(4A), 1993, 459–471.

    Google Scholar 

  25. Baumgarte, J., 'Stabilization of constraints and integrals of motion in dynamical systems', Computer Methods in Applied Mechanics and Engineering 1, 1972, 1–16.

    Google Scholar 

  26. Eich, E. and Hanke, M., 'Regularization methods for constrained mechanical multibody systems', Zeitschrift für Angewandte Mathematik und Mechanik 75(10), 1995, 761–773.

    Google Scholar 

  27. Lin, S.-T. and Hong, M.-C., 'Stabilization method for numerical integration of multibody mechanical systems', Journal of Mechanical Design 120, 1998, 565–572.

    Google Scholar 

  28. Gear, C.W., Leimkuhler, B.J. and Gupta, G.K., 'Automatic integration of Euler-Lagrange equations with constraints', Journal of Computational and Applied Mathematics 12, 1985, 77–90.

    Google Scholar 

  29. Park, K.C. and Chiou, J.C., 'Stabilization of computational procedures for constrained dynamical systems', Journal of Guidance, Control and Dynamics 11(4), 1988, 365–370.

    Google Scholar 

  30. Park, K.C., Chiou, J.C. and Downer, J.D., 'Explicit-implicit staggered procedure for multibody dynamics analysis', Journal of Guidance, Control and Dynamics 13(3), 1990, 562–570.

    Google Scholar 

  31. Chiou, J.C., Park, K.C. and Farhat, C., 'A natural partitioning scheme for parallel simulation of multibody systems', International Journal for Numerical Methods in Engineering 36, 1993, 945–967.

    Google Scholar 

  32. Bayo, E., Garcia De Jalon, J. and Serna, M.A., 'A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems', Computer Methods in Applied Mechanics and Engineering 71, 1988, 183–195.

    Google Scholar 

  33. Bayo, E. and Ledesma, R., 'Augmented Lagrangian and mass-orthogonal projection methods for constrained multibody dynamics', Nonlinear Dynamics 9, 1996, 113–130.

    Google Scholar 

  34. Shampine, L.F., 'Conservation laws and the numerical solution of ODEs', Computers and Mathematics with Applications 12B(5/6), 1986, 1287–1296.

    Google Scholar 

  35. Eich, E., 'Convergence results for a coordinate projection method applied to mechanical systems with algebraic constraints', SIAM Journal on Numerical Analysis 30(5), 1993, 1467–1482.

    Google Scholar 

  36. Yen, J., Petzold, L. and Raha, S., 'A time integration algorithm for flexible mechanism dynamics: The DAE α-method', Computer Methods in Applied Mechanics and Engineering 158, 1998, 341–355.

    Google Scholar 

  37. J. Yen, J. and Petzold, L.R., 'An efficient Newton-type iteration for the numerical solution of highly oscillatory constrained multibody dynamic systems', SIAM Journal on Scientific Computing 19(5), 1998, 1513–1534.

    Google Scholar 

  38. Pars, L.A., A Treatise on Analytical Dynamics, Heinemann, London, 1965.

    Google Scholar 

  39. Udwadia, F.E. and Kalaba, R.E., 'A new perspective on constrained motion', Proceedings of the Royal Society of London Series A - Mathematical, Physical and Engineering Sciences 439, 1992, 407–410.

    Google Scholar 

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Tseng, FC., Hulbert, G.M. A Gluing Algorithm for Network-Distributed Multibody Dynamics Simulation. Multibody System Dynamics 6, 377–396 (2001). https://doi.org/10.1023/A:1012279120194

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