On an implementation of the Hilber-Hughes-Taylor method in the context of index 3 differential-algebraic equations of multibody dynamics (DETC2005-85096)

Journal of Computational and Nonlinear Dynamics

Volumn 2, Issue 1, 2007, Pages 73-85

  Negrut, Dan ^a   Rampalli, Rajiv ^b   Ottarsson, Gisli ^b   Sajdak, Anthony ^b  

^a University of Wisconsin Madison   (United States)

^b MSC SOFTWARE CORPORATION   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; JACOBIAN MATRICES;

FLEXIBLE BODIES; HILBER-HUGHES-TAYLOR IMPLICIT METHOD; INTEGRATION STEP-SIZE CONTROL; MULTIBODY DYNAMICS;

COMPUTATIONAL MECHANICS;

EID: 34248386510     PISSN: 15551423     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2389231     Document Type: Article

References (39)

1. Hilber, H. M., Hughes, T. J. R., and Taylor, R. L., 1977, "Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics," Earthquake Eng. Struct. Dyn., 5, pp. 283-292.
2. Newmark, N. M., 1959, "A method of computation for structural dynamics," J. Engrg. Mech. Div., 85, pp. 67-94.
3. Ascher, U. M., and Petzold, L. R., 1998, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, Philadelphia, PA.
4. Hughes, T. J. R., 1987, Finite Element Method - Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ.
5. Cardona, A., and Geradin, M., 1994, "Numerical Integration of Second Order Differential-Algebraic Systems in Flexible Mechanics Dynamics," in Computer-Aided Analysis of Rigid and Flexible Mechanical Systems, M. F. O. S. Pereira and J. A. C. Ambrosio, eds., Kluwer Academic, Dordrecht.
6. Shabana, A. A., 1994, Computational Dynamics, Wiley, New York.
7. Pars, L. A., 1965, A Treatise on Analytical Dynamics, Wiley, New York.
8. Haug, E. J. 1989, Computer-Aided Kinematics and Dynamics of Mechanical Systems, Prentice-Hall, Englewood Cliffs, NJ.
9. Brenan, K. E., Campbell, S. L., and Petzold, L. R., 1989, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, New York.
10. Le Vey, G., 1994, "Differential Algebraic Equations - A New Look at the Index," Technical report, Institut de Recherche en Informatique et Systemes Aleatoires.
11. Kunkel, P., and Mehrmann, V., 2006, Differential Algebraic Equations. Analysis and Numerical Solution, European Math. Soc. Textbooks in Mathematics, Zurich.
12. Petzold, L. R., 1982, "Differential-Algebraic Equations are not ODE's," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput., 3(3), pp. 367-384.
13. Bauchau, O. A., Bottasso, C. L., and Trainelli, L., 2003, "Robust Integration Schemes for Flexible Multibody Systems," Comput. Methods Appl. Mech. Eng., 192, pp. 395-420.
14. Eich-Sollner, E., and Fuhrer, C., 1998, Numerical Methods in Multibody Dynamics, Teubner-Verlag, Stuttgart.
15. Anderson, K. S., and Oghbaei, M., 2005, "A Dynamics Simulation of Multibody Systems Using a New State-Time Methodology," Multibody Syst. Dyn., 14(1), pp. 61-80.
16. Hairer, E., and Wanner, G., 1991, Solving Ordinary Differential Equations, Vol. II of Computational Mathematics, Springer-Verlag, New York.
17. Lubich, C., Nowak, U., Pohle, U., and Engstler, C., 1995, "MEXX - Numerical Software for the Integration of Constrained Mechanical Multibody Systems," Mech. Struct. Mach., 23, pp. 473-495.
18. Potra, F. A., 1993, "Implementation of Linear Multistep Methods for Solving Constrained Equations of Motion," SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 30(3), pp. 774-789.
19. Yen, J., Petzold, L., and Raha, S., 1996, "A Time Integration Algorithm for Flexible Mechanism Dynamics: The DAE α-Method," Technical report TR96-024, Dept. of Comp. Sci., University of Minnesota.
20. Garcia de Jalon, J., and Bayo, E., 1994, Kinematic and Dynamic Simulation of Multibody Systems. The Real-Time Challenge, Springer-Verlag, Berlin.
21. Cuadrado, J., Dopico, D., Naya, M. N., and Gonzalez, M., 2004, "Penalty, Semi-recursive and Hybrid Methods for MBS Real-Time Dynamics in the Context of Structural Integrators," Multibody Syst. Dyn., 12, pp. 117-132.
22. Baumgarte, J., 1972, "Stabilization of Constraints and Integrals of Motion in Dynamical Systems," Comput. Methods Appl. Mech. Eng., 1, pp. 1-16.
23. Owren, B., and Simonsen, H., 1995, "Alternative Integration Methods for Problems in Structural Dynamics," Comput. Methods Appl. Mech. Eng., 122, pp. 1-10.
24. Jay, L. O., 1998, "Structure Preservation for Constrained Dynamics With Super Partitioned Additive Runge-Kutta Methods," SIAM J. Sci. Comput. (USA), 20, pp. 416-446.
25. Schaub, M., and Simeon, B., 2002, "Automatic h-Scaling for the Efficient Time Integration of Stiff Mechanical Systems," Multibody Syst. Dyn., 8, pp. 329-345.
26. Cardona, A., and Geradin, M., 1989, "Time Integration of the Equation of Motion in Mechanical Analysis," Comput. Struct., 33, pp. 881-820.
27. Lötstedt, C., and Petzold, L., 1986, "Numerical Solution of Nonlinear Differential Equations With Algebraic Constraints I: Convergence Results for Backward Differentiation Formulas," Math. Comput., 174, pp. 491-516.
28. Brenan, K., and Engquist, B. E., 1988, "Backward Differentiation Approximations of Nonlinear Differential/Algebraic Systems," Math. Comput., 51(184), pp.659-676.
29. Jay, L. O., and Negrut, D., "On an Extension of the HHT Method for Index 3 Differential Algebraic Equations," Electron. Trans. Numer. Anal., submitted.
30. Dennis, J., and Schnabel, R., 1983, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ.
31. MSCsoftware, 2005, ADAMS User Manual. Also available online at http://www.mscsoftware.com
32. Gear, C. W., 1971, Numerical Initial Value Problems of Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ.
33. Gavrea, B., Negrut, D., and Potra, F., 2005, "The Newmark Integration Method for Simulation of Multibody Systems: Analytical Considerations (IMECE 2005-81770)," in Proceedings of the International Mechanical Engineering Congress and Exposition, Orlando, FL, ASME, New York.
34. Zienkiewicz, O. C., and Xie, Y. M., 1991, "A Simple Error Estimator and Adaptive Time-Stepping Procedure for Dynamic Analysis," Earthquake Eng. Struct. Dyn., 20, pp. 871-887.
35. Bruls, O., Duysinx, P., and Golinval, J., 2005, "A Unified Finite Element Framework for the Dynamic Analysis of Controlled Flexible Mechanisms," in Proceeding of Multibody Dynamics ECCOMAS Thematic Conference, June 21-24, Madrid, Spain.
36. Atkinson, K. E., 1989, An Introduction to Numerical Analysis, 2nd ed., Wiley, New York.
37. Gear, C. W., Gupta, G., and Leimkuhler, B., 1985, "Automatic Integration of the Euler-Lagrange Equations With Constraints," J. Comput. Appl. Math., 12, pp. 77-90.
38. Craig, R. R., and Bampton, M. C. C., 1968, "Coupling of Substructures for Dynamics Analyses," AIAA J., 6(7), pp. 1313-1319.
39. Chung, J., and Hulbert, G. M., 1993, "A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method," ASME J. Appl. Mech., 60(2), pp. 371-375.