A self-stabilized algorithm for enforcing constraints in multibody systems

International Journal of Solids and Structures

Volumn 40, Issue 13-14, 2003, Pages 3253-3271

  Bauchau, Olivier A ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

Constraint stabilization; Multibody dynamics; Nonlinear constraints

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; ELASTICITY; LAGRANGE MULTIPLIERS; NONLINEAR SYSTEMS;

MULTIBODY SYSTEMS;

STRUCTURAL ANALYSIS;

ALGORITHM;

EID: 0037983616     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(03)00159-8     Document Type: Article

References (50)

1. Agrawal O.P. Saigal S. Dynamic analysis of multi-body systems using tangent coordinates Computers and Structures 31 1989 349 355
2. Amirouche F.M.L. Computational Methods in Multibody Dynamics 1992 Prentice-Hall Englewood Cliffs, NJ
3. Amirouche F.M.L. Jia T. Ider S.K. A recursive householder transformation for complex dynamical systems with constraints Journal of Applied Mechanics 55 1988 729 734
4. Angeles J. Spatial Kinematic Chains 1982 Springer-Verlag Berlin
5. Bauchau O.A. Computational schemes for flexible, nonlinear multi-body systems Multibody System Dynamics 2 1998 169 225
6. Bauchau O.A. Bottasso C.L. On the design of energy preserving and decaying schemes for flexible, nonlinear multi-body systems Computer Methods in Applied Mechanics and Engineering 169 1999 61 79
7. Bauchau O.A. Theron N.J. Energy decaying schemes for nonlinear elastic multi-body systems Computers and Structures 59 1996 317 331
8. Bauchau, O.A., Trainelli, L., in press. The vectorial parameterization of rotation. Nonlinear Dynamics
9. Bauchau O.A. Damilano G. Theron N.J. Numerical integration of nonlinear elastic multi-body systems International Journal for Numerical Methods in Engineering 38 1995 2727 2751
10. Bauchau O.A. Choi J.Y. Bottasso C.L. Time integrators for shells in multibody dynamics International Journal of Computers and Structures 80 2002 871 889
11. Bauchau O.A. Bottasso C.L. Trainelli L. Robust integration schemes for flexible multibody systems Computer Methods in Applied Mechanics and Engineering 192 2003 395 420
12. Baumgarte J. Stabilization of constraints and integrals of motion in dynamic systems Computer Methods in Applied Mechanics and Engineering 1 1972 1 16
13. Bayo E. Ledesma R. Augmented Lagrangian and mass-orthogonal projection methods for constrained multibody dynamics Nonlinear Dynamics 9 1996 113 130
14. Bayo E. Garcia de Jalon J. 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
15. Borri, M., Croce, A., Trainelli, L., in press. The embedded projection method: A general index reduction procedure for constrained system dynamics. Computer and Mathematics with Applications
16. Bottasso C.L. Borri M. Energy preserving/decaying schemes for non-linear beam dynamics using the helicoidal approximation Computer Methods in Applied Mechanics and Engineering 143 1997 393 415
17. Bottasso C.L. Borri M. Trainelli L. Integration of elastic multibody systems by invariant conserving/dissipating algorithms. Part I: formulation Computer Methods in Applied Mechanics and Engineering 190 2001 3669 3699
18. Bottasso C.L. Borri M. Trainelli L. Integration of elastic multibody systems by invariant conserving/dissipating algorithms. Part II: numerical schemes and applications Computer Methods in Applied Mechanics and Engineering 190 2001 3701 3733
19. Brenan K.E. Campbell S.L. Petzold L.R. Numerical Solution of Initial-Value Problems in Differential-Algebraic Problems 1989 North-Holland New York
20. Cardona A. Géradin M. Time integration of the equations of motion in mechanism analysis Computers and Structures 33 3 1989 801 820
21. Chung J. 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
22. Gear C.W. Differential-algebraic equation index transformations SIAM Journal on Scientific and Statistical Computing 9 1 1988 40 47
23. Gear C.W. Petzold L.R. ODE methods for the solution of differential/algebraic systems SIAM Journal on Numerical Analysis 21 4 1984 716 728
24. Gear C.W. Leimkuhler B. Gupta G.K. Automatic integration of Euler-Lagrange equations with constraints Journal of Computational and Applied Mathematics 12 1985 77 90
25. Géradin M. Cardona A. Flexible Multibody System: A Finite Element Approach 2000 John Wiley - Sons New York
26. Hilber H.M. Hughes T.J.R. Taylor R.L. Improved numerical dissipation for time integration algorithms in structural dynamics Earthquake Engineering and Structural Dynamics 5 1977 282 292
27. Hildebrand F.B. Advanced Calculus for Applications second ed. 1976 Prentice Hall Englewood Cliffs, NJ
28. Kane T.R. Levinson D.A. Dynamics: Theory and Applications 1985 McGraw-Hill New York
29. Kim S.S. 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
30. Kurdila A. Papastavridis J.G. 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
31. Liang C.G. Lance G.M. A differentiable null space method for constrained dynamic analysis Journal of Mechanisms, Transmissions and Automation in Design 109 1987 405 411
32. Lotstedt P. Petzold L.R. Numerical solution of nonlinear differential equations with algebraic constraints I: Convergence results for backward differentiation formulas Mathematics of Computation 46 1986 491 516
33. Lotstedt P. Petzold L.R. Numerical solution of nonlinear differential equations with algebraic constraints II: Practical implications SIAM Journal on Scientific and Statistical Computing 7 1986 720 733
34. Mani N.K. Haug E.J. Atkinson K.E. Application of the singular value decomposition for analysis of mechanical system dynamics Journal of Mechanisms, Transmission, and Automation in Design 107 1985 82 87
35. Newmark N.M. A method of computation for structural dynamics Journal of the Engineering Mechanics Division 85 1959 67 94
36. Nikravesh P.E. Computer-Aided Analysis of Mechanical Systems 1988 Prentice-Hall Englewood Cliffs, NJ
37. Orlandea N. Chace M.A. Calahan D.A. A sparsity oriented approach to the dynamic analysis and design of mechanical systems. Parts I and II ASME Journal of Engineering for Industry 99 3 1977 773 784
38. 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
39. Park K.C. Chiou J.C. Stabilization of computational procedures for constrained dynamical systems Journal of Guidance, Control, and Dynamics 11 4 1988 365 370
40. Park K.C. Chiou J.C. Downer J.D. Explicit-implicit staggered procedure for multibody dynamics analysis Journal of Guidance, Control, and Dynamics 13 3 1988 562 570
41. Puso M.A. An energy and momentum conserving method for rigid-flexible body dynamics International Journal for Numerical Methods in Engineering 53 2002 1393 1414
42. Schiehlen W.O. Multibody System Handbook 1990 Springer-Verlag Berlin
43. Simo J.C. Tarnow N. The discrete energy-momentum method. Conserving algorithms for nonlinear dynamics ZAMP 43 1992 757 792
44. Simo J.C. Tarnow N. A new energy and momentum conserving algorithm for the nonlinear dynamics of shells International Journal for Numerical Methods in Engineering 37 1994 2527 2549
45. Simo J.C. Wong K. Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum International Journal for Numerical Methods in Engineering 31 1991 19 52
46. Simo J.C. Tarnow N. Doblare M. Non-linear dynamics of three-dimensional rods: Exact energy and momentum conserving algorithms International Journal for Numerical Methods in Engineering 38 1995 1431 1473
47. Singh R.P. Likins P.W. Singular value decomposition for constrained dynamical systems Journal of Applied Mechanics 52 1985 943 948
48. Stol, K., Bir, G., Balas, M., 1999. Linearized dynamics and operating modes of a simple wind turbine model. In: Proceedings of the 37th AIAA Aerospace Sciences Meeting and Exhibit. 11-14 January, Reno, Nevada, pp. 135-142, NICH Report No. 32548
49. Walton, W.C., Steeves, E.C., 1969. A new matrix theorem and its application for establishing independent coordinates for complex dynamical systems with constraints. Technical Report NASA TR R-326, NASA
50. Wehage R.A. Haug E.J. Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems ASME Journal of Mechanical Design 104 1982 247 255