Energy-momentum conserving integration of multibody dynamics

Multibody System Dynamics

Volumn 17, Issue 4, 2007, Pages 243-289

  Betsch, Peter ^a   Uhlar, Stefan ^a  

^a UNIVERSITY OF SIEGEN   (Germany)

Author keywords

Conserving time integration; Constrained mechanical systems; Differential algebraic equations; Multibody dynamics; Parallel manipulators

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; COMPUTATIONAL MECHANICS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ENERGY CONSERVATION; INTEGRATION; MANIPULATORS;

CONSERVING TIME INTEGRATION; CONSTRAINED MECHANICAL SYSTEMS; MULTIBODY DYNAMICS; PARALLEL MANIPULATORS;

SYSTEMS ANALYSIS;

EID: 33947699774     PISSN: 13845640     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11044-007-9043-9     Document Type: Article

References (41)

1. Angeles, J.: Fundamentals of Robotic Mechanical Systems, 2nd edn. Springer-Verlag, Germany (2003)
2. Armero, F.: Energy-dissipative momentum-conserving time-stepping algorithms for finite strain multiplicative plasticity. Comput. Methods Appl. Mech. Eng. 195, 4862-4889 (2006)
3. Bauchau, O.A., Bottasso, C.L.: On the design of energy preserving and decaying schemes for flexible, nonlinear multi-body systems. Comput. Methods Appl. Mech. Eng. 169, 61-79 (1999)
4. Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numer. 14, 1-137 (2005)
5. Betsch, P.: The discrete null space method for the energy consistent integration of constrained mechanical systems. Part I: Holonomic constraints. Comput. Methods Appl. Mech. Eng. 194(50-52), 5159-5190 (2005)
6. Betsch, P.: On the discretization of geometrically exact shells for flexible multibody dynamics. In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics (on CD), pp. 1-13, Madrid, Spain, 21-24 June 2005
7. Betsch, P.: Energy-consistent numerical integration of mechanical systems with mixed holonomic and nonholonomic constraints. Comput. Methods Appl. Mech. Eng. 195, 7020-7035 (2006)
8. Betsch, P., Leyendecker, S.: The discrete null space method for the energy consistent integration of constrained mechanical systems. Part II: Multibody dynamics. Int. J. Numer. Methods Eng. 67(4), 499-552 (2006)
9. Betsch, P., Steinmann, P.: Conservation properties of a time FE method. Part II: Time-stepping schemes for nonlinear elastodynamics. Int. J. Numer. Methods Eng. 50, 1931-1955 (2001)
10. Betsch, P., Steinmann, P.: Constrained integration of rigid body dynamics. Comput. Methods Appl. Mech. Eng. 191, 467-488 (2001)
11. Betsch, P., Steinmann, P.: Conservation properties of a time FE method. Part III: Mechanical systems with holonomic constraints. Int. J. Numer. Methods Eng. 53, 2271-2304 (2002)
12. Betsch, P., Steinmann, P.: A DAE approach to flexible multibody dynamics. Multibody Syst. Dyn. 8, 367-391 (2002)
13. Bottasso, C.L., Croce, A.: Optimal control of multibody systems using an energy preserving direct transcription method. Multibody Syst. Dyn. 12(1), 17-45 (2004)
14. Brank, B., Briseghella, L., Tonello, N., Damjanic, F.B.: On non-linear dynamics of shells: implementation of energy-momentum conserving algorithm for a finite rotation shell model. Int. J. Numer. Methods Eng. 42, 409-442(1998)
15. Crisfield, M.A., Jelenić, G.: Energy/momentum conserving time integration procedures with finite elements and large rotations. In: NATO-ARW on Compuational Aspects of Nonlinear Structures and Systems with Large Rigid Body Motion, Ambrósio, J., Kleiber, M. (eds.), pp. 181-200, Pultusk, Poland, 2-7 July 2000
16. Garcia de Jalon, J., Unda, J., Avello, A.: Natural coordinates for the computer analysis of multibody systems. Comput. Methods Appl. Mech. Eng. 56, 309-327 (1986)
17. Géradin, M., Cardona, A.: Flexible Multibody Dynamics: a Finite Element Approach. Wiley, New York (2001)
18. Gill, P.E., Murray, W., Wright, M.H.: Practical Optimization. Academic, New York (1981)
19. Goicolea, J.M., Garcia Orden, J.C.: Dynamic analysis of rigid and deformable multibody systems with penalty methods and energy-momentum schemes. Comput. Methods Appl. Mech. Eng. 188, 789-804 (2000)
20. Gonzalez, O.: Time integration and discrete Hamiltonian systems. J. Nonlinear Sci. 6, 449-467 (1996)
21. Gonzalez, O.: Mechanical systems subject to holonomic constraints: differential-algebraic formulations and conservative integration. Physica D 132, 165-174 (1999)
22. Gonzalez, O., Simo, J.C.: On the stability of symplectic and energy-momentum algorithms for non-linear Hamiltonian systems with symmetry. Comput. Methods Appl. Mech. Eng. 134, 197-222 (1996)
23. Greenspan, D.: Conservative numerical methods for ẍ = f(x). J. Comput. Phys. 56, 28-41 (1984)
24. Groß, M., Betsch, P., Steinmann, P.: Conservation properties of a time FE method. Part TV: Higher order energy and momentum conserving schemes. Int. J. Numer. Methods Eng. 63, 1849-1897 (2005)
25. Ibrahimbegović, A., Mamouri, S., Taylor, R.L., Chen, A.J.: Finite element method in dynamics of flexible multibody systems: Modeling of holonomic constraints and energy conserving integration schemes. Multibody Syst. Dyn. 4(2-3), 195-223 (2000)
26. Khan, W.A., Krovi, V.N., Saha, S.K., Angeles, J.: Modular and recursive kinematics and dynamics for parallel manipulators. Multibody Syst. Dyn. 14(3-4), 419-455 (2005)
27. Kunkel, P., Mehrmann, V.: Differential-Algebraic Equations. European Mathematical Society, Zürich, Switzerland (2006)
28. Laursen, TA., Love, G.R.: Improved implicit integrators for transient impact problems - geometric admissibility withing the conserving framework. Int. J. Numer. Methods Eng. 53, 245-274 (2002)
29. Leimkuhler, B., Reich, S.: Simulating Hamiltonian Dynamics. Cambridge University Press, Cambridge, UK (2004)
30. Leyendecker, S., Betsch, P., Steinmann, P.: The discrete null space method for the energy consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics. To appear in Multibody Syst. Dyn.
31. Leyendecker, S., Betsch, P., Steinmann, P.: Energy-conserving integration of constrained Hamiltonian systems - a comparison of approaches. Comput. Mech. 33(3), 174-185 (2004)
32. Mohammadi Daniali, H.R., Zsombor-Murray, P.J., Angeles, J.: Singularity analysis of planar parallel manipulators. Mech. Mach. Theory 30(5), 665-678 (1995)
33. Puso, M.A.: An energy and momentum conserving method for rigid-flexible body dynamics. Int. J. Numer. Methods Eng. 53, 1393-1414 (2002)
34. Romero, I., Armero, F.: An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum conserving scheme in dynamics. Int. J. Numer. Methods Eng. 54, 1683-1716 (2002)
35. Rosenberg, R.M.: Analytical Dynamics of Discrete Systems. Plenum, New York (1977)
36. Rubin, H., Ungar, P.: Motion under a strong constraining force. Commun. Pure Appl. Math. 10(1), 65-87 (1957)
37. Saha, S.K.: Dynamics of serial multi-body systems using the decoupled natural oithogonal complement matrices. ASME J. Appl. Mech. 66, 986-996 (1999)
38. Saha, S.K., Schiehlen, W.O.: Recursive kinematics and dynamics for parallel structured closed loop multibody systems. Mech. Struct. Mach. 29(2), 143-175 (2001)
39. Simo, J.C., Tarnow, N.: The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. Z. Angew. Math. Phys. (ZAMP) 43, 757-792 (1992)
40. Simo, J.C., Tarnow, N., Wong, K.K.: Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics. Comput. Methods Appl. Mech. Eng. 100, 63-116 (1992)
41. Simo, J.C., Wong, K.K.: Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum. Int. J. Numer. Methods Eng. 31, 19-52 (1991)