메뉴 건너뛰기




Volumn 88, Issue 9, 2008, Pages 677-708

Variational integrators for constrained dynamical systems

Author keywords

Constrained dynamical systems; Differential algebraic equations; Flexible multibody dynamics; Variational time integration

Indexed keywords


EID: 55449088324     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200700173     Document Type: Article
Times cited : (139)

References (54)
  • 2
    • 84968499113 scopus 로고
    • Symplectic integration of constrained Hamiltonian systems
    • B. Leimkuhler and S. Reich, Symplectic integration of constrained Hamiltonian systems, Math. Comput. 63, 589-605 (1994).
    • (1994) Math. Comput , vol.63 , pp. 589-605
    • Leimkuhler, B.1    Reich, S.2
  • 3
    • 0012000774 scopus 로고    scopus 로고
    • A sympletic integrator for Riemannian manifolds
    • B. Leimkuhler and G. W. Patrick, A sympletic integrator for Riemannian manifolds, J. Nonlinear Sci. 6(4), 367-384 (1996).
    • (1996) J. Nonlinear Sci , vol.6 , Issue.4 , pp. 367-384
    • Leimkuhler, B.1    Patrick, G.W.2
  • 4
    • 0000761544 scopus 로고
    • Momentum conserving symplectic integrators
    • S. Reich, Momentum conserving symplectic integrators, Physica D 76(4), 375-383 (1994).
    • (1994) Physica D , vol.76 , Issue.4 , pp. 375-383
    • Reich, S.1
  • 5
    • 33646234930 scopus 로고    scopus 로고
    • Geometric integrators for odes
    • R. McLachlan and G. Quispel, Geometric integrators for odes, J. Phys. A 39(19), 5251-5286 (2006).
    • (2006) J. Phys. A , vol.39 , Issue.19 , pp. 5251-5286
    • McLachlan, R.1    Quispel, G.2
  • 6
    • 0034516803 scopus 로고    scopus 로고
    • Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanical Systems
    • C. Kane, J. Marsden, M. Ortiz, and M. West, Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanical Systems, Int. J. Numer. Methods Eng. 49, 1295-1325 (2000).
    • (2000) Int. J. Numer. Methods Eng , vol.49 , pp. 1295-1325
    • Kane, C.1    Marsden, J.2    Ortiz, M.3    West, M.4
  • 8
    • 84959193128 scopus 로고    scopus 로고
    • Discrete mechanics and variational integrators
    • J. E. Marsden and M. West, Discrete mechanics and variational integrators, Acta Numer. 10, 357-514 (2001).
    • (2001) Acta Numer , vol.10 , pp. 357-514
    • Marsden, J.E.1    West, M.2
  • 9
    • 0031210701 scopus 로고    scopus 로고
    • Mechanical integrators derived from a discrete variational principle
    • J. Wendlandt and J. Marsden, Mechanical integrators derived from a discrete variational principle, Physica D 106, 223-246 (1997).
    • (1997) Physica D , vol.106 , pp. 223-246
    • Wendlandt, J.1    Marsden, J.2
  • 10
    • 25444502638 scopus 로고    scopus 로고
    • The discrete null space method for the energy consistent integration of constrained mechanical systems. Part I: Holonomic constraints
    • P. Betsch, 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).
    • (2005) Comput. Methods Appl. Mech. Eng , vol.194 , Issue.50-52 , pp. 5159-5190
    • Betsch, P.1
  • 11
    • 0002510376 scopus 로고
    • Numerical solution of nonlinear differential equations with algebraic constraints II: Practical implications
    • L. Petzold and P. Loetstedt, Numerical solution of nonlinear differential equations with algebraic constraints II: Practical implications, SIAM J. Sci. Comput. 7(3), 720-733 (1986).
    • (1986) SIAM J. Sci. Comput , vol.7 , Issue.3 , pp. 720-733
    • Petzold, L.1    Loetstedt, P.2
  • 13
    • 3042698421 scopus 로고    scopus 로고
    • Energy-conserving integration of constrained Hamiltonian systems - a comparison of approaches
    • S. Leyendecker, P. Betsch, and P. Steinmann, Energy-conserving integration of constrained Hamiltonian systems - a comparison of approaches, Comput. Mech. 33, 174-185 (2004).
    • (2004) Comput. Mech , vol.33 , pp. 174-185
    • Leyendecker, S.1    Betsch, P.2    Steinmann, P.3
  • 14
    • 33746166784 scopus 로고    scopus 로고
    • The discrete null space method for the energy consistent integration of constrained mechanical systems. Part II: Multibody dynamics
    • P. Betsch and S. Leyendecker, 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).
    • (2006) Int. J. Numer. Methods Eng , vol.67 , Issue.4 , pp. 499-552
    • Betsch, P.1    Leyendecker, S.2
  • 16
    • 38849155239 scopus 로고    scopus 로고
    • The discrete null space method for the energy consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics
    • DOI 10.1007/s11044-007-9056-4
    • S. Leyendecker, P. Betsch, and P. Steinmann, The discrete null space method for the energy consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics, Multibody Syst. Dyn. 19, 45-72 (2008), DOI 10.1007/s11044-007-9056-4.
    • (2008) Multibody Syst. Dyn , vol.19 , pp. 45-72
    • Leyendecker, S.1    Betsch, P.2    Steinmann, P.3
  • 18
    • 0025238246 scopus 로고
    • The modeling of holonomic mechanical systems using a natural orthogonal complement
    • J. Angeles and S. Lee, The modeling of holonomic mechanical systems using a natural orthogonal complement, Trans. Can. Soc. Mech. Eng. 13(4), 81-89 (1989).
    • (1989) Trans. Can. Soc. Mech. Eng , vol.13 , Issue.4 , pp. 81-89
    • Angeles, J.1    Lee, S.2
  • 20
    • 0003014117 scopus 로고    scopus 로고
    • Time Integration and Discrete Hamiltonian Systems
    • O. Gonzalez, Time Integration and Discrete Hamiltonian Systems, J. Nonlinear Sci. 6, 449-467 (1996).
    • (1996) J. Nonlinear Sci , vol.6 , pp. 449-467
    • Gonzalez, O.1
  • 21
    • 0037051754 scopus 로고    scopus 로고
    • Conserving properties of a time FEmethod - Part III: Mechanical systems with holonomic constraints
    • P. Betsch and P. Steinmann, Conserving properties of a time FEmethod - Part III: Mechanical systems with holonomic constraints, Int. J. Numer. Methods Eng. 53, 2271-2304 (2002).
    • (2002) Int. J. Numer. Methods Eng , vol.53 , pp. 2271-2304
    • Betsch, P.1    Steinmann, P.2
  • 24
    • 84867951207 scopus 로고    scopus 로고
    • On the gamma-convergence of discrete dynamics and variational integrators
    • S. Müller and M. Ortiz, On the gamma-convergence of discrete dynamics and variational integrators, J. Nonlinear Sci. 14(4), 153-212 (2004).
    • (2004) J. Nonlinear Sci , vol.14 , Issue.4 , pp. 153-212
    • Müller, S.1    Ortiz, M.2
  • 25
    • 0037199848 scopus 로고    scopus 로고
    • Frame-indifferent beam finite elements based upon the geometrically exact beam theory
    • P. Betsch and P. Steinmann, Frame-indifferent beam finite elements based upon the geometrically exact beam theory, Int. J. Numer. Methods Eng. 54, 1775-1788 (2002).
    • (2002) Int. J. Numer. Methods Eng , vol.54 , pp. 1775-1788
    • Betsch, P.1    Steinmann, P.2
  • 26
    • 0038495088 scopus 로고    scopus 로고
    • Constrained dynamics of geometrically exact beams
    • P. Betsch and P. Steinmann, Constrained dynamics of geometrically exact beams, Comput. Mech. 31, 49-59 (2003).
    • (2003) Comput. Mech , vol.31 , pp. 49-59
    • Betsch, P.1    Steinmann, P.2
  • 27
    • 0008582162 scopus 로고    scopus 로고
    • Mechanical systems subject to holonomic constraints: Differential-algebraic formulations and conservative integration
    • O. Gonzalez, Mechanical systems subject to holonomic constraints: differential-algebraic formulations and conservative integration, Physica D 132, 165-174 (1999).
    • (1999) Physica D , vol.132 , pp. 165-174
    • Gonzalez, O.1
  • 28
    • 0035941058 scopus 로고    scopus 로고
    • Constrained integration of rigid body dynamics
    • P. Betsch and P. Steinmann, Constrained integration of rigid body dynamics, Comput. Methods Appl. Mech. Eng. 191, 467-488 (2001).
    • (2001) Comput. Methods Appl. Mech. Eng , vol.191 , pp. 467-488
    • Betsch, P.1    Steinmann, P.2
  • 33
    • 26844501382 scopus 로고    scopus 로고
    • Coordinate-free kinematic analysis of overconstrained mechanisms with mobility one
    • J. Lerbet, Coordinate-free kinematic analysis of overconstrained mechanisms with mobility one, Z. Angew. Math. Mech. 85(10), 740-747 (2005).
    • (2005) Z. Angew. Math. Mech , vol.85 , Issue.10 , pp. 740-747
    • Lerbet, J.1
  • 34
    • 4244083504 scopus 로고
    • Differential-algebraische-Gleichungssysteme in mechanischen Mehrkörpersystemen
    • PhD thesis, Technische Universität München
    • C. Führer, Differential-algebraische-Gleichungssysteme in mechanischen Mehrkörpersystemen. Theorie, numerische Ansätze und Anwendungen, PhD thesis, Technische Universität München, 1988.
    • (1988) Theorie, numerische Ansätze und Anwendungen
    • Führer, C.1
  • 35
    • 0022739057 scopus 로고
    • QR decomposition for state space representation of constrained mechanical dynamic systems
    • S. Kim and M. Vanderploeg, QR decomposition for state space representation of constrained mechanical dynamic systems, J. Mech. Trans. Auto. Des. 108, 183-188 (1986).
    • (1986) J. Mech. Trans. Auto. Des , vol.108 , pp. 183-188
    • Kim, S.1    Vanderploeg, M.2
  • 36
    • 55449100650 scopus 로고    scopus 로고
    • E. Kreuzer, Symbolische Berechnung der Bewegungsgleichungen von Mehrkörpersystemen (Fortschrittsbericht der VDI Zeitschriften, Düsseldorf, 1979).
    • E. Kreuzer, Symbolische Berechnung der Bewegungsgleichungen von Mehrkörpersystemen (Fortschrittsbericht der VDI Zeitschriften, Düsseldorf, 1979).
  • 37
    • 55449126742 scopus 로고    scopus 로고
    • erw. Aufl, Verlag Freies Geistesleben, Stuttgart
    • P. Schatz, Rhythmusforschung und Technik, 2., erw. Aufl. (Verlag Freies Geistesleben, Stuttgart, 1998).
    • (1998) Rhythmusforschung und Technik , vol.2
    • Schatz, P.1
  • 39
    • 0037199851 scopus 로고    scopus 로고
    • An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum scheme in dynamics
    • I. Romero and F. Armero, An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum scheme in dynamics, Int. J. Numer. Methods Eng. 54, 1683-1716 (2002).
    • (2002) Int. J. Numer. Methods Eng , vol.54 , pp. 1683-1716
    • Romero, I.1    Armero, F.2
  • 41
    • 0032299057 scopus 로고    scopus 로고
    • Interpolation of rotational variables in non-linear dynamics of 3d beams
    • G. Jelenić and M. Crisfield, Interpolation of rotational variables in non-linear dynamics of 3d beams, Int. J. Numer. Methods Eng. 43, 1193-1222 (1998).
    • (1998) Int. J. Numer. Methods Eng , vol.43 , pp. 1193-1222
    • Jelenić, G.1    Crisfield, M.2
  • 42
    • 0032026641 scopus 로고    scopus 로고
    • Finite rotations in dynamics of beams and implicit time-stepping schemes
    • A. Ibrahimbegović and S. Mamouri, Finite rotations in dynamics of beams and implicit time-stepping schemes, Int. J. Numer. Methods Eng. 41, 781-814 (1998).
    • (1998) Int. J. Numer. Methods Eng , vol.41 , pp. 781-814
    • Ibrahimbegović, A.1    Mamouri, S.2
  • 43
    • 33746451257 scopus 로고    scopus 로고
    • Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
    • M. Crisfield and G. Jelenić, Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation, Proc. R. Soc. Lond. A 455, 1125-1147 (1999).
    • (1999) Proc. R. Soc. Lond. A , vol.455 , pp. 1125-1147
    • Crisfield, M.1    Jelenić, G.2
  • 44
    • 0023964748 scopus 로고
    • On the dynamics in space of rods undergoing large motions - A geometrically exact approach
    • J. Simo and L. Vu-Quoc, On the dynamics in space of rods undergoing large motions - A geometrically exact approach, Comput. Methods Appl. Mech. Eng. 66, 125-161 (1988).
    • (1988) Comput. Methods Appl. Mech. Eng , vol.66 , pp. 125-161
    • Simo, J.1    Vu-Quoc, L.2
  • 45
    • 0032647649 scopus 로고    scopus 로고
    • Geometrically exact 3d beam theory: Implementation of a strain-invariant finite element for statics and dynamics
    • G. Jelenić and M. Crisfield, Geometrically exact 3d beam theory: implementation of a strain-invariant finite element for statics and dynamics, Comput. Methods Appl. Mech. Eng. 171, 141-171 (1999).
    • (1999) Comput. Methods Appl. Mech. Eng , vol.171 , pp. 141-171
    • Jelenić, G.1    Crisfield, M.2
  • 46
    • 33644591129 scopus 로고    scopus 로고
    • Objective energy-momentum conserving integration for the constrained dynamics of geometrically exact beams
    • S. Leyendecker, P. Betsch, and P. Steinmann, Objective energy-momentum conserving integration for the constrained dynamics of geometrically exact beams, Comput. Methods Appl. Mech. Eng. 195, 2313-2333 (2006).
    • (2006) Comput. Methods Appl. Mech. Eng , vol.195 , pp. 2313-2333
    • Leyendecker, S.1    Betsch, P.2    Steinmann, P.3
  • 47
    • 0029359498 scopus 로고
    • Numerical integration of non-linear elastic multibody systems
    • O. Bauchau, G. Damilano, and N. Theron, Numerical integration of non-linear elastic multibody systems, Int. J. Numer. Methods Eng. 38, 2727-2751 (1995).
    • (1995) Int. J. Numer. Methods Eng , vol.38 , pp. 2727-2751
    • Bauchau, O.1    Damilano, G.2    Theron, N.3
  • 48
    • 0037119515 scopus 로고    scopus 로고
    • Energy consering/decaying implicit time-stepping scheme for nonlinear dynamics of three-dimensional beams undergoing finite rotations
    • A. Ibrahimbegović and S. Mamouri, Energy consering/decaying implicit time-stepping scheme for nonlinear dynamics of three-dimensional beams undergoing finite rotations, Comput. Methods Appl. Mech. Eng. 191, 4241-4258 (2002).
    • (2002) Comput. Methods Appl. Mech. Eng , vol.191 , pp. 4241-4258
    • Ibrahimbegović, A.1    Mamouri, S.2
  • 49
    • 0027886658 scopus 로고
    • Assessment of Energy-Momentum and Symplectic Schemes for Stiff Dynamical Systems
    • American Society of Mechanical Engineers, New Orleans, Louisiana
    • J. C. Simo and O. Gonzalez, Assessment of Energy-Momentum and Symplectic Schemes for Stiff Dynamical Systems, in: Proceedings of the ASME Winter Annual Meeting (American Society of Mechanical Engineers, New Orleans, Louisiana, 1993).
    • (1993) Proceedings of the ASME Winter Annual Meeting
    • Simo, J.C.1    Gonzalez, O.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.