메뉴 건너뛰기




Volumn 5, Issue 3, 2010, Pages 1-11

Variational integrators and energy-momentum schemes for flexible multibody dynamics

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL ALGEBRAIC EQUATIONS; DISCRETE SYSTEMS; FLEXIBLE COMPONENTS; FLEXIBLE MULTI-BODY DYNAMICS; NONLINEAR FINITE ELEMENT METHOD; NUMERICAL EXAMPLE; NUMERICAL INTEGRATIONS; STRUCTURE-PRESERVING; VARIATIONAL INTEGRATORS;

EID: 77955256760     PISSN: 15551415     EISSN: 15551423     Source Type: Journal    
DOI: 10.1115/1.4001388     Document Type: Article
Times cited : (31)

References (48)
  • 1
    • 34249830447 scopus 로고
    • The Discrete Energy-Momentum Method. Conserving Algorithms for Nonlinear Elastodynamics
    • Simo, J. C., and Tarnow, N., 1992, "The Discrete Energy-Momentum Method. Conserving Algorithms for Nonlinear Elastodynamics," Z. Angew. Math. Phys., 43, pp. 757-792.
    • (1992) Z. Angew. Math. Phys. , vol.43 , pp. 757-792
    • Simo, J.C.1    Tarnow, N.2
  • 2
    • 0030217555 scopus 로고    scopus 로고
    • On the Stability of Symplectic and Energy-Momentum Algorithms for Non-Linear Hamiltonian Systems With Symmetry
    • Gonzalez, O., and Simo, J. C., 1996, "On the Stability of Symplectic and Energy-Momentum Algorithms for Non-Linear Hamiltonian Systems With Symmetry," Comput. Methods Appl. Mech. Eng., 134, pp. 197-222.
    • (1996) Comput. Methods Appl. Mech. Eng. , vol.134 , pp. 197-222
    • Gonzalez, O.1    Simo, J.C.2
  • 3
    • 0032739316 scopus 로고    scopus 로고
    • On the Design of Energy Preserving and Decaying Schemes for Flexible, Nonlinear Multi-Body Systems
    • Bauchau, O. A., and Bottasso, C. L., 1999, "On the Design of Energy Preserving and Decaying Schemes for Flexible, Nonlinear Multi-Body Systems," Comput. Methods Appl. Mech. Eng., 169, pp. 61-79.
    • (1999) Comput. Methods Appl. Mech. Eng. , vol.169 , pp. 61-79
    • Bauchau, O.A.1    Bottasso, C.L.2
  • 4
    • 0001722832 scopus 로고    scopus 로고
    • Finite Element Method in Dynamics of Flexible Multibody Systems: Modeling of Holonomic Constraints and Energy Conserving Integration Schemes
    • Ibrahimbegović, A., Mamouri, S., Taylor, R. L., and Chen, A. J., 2000, "Finite Element Method in Dynamics of Flexible Multibody Systems: Modeling of Holonomic Constraints and Energy Conserving Integration Schemes," Multibody Syst. Dyn., 4(2-3), pp. 195-223.
    • (2000) Multibody Syst. Dyn. , vol.4 , Issue.2-3 , pp. 195-223
    • Ibrahimbegović, A.1    Mamouri, S.2    Taylor, R.L.3    Chen, A.J.4
  • 6
    • 34948902207 scopus 로고    scopus 로고
    • An Energy Preserving/Decaying Scheme for Nonlinearly Constrained Multibody Systems
    • Lens, E., and Cardona, A., 2007, "An Energy Preserving/Decaying Scheme for Nonlinearly Constrained Multibody Systems," Multibody Syst. Dyn., 18(3), pp. 435-470.
    • (2007) Multibody Syst. Dyn. , vol.18 , Issue.3 , pp. 435-470
    • Lens, E.1    Cardona, A.2
  • 8
    • 55449088324 scopus 로고    scopus 로고
    • Variational Integrators For Constrained Dynamical Systems
    • Leyendecker, S., Marsden, J. E., and Ortiz, M., 2008, "Variational Integrators For Constrained Dynamical Systems," Z. Angew. Math. Mech., 88(9), pp. 677-708.
    • (2008) Z. Angew. Math. Mech. , vol.88 , Issue.9 , pp. 677-708
    • Leyendecker, S.1    Marsden, J.E.2    Ortiz, M.3
  • 9
    • 84959193128 scopus 로고    scopus 로고
    • Discrete Mechanics and Variational Integrators
    • Marsden, J. E., and West, M., 2001, "Discrete Mechanics and Variational Integrators," Acta Numerica, 10, pp. 357-514.
    • (2001) Acta Numerica , vol.10 , pp. 357-514
    • Marsden, J.E.1    West, M.2
  • 12
    • 0035941058 scopus 로고    scopus 로고
    • Constrained Integration of Rigid Body Dynamics
    • Betsch, P., and Steinmann, P., 2001, "Constrained Integration of Rigid Body Dynamics," Comput. Methods Appl. Mech. Eng., 191, pp. 467-488.
    • (2001) Comput. Methods Appl. Mech. Eng. , vol.191 , pp. 467-488
    • Betsch, P.1    Steinmann, P.2
  • 13
    • 33746166784 scopus 로고    scopus 로고
    • The Discrete Null Space Method for the Energy Consistent Integration of Constrained Mechanical Systems. Part II: Multibody Dynamics
    • Betsch, P., and Leyendecker, S., 2006, "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), pp. 499-552.
    • (2006) Int. J. Numer. Methods Eng. , vol.67 , Issue.4 , pp. 499-552
    • Betsch, P.1    Leyendecker, S.2
  • 14
    • 33947699774 scopus 로고    scopus 로고
    • Energy-Momentum Conserving Integration of Multibody Dynamics
    • Betsch, P., and Uhlar, S., 2007, "Energy-Momentum Conserving Integration of Multibody Dynamics," Multibody Syst. Dyn., 17(4), pp. 243-289.
    • (2007) Multibody Syst. Dyn. , vol.17 , Issue.4 , pp. 243-289
    • Betsch, P.1    Uhlar, S.2
  • 15
    • 68249140850 scopus 로고    scopus 로고
    • Conserving Integrators for Parallel Manipulators
    • J.-H. Ryu, ed., I-Tech Education and Publishing, Vienna, Austria
    • Uhlar, S., and Betsch, P., 2008, "Conserving Integrators for Parallel Manipulators," Parallel Manipulators, J.-H. Ryu, ed., I-Tech Education and Publishing, Vienna, Austria, pp. 75-108.
    • (2008) Parallel Manipulators , pp. 75-108
    • Uhlar, S.1    Betsch, P.2
  • 16
    • 68249154904 scopus 로고    scopus 로고
    • A Rotationless Formulation of Multibody Dynamics: Modeling of Screw Joints and Incorporation of Control Constraints
    • Uhlar, S., and Betsch, P., 2009, "A Rotationless Formulation of Multibody Dynamics: Modeling of Screw Joints and Incorporation of Control Constraints," Multibody Syst. Dyn., 22(1), pp. 69-95.
    • (2009) Multibody Syst. Dyn. , vol.22 , Issue.1 , pp. 69-95
    • Uhlar, S.1    Betsch, P.2
  • 17
    • 0037199848 scopus 로고    scopus 로고
    • Frame-Indifferent Beam Finite Elements Based Upon the Geometrically Exact Beam Theory
    • Betsch, P., and Steinmann, P., 2002, "Frame-Indifferent Beam Finite Elements Based Upon the Geometrically Exact Beam Theory," Int. J. Numer. Methods Eng., 54, pp. 1775-1788.
    • (2002) Int. J. Numer. Methods Eng. , vol.54 , pp. 1775-1788
    • Betsch, P.1    Steinmann, P.2
  • 18
    • 0038495088 scopus 로고    scopus 로고
    • Constrained Dynamics of Geometrically Exact Beams
    • Betsch, P., and Steinmann, P., 2003, "Constrained Dynamics of Geometrically Exact Beams," Comput. Mech., 31, pp. 49-59.
    • (2003) Comput. Mech. , vol.31 , pp. 49-59
    • Betsch, P.1    Steinmann, P.2
  • 19
    • 33644591129 scopus 로고    scopus 로고
    • Objective Energy-Momentum Conserving Integration for the Constrained Dynamics of Geometrically Exact Beams
    • Leyendecker, S., Betsch, P., and Steinmann, P., 2006, "Objective Energy-Momentum Conserving Integration for the Constrained Dynamics of Geometrically Exact Beams," Comput. Methods Appl. Mech. Eng., 195, pp. 2313-2333.
    • (2006) Comput. Methods Appl. Mech. Eng. , vol.195 , pp. 2313-2333
    • Leyendecker, S.1    Betsch, P.2    Steinmann, P.3
  • 20
    • 84963647480 scopus 로고    scopus 로고
    • A Nonlinear Finite Element Framework for Flexible Multibody Dynamics: Rotationless Formulation and Energy-Momentum Conserving Discretization
    • C. L. Bottasso, ed., Springer-Verlag, Berlin
    • Betsch, P., and Sänger, N., 2009, "A Nonlinear Finite Element Framework for Flexible Multibody Dynamics: Rotationless Formulation and Energy-Momentum Conserving Discretization," Multibody Dynamics: Computational Methods and Applications (Computational Methods in Applied Sciences), C. L. Bottasso, ed., Springer-Verlag, Berlin, Vol. 12, pp. 119-141.
    • (2009) Multibody Dynamics: Computational Methods and Applications (Computational Methods in Applied Sciences) , vol.12 , pp. 119-141
    • Betsch, P.1    Sänger, N.2
  • 21
    • 61849088899 scopus 로고    scopus 로고
    • On the Use of Geometrically Exact Shells in a Conserving Framework for Flexible Multibody Dynamics
    • Betsch, P., and Sänger, N., 2009, "On the Use of Geometrically Exact Shells in a Conserving Framework for Flexible Multibody Dynamics," Comput. Methods Appl. Mech. Eng., 198, pp. 1609-1630.
    • (2009) Comput. Methods Appl. Mech. Eng. , vol.198 , pp. 1609-1630
    • Betsch, P.1    Sänger, N.2
  • 22
    • 0037051754 scopus 로고    scopus 로고
    • Conservation Properties of a Time FE Method. Part III: Mechanical Systems With Holonomic Constraints
    • Betsch, P., and Steinmann, P., 2002, "Conservation Properties of a Time FE Method. Part III: Mechanical Systems With Holonomic Constraints," Int. J. Numer. Methods Eng., 53, pp. 2271-2304.
    • (2002) Int. J. Numer. Methods Eng. , vol.53 , pp. 2271-2304
    • Betsch, P.1    Steinmann, P.2
  • 23
    • 0036815742 scopus 로고    scopus 로고
    • A DAE Approach to Flexible Multibody Dynamics
    • Betsch, P., and Steinmann, P., 2002, "A DAE Approach to Flexible Multibody Dynamics," Multibody Syst. Dyn., 8, pp. 365-389.
    • (2002) Multibody Syst. Dyn. , vol.8 , pp. 365-389
    • Betsch, P.1    Steinmann, P.2
  • 24
    • 38849155239 scopus 로고    scopus 로고
    • The Discrete Null Space Method for the Energy Consistent Integration of Constrained Mechanical Systems. Part III: Flexible Multibody Dynamics
    • Leyendecker, S., Betsch, P., and Steinmann, P., 2008, "The Discrete Null Space Method for the Energy Consistent Integration of Constrained Mechanical Systems. Part III: Flexible Multibody Dynamics," Multibody Syst. Dyn., 19(1-2), pp. 45-72.
    • (2008) Multibody Syst. Dyn. , vol.19 , Issue.1-2 , pp. 45-72
    • Leyendecker, S.1    Betsch, P.2    Steinmann, P.3
  • 25
    • 34250221087 scopus 로고    scopus 로고
    • Twenty-Five Years of Natural Coordinates
    • García de Jalón, J., 2007, "Twenty-Five Years of Natural Coordinates," Multibody Syst. Dyn., 18(1), pp. 15-33.
    • (2007) Multibody Syst. Dyn. , vol.18 , Issue.1 , pp. 15-33
    • García de Jalón, J.1
  • 26
    • 0000008977 scopus 로고
    • Discrete Versions of Some Classical Integrable Systems and Factorization of Matrix Polynomials
    • Moser, J., and Veselov, A. P., 1991, "Discrete Versions of Some Classical Integrable Systems and Factorization of Matrix Polynomials," Commun. Math. Phys., 139(2), pp. 217-243.
    • (1991) Commun. Math. Phys. , vol.139 , Issue.2 , pp. 217-243
    • Moser, J.1    Veselov, A.P.2
  • 28
    • 0024619943 scopus 로고
    • On a Stress Resultant Geometrically Exact Shell Model. Part I: Formulation and Optimal Parametrization
    • Simo, J. C., and Fox, D. D., 1989, "On a Stress Resultant Geometrically Exact Shell Model. Part I: Formulation and Optimal Parametrization," Comput. Methods Appl. Mech. Eng., 72, pp. 267-304.
    • (1989) Comput. Methods Appl. Mech. Eng. , vol.72 , pp. 267-304
    • Simo, J.C.1    Fox, D.D.2
  • 29
    • 0003610563 scopus 로고
    • Cambridge University Press, Cambridge, England
    • Marsden, J. E., 1992, Lectures on Mechanics, Cambridge University Press, Cambridge, England.
    • (1992) Lectures on Mechanics
    • Marsden, J.E.1
  • 30
    • 0031210701 scopus 로고    scopus 로고
    • Mechanical Integrators Derived From a Discrete Variational Principle
    • Wendlandt, J. M., and Marsden, J. E., 1997, "Mechanical Integrators Derived From a Discrete Variational Principle," Physica D, 106, pp. 223-246.
    • (1997) Physica D , vol.106 , pp. 223-246
    • Wendlandt, J.M.1    Marsden, J.E.2
  • 31
    • 0008582162 scopus 로고    scopus 로고
    • Mechanical Systems Subject to Holonomic Constraints: Differential-Algebraic Formulations and Conservative Integration
    • Gonzalez, O., 1999, "Mechanical Systems Subject to Holonomic Constraints: Differential-Algebraic Formulations and Conservative Integration," Physica D, 132, pp. 165-174.
    • (1999) Physica D , vol.132 , pp. 165-174
    • Gonzalez, O.1
  • 34
    • 79956148679 scopus 로고    scopus 로고
    • Energy-Momentum Conserving Schemes for Frictionless Dynamic Contact Problems. Part I: NTS Method
    • P. Wriggers and U. Nackenhorst, eds., Springer-Verlag, Berlin
    • Betsch, P., and Hesch, C., 2007, "Energy-Momentum Conserving Schemes for Frictionless Dynamic Contact Problems. Part I: NTS Method," IUTAM Symposium on Computational Methods in Contact Mechanics, P. Wriggers and U. Nackenhorst, eds., Springer-Verlag, Berlin, Vol. 3, pp. 77-96.
    • (2007) IUTAM Symposium on Computational Methods in Contact Mechanics , vol.3 , pp. 77-96
    • Betsch, P.1    Hesch, C.2
  • 35
    • 0003014117 scopus 로고    scopus 로고
    • Time Integration and Discrete Hamiltonian Systems
    • Gonzalez, O., 1996, "Time Integration and Discrete Hamiltonian Systems," J. Nonlinear Sci., 6, pp. 449-467.
    • (1996) J. Nonlinear Sci. , vol.6 , pp. 449-467
    • Gonzalez, O.1
  • 36
    • 38849137982 scopus 로고    scopus 로고
    • Time-Step-Size-Independent Conditioning and Sensitivity to Perturbations in the Numerical Solution of Index Three Differential Algebraic Equations
    • (USA)
    • Bottasso, C. L., Bauchau, O. A., and Cardona, A., 2007, "Time-Step-Size-Independent Conditioning and Sensitivity to Perturbations in the Numerical Solution of Index Three Differential Algebraic Equations," SIAM J. Sci. Comput. (USA), 29(1), pp. 397-414.
    • (2007) SIAM J. Sci. Comput. , vol.29 , Issue.1 , pp. 397-414
    • Bottasso, C.L.1    Bauchau, O.A.2    Cardona, A.3
  • 37
    • 38849136022 scopus 로고    scopus 로고
    • On the Optimal Scaling of Index Three DAEs in Multibody Dynamics
    • Bottasso, C. L., Dopico, D., and Trainelli, L., 2008, "On the Optimal Scaling of Index Three DAEs in Multibody Dynamics," Multibody Syst. Dyn., 19(1-2), pp. 3-20.
    • (2008) Multibody Syst. Dyn. , vol.19 , Issue.1-2 , pp. 3-20
    • Bottasso, C.L.1    Dopico, D.2    Trainelli, L.3
  • 39
    • 25444502638 scopus 로고    scopus 로고
    • The Discrete Null Space Method for the Energy Consistent Integration of Constrained Mechanical Systems. Part I: Holonomic Constraints
    • Betsch, P., 2005, "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), pp. 5159-5190.
    • (2005) Comput. Methods Appl. Mech. Eng. , vol.194 , Issue.50-52 , pp. 5159-5190
    • Betsch, P.1
  • 41
    • 65949103971 scopus 로고    scopus 로고
    • On the Rotationless Formulation of Multibody Dynamics and Its Conserving Numerical Integration
    • C. L. Bottasso, P. Masarati, and L. Trainelli, eds., Politecnico di Milano, Milano, Italy
    • Uhlar, S., and Betsch, P., 2007, "On the Rotationless Formulation of Multibody Dynamics and Its Conserving Numerical Integration," Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics, C. L. Bottasso, P. Masarati, and L. Trainelli, eds., Politecnico di Milano, Milano, Italy.
    • (2007) Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics
    • Uhlar, S.1    Betsch, P.2
  • 42
    • 1442340228 scopus 로고    scopus 로고
    • A 3D Mortar Method for Solid Mechanics
    • Puso, M. A., 2004, "A 3D Mortar Method for Solid Mechanics," Int. J. Numer. Methods Eng., 59, pp. 315-336.
    • (2004) Int. J. Numer. Methods Eng. , vol.59 , pp. 315-336
    • Puso, M.A.1
  • 43
    • 77950009195 scopus 로고    scopus 로고
    • Transient Three-Dimensional Domain Decomposition Problems: Frame-Indifferent Mortar Constraints and Conserving Integration
    • Hesch, C., and Betsch, P., 2009, "Transient Three-Dimensional Domain Decomposition Problems: Frame-Indifferent Mortar Constraints and Conserving Integration," Int. J. Numer. Methods Eng., 82, pp. 329-358.
    • (2009) Int. J. Numer. Methods Eng. , vol.82 , pp. 329-358
    • Hesch, C.1    Betsch, P.2
  • 44
    • 60949108081 scopus 로고    scopus 로고
    • A Mortar Method for Energy-Momentum Conserving Schemes in Frictionless Dynamic Contact Problems
    • Hesch, C., and Betsch, P., 2009, "A Mortar Method for Energy-Momentum Conserving Schemes in Frictionless Dynamic Contact Problems," Int. J. Numer. Methods Eng., 77(10), pp. 1468-1500.
    • (2009) Int. J. Numer. Methods Eng. , vol.77 , Issue.10 , pp. 1468-1500
    • Hesch, C.1    Betsch, P.2
  • 45
    • 22744452170 scopus 로고    scopus 로고
    • Conservation Properties of a Time FE Method. Part IV: Higher Order Energy and Momentum Conserving Schemes
    • Groß, M., Betsch, P., and Steinmann, P., 2005, "Conservation Properties of a Time FE Method. Part IV: Higher Order Energy and Momentum Conserving Schemes," Int. J. Numer. Methods Eng., 63, pp. 1849-1897.
    • (2005) Int. J. Numer. Methods Eng. , vol.63 , pp. 1849-1897
    • Groß, M.1    Betsch, P.2    Steinmann, P.3
  • 46
    • 0028483709 scopus 로고
    • A New Energy and Momentum Conserving Algorithm for the Nonlinear Dynamics of Shells
    • Simo, J. C., and Tarnow, N., 1994, "A New Energy and Momentum Conserving Algorithm for the Nonlinear Dynamics of Shells," Int. J. Numer. Methods Eng., 37, pp. 2527-2549.
    • (1994) Int. J. Numer. Methods Eng. , vol.37 , pp. 2527-2549
    • Simo, J.C.1    Tarnow, N.2
  • 48
    • 68549120763 scopus 로고    scopus 로고
    • Rigid Body Dynamics in Terms of Quaternions: Hamiltonian Formulation and Conserving Numerical Integration
    • Betsch, P., and Siebert, R., 2009, "Rigid Body Dynamics in Terms of Quaternions: Hamiltonian Formulation and Conserving Numerical Integration," Int. J. Numer. Methods Eng., 79(4), pp. 444-473.
    • (2009) Int. J. Numer. Methods Eng. , vol.79 , Issue.4 , pp. 444-473
    • Betsch, P.1    Siebert, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.