Geometrically exact planar Euler-Bernoulli beam and time integration procedure for multibody dynamics
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Shabana AA, Sany JR. A survey of rail vehicle track simulations and flexible multibody dynamics. Nonlinear Dyn. 2001;26:179–212.
Escalona JL, Recuero AM. A bicycle model for education in multibody dynamics and real-time interactive simulation. Multibody Syst Dyn. 2012;27:383–402.
Xu WF, Meng DS, Chen YQ, Qian HH, Xu YS. Dynamics modeling and analysis of a flexible-base space robot for capturing large flexible spacecraft. Multibody Syst Dyn. 2014;23:357–401.
Betsch P. Energy-momentum integrators for elastic cosserat points, rigid bodies, and multibody systems. In: Betsch P, editor. Structure-preserving Integrators in nonlinear structural dynamics and flexible multibody dynamics, vol. 565. 1st ed. Springer: Cham; 2016. p. 31–89.
Arnold M, Cardona A, Brüls O. A lie algebra approach to lie group time integration of constrained systems. In: Betsch P, editor. Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics, vol. 565. 1st ed. Cham: Springer; 2016. p. 91–158.
Meng D, She Y, Xu W, Lu W, Liang B. Dynamic modeling and vibration characteristics analysis of flexible-link and flexible-joint space manipulator. Multibody Syst Dyn. 2018;43:321–47.
Pasciuto I, Ausejo S, Celigüeta JT, Suescun A, Cazön A. A hybrid dynamic motion prediction method for multibody digital human models based on a motion database and motion knowledge. Multibody Syst Dyn. 2014;32:27–53.
Habachi AE, Duprey S, Cheze L, Dumas R. A parallel mechanism of the shoulder-application to multi-body optimisation. Multibody Syst Dyn. 2015;33:439–51.
Pettersson R, Nordmark A, Eriksson A. Optimisation of multiple phase human movements. Multibody Syst Dyn. 2013;30:461–84.
Wasfy TM, Noor AK. Computational strategies for flexible multibody systems. Appl Mech Rev. 2003;56:553–613.
Reissner E. On one-dimensional finite-strain beam theory: the plane problem. J Appl Math Phys. 1972;23:795–804.
Simo JC, Vu-Quoc L. On the dynamics of flexible beams under large overall motions-the plane case: part I and II. J Appl Mech. 1986;53:849–63.
Shabana AA. Definition of the slopes and the finite element absolute nodal coordinate formulation. Multibody Syst Dyn. 1997;1:339–48.
Gerstmayr J, Irschik H. On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach. J Sound Vib. 2008;318:461–87.
Shabana AA, Berzeri M. Development of simple models for the elastic forces in the absolute nodal coordinate formulation. J Sound Vib. 2000;235:539–65.
Ding JY, Wallin M, Wei C, Recuero AM, Shabana AA. Use of independent rotation field in the large displacement analysis of beams. Nonlinear Dyn. 2014;76:1829–43.
Omar MA, Shabana AA. A two-dimensional shear deformable beam for large rotation and deformation problems. J Sound Vib. 2001;243:565–76.
Gerstmayr J, Matikainen MK, Mikkola AM. A geometrically exact beam element based on the absolute nodal coordinate formulation. Multibody Syst Dyn. 2008;20:359–84.
Gerstmayr J, Sugiyama H, Mikkola A. An overview on the developments of the absolute nodal coordinate formulation. Applied mechanics reviews. In: Proceedings of the second joint international conference on multibody system dynamics, Stuttgart, Germany; May 2012.
Shabana AA, Christensen AP. Three-dimensional absolute nodal co-ordinate formulation: plate problem. Int J Numer Methods Eng. 1997;40:2775–90.
Mikkola AM, Shabana AA. A new plate element based on the absolute nodal coordinate formulation. Paper No DETC20001/ VIB-21341, Proc of ASME 2001 DETC, Pittsburgh PA.
Gerstmayr J, Schöberl J. A 3D finite element method for flexible multibody systems. Multibody Syst Dyn. 2006;15:309–24.
Lang H, Linn J, Arnold M. Multi-body dynamics simulation of geometrically exact Cosserat rods. Multibody Syst Dyn. 2011;25:285–312.
Boer SE, Aarts RGKM, Hakvoort WBJ. Model reduction for efficient time-integration of spatial flexible multibody models. Multibody Syst Dyn. 2014;31:69–91.
Olshevskiy A, Dmitrochenko O, Kim C. Three- and four-noded planar elements using absolute nodal coordinate formulation. Multibody Syst Dyn. 2013;29:255–69.
Nachbagauer K, Pechstein AS, Irschik H, Gerstmayr J. A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation. Multibody Syst Dyn. 2011;26:245–63.
Dmitrochenko O, Mikkola A. A formal procedure and invariants of a transition from conventional finite elements to the absolute nodal coordinate formulation. Multibody Syst Dyn. 2009;22:323–39.
Borri M, Bottasso C. An intrinsic beam model based on helicoidal approximation—part 1: fomulation. Int J Numer Methods Eng. 1994;37:2267–89.
Borri M, Bottasso C. An intrinsic beam model based on helicoidal approximation—part 2: linearization and finite element implementation. Int J Numer Methods Eng. 1994;37:2291–309.
Bottasso C, Borri M. Energy preserving/decaying schemes for non-linear beam dynamics using the helicoidal approximation. Comput Methods Appl Mech Eng. 1997;143:393–415.
Merlini T, Morandini M. The helicoidal modeling in computational finite elasticity. Part I: variational formulation. Int J Solids Struct. 2004;41:5351–81.
Merlini T, Morandini M. The helicoidal modeling in computational finite elasticity. Part II: multiplicative interpolation. Int J Solids Struct. 2004;41:5383–409.
Betsch P, Uhlar S. Energy-momentum conserving integration of multibody dynamics. Multibody Syst Dyn. 2007;17:243–89.
Bauchau OA, Bottasso CL. On the design of energy preserving and decaying schemes for flexible, nonlinear multi-body systems. Comput Methods Appl Mech Eng. 1999;169:61–79.
Simo JC, Tarnow N. The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. J Appl Math Phys. 1992;43:757–92.
Goicolea JM, Garcia Orden JC. Dynamic analysis of rigid and deformable multibody systems with penalty methods and energy-momentum schemes. Comput Methods Appl Mech Eng. 2000;188:789–804.
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. Multibody Syst Dyn. 2008;19:45–72.
Bottasso CL, Croce A. Optimal control of multibody systems using an energy preserving direct transcription method. Multibody Syst Dyn. 2004;12:17–45.
Géradin M, Cardona A. Flexible multibody dynamics: a finite element approach. New York: Wiley; 2001.
Sansour C, Wriggers P, Sansour J. Nonlinear dynamics of shells: theory, finite element formulation, and integration schemes. Nonlinear Dyn. 1997;13:279–305.
Sansour C, Wagner W, Wriggers P, Sansour J. An energy- momentum integration scheme and enhanced strain finite elements for the non-linear dynamics of shells. Int J Non-Linear Mech. 2002;37:951–66.