A review of the current state of the absolute nodal coordinate formulation (ANCF) is proposed for large-displacement and large-deformation problems in flexible multibody dynamics. The review covers most of the known implementations of different kinds of finite elements including thin and thick planar and spatial beams and plates, their geometrical description inherited from FEM, and formulations of the most important elements of equations of motion. Much attention is also paid to simulation examples that show reasonableness and accuracy of the formulations applied to real physical problems and that are compared with experiments having significant geometrical nonlinearity. Current and further development directions of the ANCF are also briefly outlined.
Issue Section:
Research Papers
1.
Shabana
, A. A.
, 1997, “Flexible Multibody Dynamics: Review of Past and Recent Developments
,” Multibody Syst. Dyn.
1384-5640, 1
, pp. 189
–222
.2.
Song
, J. O.
, and Haug
, E. J.
, 1980, “Dynamic Analysis of Planar Flexible Mechanisms
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 24
, pp. 359
–381
.3.
Shabana
, A. A.
, and Wehage
, R. A.
, 1983, “Coordinate Reduction Technique for Transient Analysis of Special Substructureswith Large Angular Rotations
,” J. Struct. Mech.
0360-1218, 11
(3
), pp. 401
–431
.4.
Belytschko
, T.
, and Hsieh
, B. J.
, 1973, “Nonlinear Transient Finite Element Analysis with Convected Coordinates
,” Int. J. Numer. Methods Eng.
0029-5981, 7
, pp. 255
–271
.5.
Rankin
, C. C.
, and Brogan
, F. A.
, 1986, “An element Independent Corotational Procedure for the Treatment of Large Rotations
,” ASME J. Pressure Vessel Technol.
0094-9930, 108
, pp. 165
–174
.6.
Simo
, J. C.
, 1985, “A Finite Strain Beam Formulation. The Three-Dimensional Dynamic Problem, Part I
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 49
, pp. 55
–70
.7.
Simo
, J. C.
, and Vu-Quoc
, L.
, 1986, “A Three-Dimensional Finite Strain Rod Model, Part II: Computational Aspects
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 58
, pp. 79
–116
.8.
Shabana
, A. A.
, 1996, “An Absolute Nodal Coordinate Formulation for the Large Rotation and Large Deformation Analysis of Flexible Bodies
,” Techn. Rep. No. MBS96–1-UIC, Univ. of Illinois at Chicago
, Chicago IL.9.
Zienkiewicz
, O. C.
, and Taylor
, R. L.
, 1991, The Finite Element Method, Volume 2: Solid and Fluid Mechanics
, 4th edition, McGraw-Hill Book Company
.10.
Berzeri
, M.
, and Shabana
, A. A.
, 2000, “Development of Simple Models for the Elastic Forces in the Absolute Nodal Co-ordinate Formulation
,” J. Sound Vib.
0022-460X, 235
(4
), pp. 539
–565
.11.
Shabana
, A. A.
, Hussien
, H. A.
, and Escalona
, J. L.
, 1997, “Absolute Nodal Coordinate Formulation
,” Proceedings of the 16th ASME Biennial Conference on Mechanical Vibration and Noice
, ASME
, New York.12.
Takahashi
, Y.
, and Shimizu
, N.
, 1999, “Study on Elastic Forces of the Absolute Nodal Coordinate Formulation for Deformable Beams
,” ASME Proceedings of Design Engineering Technical Conference
, VIB–8203, ASME
, New York.13.
Campanelli
, M.
, Berzeri
, M.
, and Shabana
, A. A.
, 2000, “Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems
,” J. Mech. Des.
1050-0472, 122
, p. 498
.14.
Yoo
, W.-S.
, Lee
, J.-H.
, Park
, S.-J.
, Sohn
, J.-H.
, Dmitrochenko
, O. N.
, and Pogorelov
, D. Yu.
,2003, “Large Oscillations of a Thin Cantilever Beam: Physical Experiments and Simulation using Absolute Nodal Coordinate Formulation
,” Nonlinear Dyn.
0924-090X, 34
(1
), pp. 3
–29
.15.
Shabana
, A. A.
, 1998, Dynamics of Multibody Systems
, 2nd edition, Cambridge University Press
, New York.16.
Dmitrochenko
, O.
, 2002, “Methods of Dynamical Simulation of Hybrid Systems with Accounting Geometrical Non-Linearity
,” Dynamics, Strength and Reliability of Transport Machines
, BSTU
, Bryansk, pp. 24
–34
(in Russian).17.
Dmitrotchenko
, O. N.
, 2002, “Efficient Simulation of Rigid-Flexible Multibody Dynamics: Some Implementations and Results
,” Proc. of NATO ASI on Virtual Nonlinear Multibody Systems 1
, Prague, pp. 51
–56
.18.
Dmitrochenko
, O. N.
, and Pogorelov
, D. Yu.
, 2003, “Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation
,” Multibody Syst. Dyn.
1384-5640, 10
(1
), pp. 17
–43
.19.
Yoo
, W.-S.
, Lee
, J.-H.
, Park
, S.-J.
, Sohn
, J.-H.
, Pogorelov
, D. Yu.
, and Dmitrochenko
, O. N.
, 2004, “Large Deflection Analysis of a Thin Plate: Computer Simulations and Experiments
,” Multibody Syst. Dyn.
1384-5640, 11
(2
), pp. 185
–208
.20.
Yoo
, Wan-Suk
, Dmitrochenko
, O.
, Park
, S. J.
, and Lim
, O. K.
, 2005, “A New Thin Spatial Beam Element Using the Absolute Nodal Coordinates: Application to a Rotating Strip
,” Mech. Based Des. Struct. Mach.
1539-7734, submitted.21.
Omar
, M. A.
, and Shabana
, A. A.
, 2001, “A Two-Dimensional Shear Deformation Beam for Large Rotation and Deformation
,” J. Sound Vib.
0022-460X, 243
(3
), pp. 565
–576
.22.
García-Vallejo
, D.
, Mayo
, J.
, Escalona
, J. L.
, and Domínguez
, J.
, 2004, “Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate Formulation
,” Nonlinear Dyn.
0924-090X, 35
, pp. 313
–329
.23.
Shabana
, A. A.
, and Yakoub
, R. Y.
, 2004, “Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory
,” ASME J. Mech. Des.
1050-0472, 123
, pp. 606
–621
.24.
Mikkola
, A. M.
, and Shabana
, A. A.
, 2001, “A New Plate Element based on the Absolute Nodal Coordinate Formulation
,” Proc. of ASME 2001 DETC
, ASME
, New York.25.
Hakala
, M.
, 1986, Finite Element Methods in Structural Mechanics
, Otapaino
, Espoo (in Finnish).26.
Sopanen
, J. T.
, and Mikkola
, A. M.
, 2003, “Studies on the Stiffness Properties of the Absolute Nodal Coordinate Formulation for Three-Dimensional Beams
,” Abstracts of ASME DETC
, DETC2003/VIB–48325, ASME
, New York, p. 594
.27.
Dufva
, K.
, and Shabana
, A. A.
, 2005, “Use of the Absolute Nodal Coordinate Formulation in the Analysis of Thin Plate Structures
,” Techn. Rep. No. MBS05–1-UIC, Univ. of Illinois at Chicago
, Chicago IL.28.
Timoshenko
, S. P.
, and Woinowsky-Krieger
, S.
, 1991, Theory of Plates and Shells
, 2nd edition, McGraw-Hill Book Company
.29.
Pogorelov
, D.
, 1997, “Some Developments in Computational Techniques in Modeling Advanced Mechanical Systems
,” Proceedings of IUTAM Symposium on Interaction between Dynamics and Control in Advanced Mechanical Systems
, D. H.
van Campen
, ed., Kluwer Academic Publishers
, Dordrecht, pp. 313
–320
.30.
Yoo
, Wan-Suk
, Park
, Su-Jin
, Park
, Jun-Yong
, and Sohn
, Jeong-Hyun
, 2004, “Experiments and Computer Simulations of a Stepped Cantilever Beam with a Hybrid Coordinate Formulation
,” Mech. Based Des. Struct. Mach.
1539-7734, 32
(4
), pp. 515
–532
.31.
Yoo
, Wan-Suk
, and Sohn
, J. H.
, 2005, “Large Deformation of Beam with base Motions: Flexible Multibody Simulations and Experiments
,” Comput. Methods Appl. Mech. Eng.
0045-7825, in press.32.
von Dombrowski
, S.
, 2002, “Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates
,” Multibody Syst. Dyn.
1384-5640, 8
, pp. 409
–432
.33.
Craig
, R. R.
, Structural Dynamics
.34.
Dmitrochenko
, O.
, Yoo
, Wan-Suk
, and Pogorelov
, D.
, 2003, “Helicoseir as Shape of a Rotating Chain (II): 3D Theory and Simulation Using ANCF
,” Multibody Syst. Dyn.
1384-5640, submitted.35.
Gerstmayr
, J.
, 2003, “Strain Tensors in the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation
,” Nonlinear Dyn.
0924-090X, 34
, pp. 133
–145
.36.
Silverman
, M. P.
, Strange
, Wayne
, and Lipscombe
, T. C.
, 1998, “‘String Theory’: Equilibrium Configurations of a Helicoseir
,” Eur. J. Phys.
0143-0807, 19
, pp. 379
–387
.37.
Dmitrochenko
, O.
, Yoo
, Wan-Suk
, and Pogorelov
, D.
, 2004, “Helicoseir as Shape of a Rotating Chain (I): 2D Theory and Simulation Using ANCF
,” Multibody Syst. Dyn.
1384-5640, submitted.38.
Kübler
, L.
, Eberhard
, P.
, and Geisler
, J.
, 2003, “Flexible Multibody Systems with Large Deformations Using Absolute Nodal Coordinates for Isoparametric Solid Brick Elements
,” Abstracts of ASME DETC
, DETC2003/VIB–48303, ASME
, New York, p. 573
.39.
Takahashi
, Y.
, Shimizu
, N.
, and Suzuki
, K.
, 2002, “Introduction of Damping Matrix Into Absolute Nodal Coordinate Formulation
,” Proceedings of the 1st Asian Conference on Multibody Dynamics
, pp. 33
–40
.40.
Bathe
, K.-J.
, 1996, Finite Element Procedures
, Prentice Hall
, New Jersey.41.
Kübler
, L.
, Eberhard
, P.
, and Geisler
, J.
, 2003, “Flexible Multibody Systems with Large Deformations and Nonlinear Structural Damping Using Absolute Nodal Coordinates
,” Nonlinear Dyn.
0924-090X, 34
, pp. 31
–52
.42.
García-Vallejo
, D.
, Valverde
, J.
, and Domínguez
, J.
, 2005, “An Internal Damping Model for the Absolute Nodal Coordinate Formulation
,” Nonlinear Dyn.
0924-090X, in press.43.
Sugiyama
, H.
, and Shabana
, A. A.
, 2003, “Use of Plasticity Theory in Flexible Multibody System Dynamics
,” Abstr. of ASME DETC
, DETC2003/VIB–48326, ASME
, New York, p. 595
.44.
Gerstmayr
, J.
, 2004, “The Absolute Coordinate Formulation with Elasto-Plastic Deformations
,” Multibody Syst. Dyn.
1384-5640, 12
, pp. 363
–383
.45.
Sugiyama
, H.
, Escalona
, J. L.
, and Shabana
, A. A.
, 2003, “Spatial Joint Constraints in Flexible Multibody Systems Using the Absolue Nodal Coordinate Formulation
,” Abstr. of ASME DETC
, DETC2003/VIB–48354, ASME
, New York, p. 621
.46.
Gear
, C. W.
, Gupta
, G. K.
, and Leimkuhler
, B.
, 1985, “Automatic Integration of Euler-Lagrange Equations With Constraints
,” J. Comput. Appl. Math.
0377-0427, 12
(13
), pp. 77
–90
.47.
Neukirch
, S.
, van der Heijden
, G. H. M.
, and Thompson
, J. M. T.
, 2002, “Writhing Instabilities of Twisted Rods: From Infinite to Finite Length
,” J. Mech. Phys. Solids
0022-5096, 50
, pp. 1175
–1191
.48.
Palii
, O. M.
, (ed.), 1982, Handbook on Ship Structural Mechanics
, 2
, Shipbuilding Publishers
, Leningrad, 1982 (In Russian).49.
Pogorelov
, D.
, 1998, “Differential-Algebraic Equations in Multibody System Modeling
,” Numer. Algorithms
1017-1398, 19
, pp. 183
–194
.50.
Schiehlen
, W.
, (ed.), 1990, Multibody Systems Handbook
, Springer Verlag
, Berlin.51.
Schiehlen
, W.
, 1997, “Multibody System Dynamics: Roots and Perspectives
,” Multibody Syst. Dyn.
1384-5640, 1
, pp. 149
–188
.52.
Schwertassek
, R.
, 1997, “Flexible Bodies in Multibody Systems
,” Computational Methods in Mechanical Systems
, 161
, pp. 329
–363
.53.
Shabana
, A. A.
, and Christensen
, A. P.
, 1997, “Three-Dimensional Absolute Nodal Coordinate Formulation: Plate Problem
,” Int. J. Numer. Methods Eng.
0029-5981, 40
, pp. 2775
–2790
.Copyright © 2006
by American Society of Mechanical Engineers
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