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TECHNICAL PAPERS

Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications

[+] Author and Article Information
Refaat Y. Yakoub, Ahmed A. Shabana

Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor St., Chicago, IL 60607-7022

J. Mech. Des 123(4), 614-621 (May 01, 2000) (8 pages) doi:10.1115/1.1410099 History: Received May 01, 2000
Copyright © 2001 by ASME
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References

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Simo,  J. C., 1985, “A Finite Strain Beam Formulation. The Three Dimensional Dynamics Problem. Part I,” Journal of Computer Methods in Applied Mechanics and Engineering, 49, pp. 55–70.
Shabana, A. A., and Yakoub, R., 2001, “Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory,” Submitted to the ASME J. Mech. Des., a companion paper.
Shabana, A. A., 1996, “An Absolute Nodal Coordinate Formulation for the Large Rotation and Deformation Analysis of Flexible Bodies,” Technical Report MBS96-1-UIC, University of Illinois at Chicago, Chicago, IL.
Shabana,  A. A., 1997, “Flexible Multibody Dynamics: Review of Past and Recent Developments,” Multibody System Dynamics, 1, pp. 189–222.
Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd edition, Cambridge University Press, Cambridge.
Shabana,  A. A., 1998, “Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics,” Nonlinear Dyn., 16, pp. 293–306.
Shabana,  A. A., Hussien,  H. A., and Escalona,  J. L., 1998, “Application of the Absolute Nodal Coordinate Formulation to Large Rotation and Large Deformation Problems,” ASME J. Mech. Des., 120, pp. 188–195.
Argyris,  J. H., Balmer,  H., Doltsinis,  J. St., Dunne,  P. C., Haase,  M., Kleiber,  M., Male-jannakis,  G. A., Mlejnek,  H.-P., Müller,  M., and Scharpf,  D. W., 1979, “Finite Element Method-The Natural Approach,” Comput. Methods Appl. Mech. Eng., 17/18, pp. 1–106.
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Rankin,  C. C., and Brogan,  F. A., 1986, “An Element Independent Corotational Procedure for the Treatment of Large Rotations,” ASME J. Pressure Vessel Technol., 108, 165–174.
Bonet, J., and Wood, R. D., 1997, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, Cambridge.
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Gere, J. M., and Timoshenko, S. P., 1984, Mechanics of Material, 2nd edition, Brooks/Cole Engineering Division, Monterey, California.
Yakoub,  R. Y., and Shabana,  A. A., 1999, “Use of Cholesky Coordinates and the Absolute Nodal Coordinate Formulation in the Computer Simulation of Flexible Multibody Systems,” Journal of Nonlinear Dynamics, 20, pp. 267–282.
Yakoub, R. Y., 2001, “A New Three Dimensional Absolute Coordinate Based Beam Element With Application to Wheel/Rail Interaction,” Ph.D. Thesis, Department of Mechanical Engineering, University of Illinois at Chicago.
Cowper,  G. R., 1966, “The Shear Coefficient in Timoshenko Beam Theory,” ASME J. Appl. Mech., 33, pp. 335–340.
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Figures

Grahic Jump Location
Four-noded beam element
Grahic Jump Location
Three dimensional pendulum
Grahic Jump Location
Displacement of the tip of the pendulum, Model I
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Displacement of the tip of the pendulum, Model II
Grahic Jump Location
Deflection of the mid-point, Model II
Grahic Jump Location
Beam transverse deflection
Grahic Jump Location
Deflection of the mid-point, Model III, (E=2.0E06Pa)
Grahic Jump Location
Deflection of the mid-point, Model III, (E=2.0E07Pa)
Grahic Jump Location
Simulation of the pendulum motion (Model III)
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Pendulum system energy (Model III)
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Comparison using different number of elements

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