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TECHNICAL PAPERS

Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity

[+] Author and Article Information
Ahmed A. Shabana

Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60607

Aki M. Mikkola

Department of Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankatu 34, 53851 Lappeenranta, Finland

J. Mech. Des 125(2), 342-350 (Jun 11, 2003) (9 pages) doi:10.1115/1.1564569 History: Received November 01, 2001; Revised September 01, 2002; Online June 11, 2003
Copyright © 2003 by ASME
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References

Hughes,  T. J. R., and Winget,  J., 1980, “Finite Rotation Effects in Numerical Integration of Rate Constitutive Equation Arising in Large Deformation Analysis,” Int. J. Numer. Methods Eng., 15(12), pp. 1862–1867.
Garćia de Jalón, J., and Bayo, E., 1994, Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge, Springer-Verlag.
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, pp. 165–174.
Simo,  J. C., and Vu-Quoc,  L., 1986, “On the Dynamics of Flexible Beams Under Large Overall Motion-the Plane Case: Part I,” ASME J. Appl. Mech., 53, pp. 849–854.
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.
Mikkola, A. M., and Shabana, A. A., 2001, “A New Plate Element Based on the Absolute Nodal Coordinate Formulation,” Proceedings of the 2001 ASME International Design Engineering Technical Conferences, September 9–12, 2001, Pittsburgh, Pennsylvania.
Omar,  M. A., and Shabana,  A. A., 2001, “A Two-Dimensional Shear Deformable Beam for Large Rotation and Deformation,” J. Sound Vib., 243(3), pp. 565–576.
Shabana,  A. A., and Yakoub,  R. Y., 2001, “Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory,” ASME J. Mech. Des., 123(4), December 2001, pp. 606–613.
Yakoub,  R. Y., and Shabana,  A. A., 2001, “Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications,” ASME J. Mech. Des., 123(4), December, pp. 614–621.
Shabana A. A., 1998, Dynamics of Multibody Systems, 2nd edition, Cambridge University Press.
Bathe, K-J., 1995, Finite Element Procedures, Prentice-Hall, Inc.
Cook, R. D., Malkus, D. S., and Plesha, M. E., 1999, Concepts and Applications of Finite Element Analysis, 3rd edition, John Wiley & Sons.
Berzeri,  M., Campanelli,  M., and Shabana,  A. A., 2001, “Definition of the Elastic Forces in the Finite-Element Absolute Nodal Coordinate Formulation and the Floating Frame of Reference Formulation,” Multibody System Dynamics, 5, pp. 21–54.
Bonet, J., and Wood, R. D., 1997, Nonlinear Continuum Mechanics for Finite Element Analysis, 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.

Figures

Grahic Jump Location
Examples of slope discontinuities
Grahic Jump Location
Element and body coordinate systems
Grahic Jump Location
The rigid body rotation
Grahic Jump Location
Motion simulation of the pendulum (E=1.0×108 N/m2)
Grahic Jump Location
Trajectory of point P (E=1.0×108 N/m2)
Grahic Jump Location
Motion simulation of the pendulum (E=1.0×106 N/m2)
Grahic Jump Location
Trajectory of point P (E=1.0×106 N/m2)
Grahic Jump Location
Strain components ε1122 and ε33 along the mid-line of the horizontal element (t=0.5 s)
Grahic Jump Location
Strain components ε1122 and ε33 along the mid-line of the vertical element (t=0.5 s)
Grahic Jump Location
Energy balance (E=1.0×106 N/m2)

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