Abstract
In the finite element literature, beams and platesare not treated as isoparametric elements becausethe displacement gradients at the nodes are used todescribe infinitesimal rotations. Such alinearization of the slopes leads to incorrect rigidbody equations of motion when the beams and platesrotate as rigid bodies. A simple and efficient absolute nodal coordinate formulation, in which noinfinitesimal or finite rotations are used as nodalcoordinates, can be systematically developed andefficiently used in many large deformationapplications as well as in the analysis of curvedstructures. This formulation leads to a constantmass matrix, and as a consequence, an efficientprocedure can be used for solving for the nodalaccelerations. In the absolute nodal coordinateformulation, the displacement gradients at the nodesare determined in the undeformed referenceconfiguration using simple rigid body kinematics.The problems that arise from the linearization ofthe slopes and the use of the finite rotations asnodal coordinates are discussed in this paper.
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Shabana, A., ‘Finite element incremental approach and exact rigid body inertia’, ASME Journal of Mechanical Design, 118, 1996, 171–178.
Shabana, A., ‘An absolute nodal coordinate formulation for the large rotation and deformation analysis of flexible bodies’, Technical Report #MBS96-1-UIC, Department of Mechanical Engineering, University of Illinois at Chicago, 1996.
Simo, J.C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions-the plane case: Parts I & II’, ASME Journal of Applied Mechanics, 53, 1986, 849–863.
Belytschko, T. and Hughes, T.J.R., Computational Methods for Transient Analysis, Elsevier Science Publishers, Amsterdam, 1983.
Shabana, A.A. and Christensen, A.P., ‘Three dimensional absolute nodal coordinate formulation: Plate problem’, International Journal for Numerical Methods in Engineering, in press.
Christensen, A.P. and Shabana, A.A., ‘Exact modeling of the spatial rigid body inertia using the finite element method’, ASME Journal of Vibration and Acoustics, in press.
Shabana, A.A., Vibration of Discrete and Continuous Systems, Second Edition, Springer-Verlag, New York, 1996.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shabana, A. Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation. Multibody System Dynamics 1, 339–348 (1997). https://doi.org/10.1023/A:1009740800463
Issue Date:
DOI: https://doi.org/10.1023/A:1009740800463