Journal article
Deformation modes in the finite element absolute nodal coordinate formulation
Journal of sound and vibration, Vol.298(4), pp.1129-1149
2006
DOI: 10.1016/j.jsv.2006.06.037
Abstract
The objective of this study is to provide interpretation of the deformation modes in the finite element absolute nodal coordinate formulation using several strain definitions. In this finite element formulation, the nodal coordinates consist of absolute position coordinates and gradients that can be used to define a unique rotation and deformation fields within the element as well as at the nodal points. The results obtained in this study clearly show cross-section deformation modes eliminated when the number of the finite element nodal coordinates is systematically and consistently reduced. Using the procedure discussed in this paper one can obtain a reduced order dynamic model, eliminate position vector gradients that introduce high frequencies to the solution of some problems, achieve the continuity of the remaining gradients at the nodal points, and obtain a formulation that automatically satisfies the principle of work and energy. Furthermore, the resulting dynamic model, unlike large rotation finite element formulations, leads to a unique rotation field, and as a consequence, the obtained formulation does not suffer from the problem of coordinate redundancy that characterizes existing large deformation finite element formulations. In order to accurately define strain components that can have easy physical interpretation, a material coordinate system is introduced to define the material element rotation and deformation. Using the material coordinate system, the Timoshenko–Reissner and Euler
–Bernoulli beam models can be systematically obtained as special cases of the absolute nodal coordinate formulation beam models. While a constraint approach is used in this study to eliminate the cross-section deformation modes, it is important to point out as mentioned in this paper that lower-order finite elements, some of which already presented in previous investigations, can be efficiently used in thin and stiff structure applications.
Details
- Title: Subtitle
- Deformation modes in the finite element absolute nodal coordinate formulation
- Creators
- Hiroyuki Sugiyama - Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607, USAJohannes Gerstmayr - Institute for Technical Mechanics, Johannes Kepler University of Linz, Altenbergerstr. 69, 4040 Linz, AustriaAhmed A Shabana - Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607, USA
- Resource Type
- Journal article
- Publication Details
- Journal of sound and vibration, Vol.298(4), pp.1129-1149
- Publisher
- Elsevier Ltd
- DOI
- 10.1016/j.jsv.2006.06.037
- ISSN
- 0022-460X
- eISSN
- 1095-8568
- Language
- English
- Date published
- 2006
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984064116202771
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