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Research Papers

Review on the Absolute Nodal Coordinate Formulation for Large Deformation Analysis of Multibody Systems

[+] Author and Article Information
Johannes Gerstmayr

Austrian Center of Competence
in Mechatronics GmbH (ACCM),
Altenbergerstraße 69,
A-4040 Linz, Austria
e-mail: johannes.gerstmayr@accm.co.at

Hiroyuki Sugiyama

Department of Mechanical
and Industrial Engineering,
The University of Iowa,
Iowa City, IA 52242
e-mail: hiroyuki-sugiyama@uiowa.edu

Aki Mikkola

Department of Mechanical Engineering,
Lappeenranta University of Technology,
53850 Lappeenranta, Finland
e-mail: aki.mikkola@lut.fi

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received September 4, 2012; final manuscript received December 7, 2012; published online March 21, 2013. Assoc. Editor: José L. Escalona.

J. Comput. Nonlinear Dynam 8(3), 031016 (Mar 21, 2013) (12 pages) Paper No: CND-12-1139; doi: 10.1115/1.4023487 History: Received September 04, 2012; Revised December 07, 2012

The aim of this study is to provide a comprehensive review of the finite element absolute nodal coordinate formulation, which can be used to obtain efficient solutions to large deformation problems of constrained multibody systems. In particular, important features of different types of beam and plate elements that have been proposed since 1996 are reviewed. These elements are categorized by parameterization of the elements (i.e., fully parameterized and gradient deficient elements), strain measures used, and remedies for locking effects. Material nonlinearities and the integration of the absolute nodal coordinate formulation to general multibody dynamics computer algorithms are addressed with particular emphasis on visco-elasticity, elasto-plasticity, and joint constraint formulations. Furthermore, it is shown that the absolute nodal coordinate formulation has been applied to a wide variety of challenging nonlinear dynamics problems that include belt drives, rotor blades, elastic cables, leaf springs, and tires. Unresolved issues and future perspectives of the study of the absolute nodal coordinate formulation are also addressed in this investigation.

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Figures

Grahic Jump Location
Fig. 1

Geometric definition of basic ANCF finite elements for the 2D and 3D cases, based on the Bernoulli–Euler beam condition or the shear and cross-section deformable. The nodal coordinates are provided in parenthesis to each nodal or slope vector.

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