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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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Kerkkänen, K. S., García-Vallejo, D., and Mikkola, A. M., 2006, “Modeling of Belt-Drives Using a Large Deformation Finite Element Formulation,” Nonlinear Dyn., 43, pp. 239–256. [CrossRef]
Dufva, K., Kerkkänen, K., Maqueda, L. G., and Shabana, A. A., 2007, “Nonlinear Dynamics of Three-Dimensional Belt Drives Using the Finite-Element Method,” Nonlinear Dyn., 48, pp. 449–466. [CrossRef]
Maqueda, L. G., Mohamed, A.-N. A., and Shabana, A. A., 2010, “Use of General Nonlinear Material Models in Beam Problems: Application to Belts and Rubber Chains,” ASME J. Comput. Nonlinear Dyn., 5, p. 021003. [CrossRef]
Čepon, G., Manin, L., and Boltežar, M., 2009, “Introduction of Damping Into the Flexible Multibody Belt-Drive Model: A Numerical and Experimental Investigation,” J. Sound Vib., 324, pp. 283–296. [CrossRef]
Čepon, G., and Boltežar, M., 2008, “Dynamics of a Belt-Drive System Using a Linear Complementarity Problem for Belt-Pulley Contact Description,” J. Sound Vib., 319, pp. 1019–1035. [CrossRef]
Yu, L., Zhao, Z., and Ren, G., 2010, “Multibody Dynamics Model of Web Guiding System With Moving Web,” ASME J. Dyn. Syst., Meas., Control, 132, p. 051004. [CrossRef]
Omar, M. A., Shabana, A. A., Mikkola, A. M., Loh, W. Y., and Basch, R., 2004, “Multibody System Modeling of Leaf Springs,” J. Vib. Control, 10, pp. 1601–1638. [CrossRef]
Sugiyama, H., and Suda, Y., 2009, “Nonlinear Elastic Ring Tire Model Using the Absolute Nodal Coordinate Formulation,” Inst. Mech. Eng., Part K: J. Multi-Body Dyn., 223, pp. 211–219 [CrossRef].
Seo, J. H., Sugiyama, H., and Shabana, A. A., 2005, “Three-Dimensional Large Deformation Analysis of the Multibody Pantograph/Catenary Systems,” Nonlinear Dyn., 42, pp. 199–215. [CrossRef]
Seo, J. H., Kim, S. W., Jung, I. H., Park, T. W., Mok, J. Y., Kim, Y. G., and Chai, J. B., 2006, “Dynamic Analysis of a Pantograph-Catenary System Using Absolute Nodal Coordinates,” Veh. Syst. Dyn., 44, pp. 615–630. [CrossRef]
Shabana, A. A., Zaazaa, K. E., and Sugiyama, H., 2008, Railroad Vehicle Dynamics: A Computational Approach, CRC, Boca Raton, FL.
Kato, I., Terumichi, Y., Adachi, M., and Sogabe, K., 2005, “Dynamics of Track/Wheel Systems on High-Speed Vehicles,” J. Mech. Sci. Technol., 1, pp. 328–335. [CrossRef]
Gantoi, F. M., Brown, M. A., and Shabana, A. A., 2010, “ANCF Finite Element/Multibody System Formulation of the Ligament/Bone Insertion Site Constraints,” ASME J. Comput. Nonlinear Dyn., 5(3), p. 031006. [CrossRef]
Weed, D., Maqueda, L. G., Brown, M. A., Hussein, B. A., and Shabana, A. A., 2010, “A New Nonlinear Multibody/Finite Element Formulation for Knee Joint Ligaments,” Nonlinear Dyn., 60, pp. 357–367. [CrossRef]
Brown, M. A., Gantoi, F. M., and Shabana, A. A., 2010, “ANCF Finite Element/Multibody System Formulation of the Ligament/Bone Insertion Site Constraints,” ASME J. Comput. Nonlinear Dyn., 5, p. 031006. [CrossRef]
Stangl, M., Gerstmayr, J., and Irschik, H., 2009, “A Large Deformation Planar Finite Element for Pipes Conveying Fluid Based on the Absolute Nodal Coordinate Formulation,” ASME J. Comput. Nonlinear Dyn., 4, p. 031009. [CrossRef]
Vohar, B., Kegl, M., and Ren, Z., 2008, “Implementation of an ANCF Beam Finite Element for Dynamic Response Optimization of Elastic Manipulators,” Eng. Optimiz., 40, pp. 1137–1150. [CrossRef]
Nachbagauer, K., Zehetner, C., and Gerstmayr, J., 2011, Nonlinear Finite Element Modelling of Moving Beam Vibrations Controlled by Distributed Actuators, Advanced Dynamics and Model-Based Control of Structures and Machines, Springer, Vienna, pp. 167–174.
Sugiyama, H., Mikkola, A. M., and Shabana, A. A., 2003, “A Non-Incremental Nonlinear Finite Element Solution for Cable Problems,” ASME J. Mech. Des., 125, pp. 746–756. [CrossRef]
He, J., and Lilley, C. M., 2009, “The Finite Element Absolute Nodal Coordinate Formulation Incorporated With Surface Stress Effect to Model Elastic Bending Nanowires in Large Deformation,” Comput. Mech., 44, pp. 395–403. [CrossRef]
Khude, K., Melanz, D., Stanciulescu, I., and Negrut, D., 2011, “A Parallel GPU Implementation of the Absolute Nodal Coordinate Formulation With a Frictional/Contact Model for the Simulation of Large Flexible Body Systems,” Proceedings of the 8th International Conference on Multibody Systems, Nonlinear Dynamics and Control.

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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