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Technical Brief

# Definition of ANCF Finite Elements

[+] Author and Article Information
Ahmed A. Shabana

Department of Mechanical and Industrial Engineering,
University of Illinois at Chicago,
842 West Taylor Street,
Chicago, IL 60607
e-mail: shabana@uic.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 18, 2015; final manuscript received April 9, 2015; published online June 25, 2015. Assoc. Editor: Ahmet S. Yigit.

J. Comput. Nonlinear Dynam 10(5), 054506 (Sep 01, 2015) (5 pages) Paper No: CND-15-1069; doi: 10.1115/1.4030369 History: Received March 18, 2015; Revised April 09, 2015; Online June 25, 2015

## Abstract

Since the absolute nodal coordinate formulation (ANCF) was introduced, a large number of fully parametrized and gradient deficient finite elements were developed. Some of the finite elements (FE) proposed do not fall into the ANCF category, and for this reason, this technical brief describes the general requirements for ANCF finite elements. As discussed in this paper, some of the conventional isoparametric finite elements can describe arbitrary rigid body displacements and can be used with a nonincremental solution procedure. Nonetheless, these isoparametric elements, particularly the ones that employ position coordinates only, are of the $C0$ type and do not ensure the continuity of the position vector gradients. It is also shown that the position vector gradient continuity conditions can be described using homogeneous algebraic equations, and such conditions are different from those conditions that govern the displacement vector gradients. The use of the displacement vector gradients as nodal coordinates does not allow for an isoparametric representation that accounts for both the initial geometry and displacements using one kinematic description, can make the element assembly more difficult, and can complicate imposing linear algebraic constraint equations at a preprocessing stage. Understanding the ANCF geometric description will allow for the development of new mechanics-based computer-aided design (CAD)/analysis systems as briefly discussed in this paper.

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## References

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Shabana, A. A., 2015, “ANCF Tire Assembly Model for Multibody System Applications,” ASME J. Comput. Nonlinear Dyn., 10(2), p. 024504.
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## Figures

Fig. 1

Mechanics-based CAD/analysis models (• chassis/shackle revolute joint, ★ shackle/leaf spring revolute joint, ▲ leaf spring/axle revolute joint, and ▪ chassis/leaf spring revolute joint)

Fig. 2

Vehicle model

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