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Technical Brief

ANCF Consistent Rotation-Based Finite Element Formulation

[+] 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

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 7, 2015; final manuscript received August 10, 2015; published online September 14, 2015. Assoc. Editor: Ahmet S. Yigit.

J. Comput. Nonlinear Dynam 11(1), 014502 (Sep 14, 2015) (4 pages) Paper No: CND-15-1203; doi: 10.1115/1.4031292 History: Received July 07, 2015; Revised August 10, 2015

In this technical brief, a consistent rotation-based formulation is proposed using the absolute nodal coordinate formulation (ANCF) kinematic description. The proposed formulation defines a unique rotation field, employs one interpolation, captures shear deformations, does not suffer from the redundancy problem encountered when using large rotation vector formulations, allows for systematically describing curved geometry, and leads to elastic force definitions that eliminate high-frequency modes associated with the deformation of the cross section. The drawback of this formulation, as it is the case with the large rotation vector formulations, is the nonlinearity of the inertia forces including nonzero Coriolis and centrifugal forces. Furthermore, the formulation does not capture deformation modes that can be captured using the more general ANCF finite elements. Nonetheless, the proposed method is consistent with the continuum mechanics general description, can be related to computational geometry methods, and can be used to develop beam, plate, and shell models without violation of basic mechanics principles.

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