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contributor authorAhmed A. Shabana
date accessioned2017-05-09T00:36:46Z
date available2017-05-09T00:36:46Z
date copyrightOctober, 2010
date issued2010
identifier issn1555-1415
identifier otherJCNDDM-25733#044501_1.pdf
identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/142713
description abstractSeveral finite element formulations used in the analysis of large rotation and large deformation problems employ independent interpolations for the displacement and rotation fields. As explained in this paper, three rotations defined as field variables can be sufficient to define a space curve that represents the element centerline. The frame defined by the rotations can differ from the Frenet frame of the space curve defined by the same rotation field and, therefore, such a rotation-based representation can provide measure of twist shear deformations and captures the rotation of the beam about its axis. However, the space curve defined using the rotation interpolation has a geometry that can significantly differ from the geometry defined by an independent displacement interpolation. Furthermore, the two different space curves defined by the two different interpolations can differ by a rigid body motion. Therefore, in these formulations, the uniqueness of the kinematic representation is an issue unless nonlinear algebraic constraint equations are used to establish relationships between the two independent displacement and rotation interpolations. Nonetheless, significant geometric and kinematic differences between two independent space curves cannot always be reduced by using restoring elastic forces. Because of the nonuniqueness of such a finite element representation, imposing continuity on higher derivatives such as the curvature vector is not straight forward as in the case of the absolute nodal coordinate formulation (ANCF) that defines unique displacement and rotation fields. ANCF finite elements allow for imposing curvature continuity without increasing the order of the interpolation or the number of nodal coordinates, as demonstrated in this paper. Furthermore, the relationship between ANCF finite elements and the B-spline representation used in computational geometry can be established, allowing for a straight forward integration of computer aided design and analysis.
publisherThe American Society of Mechanical Engineers (ASME)
titleUniqueness of the Geometric Representation in Large Rotation Finite Element Formulations
typeJournal Paper
journal volume5
journal issue4
journal titleJournal of Computational and Nonlinear Dynamics
identifier doi10.1115/1.4001909
journal fristpage44501
identifier eissn1555-1423
keywordsRotation
keywordsFinite element analysis
keywordsEquations
keywordsInterpolation
keywordsDisplacement
keywordsDeformation AND Motion
treeJournal of Computational and Nonlinear Dynamics:;2010:;volume( 005 ):;issue: 004
contenttypeFulltext


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