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Spatial ANCF/CRBF beam elements

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Abstract

In this paper, the consistent rotation-based formulation (CRBF) is used to develop new three-dimensional beam elements starting with the absolute nodal coordinate formulation (ANCF) kinematic description. While the proposed elements employ orientation parameters as nodal coordinates, independent rotation interpolation is avoided, leading to unique displacement and rotation fields. Furthermore, the proposed spatial ANCF/CRBF-based beam elements adhere to the noncommutative nature of the rotation parameters, allow for arbitrarily large three-dimensional rotation, and eliminate the need for using co-rotational or incremental solution procedures. Because the proposed elements have a general geometric description consistent with computational geometry methods, accurate definitions of the shear and bending deformations can be developed and evaluated, and curved structures and complex geometries can be systematically modeled. Three new spatial ANCF/CRBF beam elements, which use absolute positions and rotation parameters as nodal coordinates, are proposed. The time derivatives of the ANCF transverse position vector gradients at the nodes are expressed in terms of the time derivatives of rotation parameters using a nonlinear velocity transformation matrix. The velocity transformation leads to lower-dimensional elements that ensure the continuity of stresses and rotations at the element nodal points. The numerical results obtained from the proposed ANCF/CRBF elements are compared with the more general ANCF beam elements and with elements implemented in a commercial FE software.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Shubhankar Kulkarni & Ahmed A. Shabana

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  1. Shubhankar Kulkarni
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  2. Ahmed A. Shabana
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Correspondence to Ahmed A. Shabana.

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Kulkarni, S., Shabana, A.A. Spatial ANCF/CRBF beam elements. Acta Mech 230, 929–952 (2019). https://doi.org/10.1007/s00707-018-2294-0

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