Affiliation:
1. Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor St., Chicago, IL 60607-7022
Abstract
This part of these two companion papers demonstrates the computer implementation of the absolute nodal coordinate formulation for three-dimensional beam elements. Two beam elements that relax the assumptions of Euler-Bernoulli and Timoshenko beam theories are developed. These two elements take into account the effect of rotary inertia, shear deformation and torsion, and yet they lead to a constant mass matrix. As a consequence, the Coriolis and centrifugal forces are identically equal to zero. Both beam elements use the same interpolating polynomials and have the same number of nodal coordinates. However, one of the elements has two nodes, while the other has four nodes. The results obtained using the two elements are compared with the results obtained using existing incremental methods. Unlike existing large rotation vector formulations, the results of this paper show that no special numerical integration methods need to be used in order to satisfy the principle of work and energy when the absolute nodal coordinate formulation is used. These results show that this formulation can be used in manufacturing applications such as high speed forming and extrusion problems in which the element cross section dimensions significantly change.
Subject
Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials
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4. Shabana, A. A., and Yakoub, R., 2001, “Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory,” Submitted to the ASME J. Mech. Des., a companion paper.
5. Shabana, A. A., 1996, “An Absolute Nodal Coordinate Formulation for the Large Rotation and Deformation Analysis of Flexible Bodies,” Technical Report MBS96-1-UIC, University of Illinois at Chicago, Chicago, IL.
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