Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications
Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications
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DOI：
10.1115/1.1410099
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发表时间：
2001-12
影响因子：
3.3
通讯作者：
R. Y. Yakoub;A. Shabana
中科院分区：
文献类型：
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作者：
R. Y. Yakoub;A. Shabana
这两篇论文的这一部分演示了三维梁单元绝对节点坐标公式的计算机实现。两个梁元素放松假设的欧拉-伯努利和Brachshenko梁理论的发展。这两个元素考虑了转动惯量、剪切变形和扭转的影响，但它们导致恒定的质量矩阵。结果，科里奥利力和离心力都等于零。两个梁单元使用相同的插值多项式，并具有相同数量的节点坐标。然而，其中一个元素有两个节点，而另一个有四个节点。使用这两个元素所获得的结果进行了比较，使用现有的增量方法所获得的结果。不同于现有的大旋转矢量公式，本文的结果表明，没有特殊的数值积分方法需要使用，以满足功能原理时，绝对节点坐标公式。这些结果表明，该配方可用于制造应用，例如元件横截面尺寸显着变化的高速成形和挤压问题。
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.