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COMPARISON OF FULLY PARAMETERIZED AND GRADIENT DEFICIENT ELEMENTS IN THE ABSOLUTE NODAL COORDINATE FORMULATION

机译:绝对结点坐标公式中完全参数化和梯度不足元素的比较

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摘要

The aim of the present paper is to evaluate six particular beam finite elements based on the absolute nodal coordinate formulation (ANCF). Specifically, accuracy, computational efficiency and numerical stability are compared for those beam finite elements. The finite elements under consideration are planar as well as spatial beams, which are formulated both for the Bernoulli-Euler case as well as for shear and cross-section deformation. While all of the investigated elements have been exposed to specific numerical tests already before, a comparative test has not been performed in the past. The numerical examples cover large deformation static and dynamic problems, which represent typical applications of such beam elements. Finally, the dynamic test problems show that the thin spatial beam formulation, which includes a rotational parameter, leads to well-known numerical instabilities.
机译:本文的目的是基于绝对节点坐标公式(ANCF)评估六个特定的梁有限元。具体而言,比较了那些梁有限元的准确性,计算效率和数值稳定性。所考虑的有限元既是平面梁又是空间梁,它们是针对伯努利-欧拉情况以及剪切变形和横截面变形而制定的。尽管之前所有研究的元素都已经进行过特定的数值测试,但过去从未进行过对比测试。数值示例涵盖了大变形的静态和动态问题,这些问题代表了此类梁单元的典型应用。最后,动态测试问题表明,包含旋转参数的薄空间梁公式会导致众所周知的数值不稳定性。

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