| 张志刚,齐朝晖,吴志刚,方慧青.考虑变形耦合的几何非线性空间梁单元[J].计算力学学报,2014,31(5):603~608,621 |
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| 考虑变形耦合的几何非线性空间梁单元 |
| A geometrical nonlinear space beam element with considering deformation coupling |
| 投稿时间：2013-06-01 修订日期：2013-11-18 |
| DOI：10.7511/jslx201405010 |
| 中文关键词: 空间梁单元 几何非线性 大转动 节点力 |
| 英文关键词:spatial beam elements geometrically nonlinearity finite rotations nodal forces |
| 基金项目:国家自然科学基金（11372057）资助项目. |
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| 中文摘要: |
| 以“精确几何模型梁单元”为代表的很多几何非线性梁单元，在构造过程中分别对描述截面转动的转角和描述截面形心位置的位移进行了独立插值，由此引起了诸如运动学描述冗余和剪切闭锁等困难。其根本原因在于单元形函数没能体现细长梁中的变形耦合关系。本文对这类传统单元进行了改造，通过深入研究单元变形之间的内在联系，提出了一种变形场完全满足Bernoulli梁变形耦合关系的新单元，避免了构造过程中对转动矢量的插值，并通过数值算例检验了单元的有效性。 |
| 英文摘要: |
| In the construction process of beam elements that are capable of tackling geometrical nonlinear problems,such as "the geometrically exact beam elements",the angles describing the rotation of beam sections and the displacements of centroids are interpolated independently.In such elements,the element shape functions cannot represent the coupling effects among the different kinds of deformations when a beam can be viewed as slender,resulting in some difficulties very hard to deal with,such as the redundancy in kinematic description and shear locking.In this paper,traditional beam elements are modified through the detailed study on the interrelations among different kinds of deformation of a beam.Based on the obtained results,we propose a new kind of beam element whose pattern of deformations are coincide with the pattern given by the Bernoulli beams theory,moreover,the interpolation of rotation vectors is not necessary.Three numerical examples are given to validate the proposed element. |
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