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力学与实践 ›› 2008, Vol. 30 ›› Issue (1): 31-34.doi: 10.6052/1000-0992-2007-264

• 应用研究 • 上一篇    下一篇

理性Timoshenko梁单元及其应用

朱炳麒 陈学宏   

  1. 河海大学机电工程学院,江苏 常州 213022 河海大学
  • 收稿日期:2007-06-18 修回日期:1900-01-01 出版日期:2008-02-08 发布日期:2008-02-08

RATIONAL TIMOSHENKO BEAM ELEMENT AND ITS APPLICATION

CHEN Xue-Hong   

  • Received:2007-06-18 Revised:1900-01-01 Online:2008-02-08 Published:2008-02-08

摘要: 将理性有限元法引入到Timoshenko梁问题中,提出了一种理性Timoshenko梁单元,克服了 剪切锁死现象. 在推导控制方程时,与传统有限元方法采用Lagrange插值不同, 理性有限元法用Timoshenko梁弯曲问题的基本解逼近单元内部场. 运用该梁单元分析 Timoshenko梁时,无需缩减积分,就能避免剪切锁死,并且极大地提高了计算精度,说明 理性有限元法具有广泛的应用前景.

关键词: 理性有限元, Timoshenko梁单元, 有限元, 剪切锁死

Abstract: Rational FEM is used in Timoshenko beam problems. A kind of rational Timoshenko beam element is proposed, to avoid shear locking. In deriving the governing equations, some basic analytic solutions of Timoshenko beam problems are used to approximate the inner field of the element. This method is different from Lagrange interpolation used in the conventional FEM. The rational Timoshenko beam element can avoid shear locking without a reduced integration. Numerical results show that the element's precision is very high. It is shown that the rational FEM has a very wide application.

Key words: rational finite element, Timoshenko beam element, finite element method, shear locking