工程力学 ›› 2019, Vol. 36 ›› Issue (6): 21-28.doi: 10.6052/j.issn.1000-4750.2018.01.0033

• 基本方法 • 上一篇    下一篇

Timoshenko梁能量守恒逐步积分算法

杨浩文1, 吴斌2, 潘天林3, 谢金哲1   

  1. 1. 哈尔滨工业大学土木工程学院, 哈尔滨 150090;
    2. 武汉理工大学土木与建筑学院, 武汉 430070;
    3. 东北电力大学建筑工程学院, 吉林 132012
  • 收稿日期:2018-01-15 修回日期:2019-03-25 出版日期:2019-06-25 发布日期:2019-05-31
  • 通讯作者: 吴斌(1970-),男,湖北人,教授,博士,博导,主要从事结构抗震研究(E-mail:wbhit@sina.com). E-mail:wbhit@sina.com
  • 作者简介:杨浩文(1992-),男,甘肃人,博士生,主要从事数值积分方法研究(E-mail:yanghwhit@163.com);潘天林(1984-),男,辽宁人,讲师,博士,主要从事结构抗震研究(E-mail:pantianlin202@126.com);谢金哲(1993-),男,湖北人,硕士生,主要从事数值积分方法研究(E-mail:453772665@qq.com).
  • 基金资助:
    国家重点研发计划课题项目(2016YFC0701106);国家重点研发计划项目(2017YFC0703605);国家自然科学基金项目(51878525)

ENERGY-CONSERVING TIME INTEGRATION METHOD FOR TIMOSHENKO BEAMS

YANG Hao-wen1, WU Bin2, PAN Tian-lin3, XIE Jin-zhe1   

  1. 1. School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China;
    2. School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China;
    3. School of Civil Engineering and Architecture, Northeast Electric Power University, Jilin 132012, China
  • Received:2018-01-15 Revised:2019-03-25 Online:2019-06-25 Published:2019-05-31

摘要: 该文提出了Timoshenko梁非线性动力分析的能量守恒逐步积分算法。采用共旋技术考虑结构的几何非线性,空间离散采用相关插值形式,避免了剪切锁定现象。在时间离散时利用多参数修正方法对等效的节点动力平衡方程进行修正,实现了离散系统在保守荷载作用下的能量守恒。算法具备二阶局部精度,与已有的平均加速度方法和隐式中点方法相比,具有更好的数值稳定性。在二维情形下与Simo方法对比,指出了Simo方法在受保守外弯矩作用时系统能量不守恒。最后,通过三个数值模拟算例验证了算法的性能和能量守恒特性。

关键词: 结构动力分析, 能量守恒算法, 几何非线性, 有限单元法, Timoshenko梁

Abstract: An energy-conserving time integration method is proposed for the nonlinear dynamic analysis of Timoshenko beams. Co-rotational techniques are used to consider its structural geometric nonlinearity, and a linked interpolation form is adopted in the spatial discretization to avoid shear-locking phenomenon of a beam. The multi-parameter correction method is used to modify the equivalent nodal dynamic equations in the time discretization, which results in the energy conservation of the discrete system under conservative loading. The method has second-order local accuracy and shows better numerical stability, compared to the average acceleration method and the implicit midpoint method. The proposed method is compared to the Simo's method in two-dimensional cases and it is found that the Simo's method does not conserve system energy under a conservative external moment. Finally, the excellent performance and energy-conserving characteristic of the algorithm are verified by three numerical simulations.

Key words: structural dynamic analysis, energy-conserving method, geometric nonlinearity, the finite element method, Timoshenko beam

中图分类号: 

  • TU311.41
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