工程力学 ›› 2018, Vol. 35 ›› Issue (10): 1-9,36.doi: 10.6052/j.issn.1000-4750.2017.06.0434

• 基本方法 •    下一篇

基于桁架单元的能量一致积分方法

潘天林1,2, 吴斌2,3   

  1. 1. 东北电力大学建筑工程学院, 吉林 132012;
    2. 哈尔滨工业大学土木工程学院, 哈尔滨 150090;
    3. 武汉理工大学土木与建筑学院, 武汉 430070
  • 收稿日期:2017-06-06 修回日期:2018-01-10 出版日期:2018-10-12 发布日期:2018-10-12
  • 通讯作者: 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). E-mail:pantianlin202@126.com
  • 作者简介:吴斌(1970-),男,湖北人,教授,博士,博导,主要从事结构抗震和防灾减灾研究(E-mail:bin.wu@hit.edu.cn).
  • 基金资助:
    国家重点研发计划项目(2016YFC0701106);青年科学基金项目(51808101);东北电力大学博士科研启动基金项目(BSJXM-2017110)

AN ENERGY CONSISTENT INTEGRATION METHOD FOR TRUSS ELEMENTS

PAN Tian-lin1,2, WU Bin2,3   

  1. 1. School of Civil Engineering and Architecture, Northeast Electric Power University, Jilin 132012, China;
    2. School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China;
    3. School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China
  • Received:2017-06-06 Revised:2018-01-10 Online:2018-10-12 Published:2018-10-12

摘要: 基于能量平衡理论,提出针对桁架单元的能量一致积分方法。该方法具有非线性无条件稳定性,2阶精度。利用中值定理证明算法参数的存在性,并给出参数的求解形式。对离散后的动力方程线性化得到用于迭代的等效刚度矩阵。实现新算法在非线性有限元程序中的嵌入,并以此为基础完成单摆、输电塔体结构的非线性动力分析。数值结果表明,经典的平均加速度方法与隐式中点方法均会表现出能量不一致现象,甚至会产生发散结果;相比而言,该文方法在不同的时间步长情况下都表现出良好的数值稳定性。

关键词: 工程力学, 时间积分算法, 能量一致, 无条件稳定性, 平均加速度方法, 桁架单元

Abstract: Based on the energy equilibrium theory, an energy consistent integration method for truss elements is proposed in this paper. The method is unconditionally stable in nonlinear systems, and its accuracy is second order. The existence of algorithm parameters is proved by mean value theorem, and the solution form of the parameters is also provided. The discrete dynamic equations are linearized to obtain the equivalent stiffness matrices for iteration. The new algorithm is embedded in a nonlinear finite element program. On the basis of this program, the nonlinear dynamic analysis of a single pendulum and a transmission tower structure is completed. The numerical results show that the classic average acceleration method and implicit midpoint method are both energy inconsistent and may even produce divergent results. In contrast, the proposed method has good stability within different time steps.

Key words: engineering mechanics, time integration algorithm, energy-consistent, unconditional stability, average acceleration method, truss elements

中图分类号: 

  • TU311.4
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