结构动力学中的广义多步显式积分算法

杨超; 朱涛; 杨冰; 阳光武; 鲁连涛; 肖守讷

doi:10.3969/j.issn.0258-2724.2017.01.019

结构动力学中的广义多步显式积分算法

doi: 10.3969/j.issn.0258-2724.2017.01.019

基金项目:

国家自然科学基金资助项目（51275432，51405402，51505390）

国家重点研发计划资助项目（2016YFB1200403，2016YFB1200404）

详细信息

作者简介:
杨超(1988-),男,博士,研究方向为列车碰撞动力学,E-mail:yangchaosky@foxmail.com

通讯作者:
肖守讷(1964-),男,研究员,研究方向为机车车辆设计及理论,E-mail:snxiao@home.swjtu.edu.cn

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出版历程
- 收稿日期: 2016-03-08
- 刊出日期: 2017-02-25

Generalized Multi-step Explicit Integration Method in Structural Dynamics

摘要

摘要: 为了开发新的时间积分算法，通过对独立变量加速度的加权，提出了广义多步显式积分算法（GMEM）.首先，在加速度显式法的基础上给出了通用的积分格式；其次，分析了所提算法的稳定性、数值耗散、数值色散和精度；最后，通过2个算例对3个广义多步显式积分算法（GMEM1、GMEM2和GMEM3-2）以及HHT-法和Newmark法进行了对比分析.分析结果表明：本文所提算法是条件稳定的，在无阻尼系统中谱半径恒等于1；3步广义多步显式法最高具有3阶精度，在无阻尼系统中不存在数值耗散；GMEM2的均方根误差约为Newmark法的1/2，约为GMEM3-2的1.8倍.
- 结构动力学 /
- 显式积分算法 /
- 数值算法 /
- 稳定性 /
- 精度
Abstract: In order to develop new time integration algorithms, a generalized multi-step explicit integration method (GMEM) was proposed by means of weighting independent variables, accelerations. Firstly, a general integration format was provided based on the acceleration explicit method. Furthermore, the stability, numerical dissipation, numerical dispersion and accuracy were analyzed. Finally, two numerical examples were employed to contrastively analyze three kinds of GMEMs (GMEM1, GMEM2 and GMEM3-2), the HHT- method and the Newmark method. The results indicate that the GMEM is conditionally stable. The spectral radius is identically equal to 1 in the system without damping. The GMEM of three steps can achieve the highest accuracy of three order. There is not numerical dissipation for the GMEM of three steps in undamped systems. The root mean square error of the GMEM2 is approximately half of that of the Newmark method, and 1.8 times that of the GMEM3-2 approximately.
- structural dynamics /
- explicit integration method /
- numerical method /
- stability /
- accuracy

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