[1]徐俊杰.结构动力分析高阶时域积分算法的研究进展[J].地震工程与工程振动,2017,01(03):080-84.[doi:10.13197/j.eeev.2017.03.80.xujj.008]
 XU Junjie.A review of higher-order accurate time step integration algorithm for structural dynamics[J].EARTHQUAKE ENGINEERING AND ENGINEERING DYNAMICS,2017,01(03):080-84.[doi:10.13197/j.eeev.2017.03.80.xujj.008]
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结构动力分析高阶时域积分算法的研究进展
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《地震工程与工程振动》[ISSN:/CN:]

卷:
01
期数:
2017年03期
页码:
080-84
栏目:
论文
出版日期:
2017-08-30

文章信息/Info

Title:
A review of higher-order accurate time step integration algorithm for structural dynamics
作者:
徐俊杰
中国地震局工程力学研究所, 中国地震局地震工程与工程振动重点实验室, 黑龙江 哈尔滨 150080
Author(s):
XU Junjie
Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
关键词:
时域连续Galerkin时域间断Galerkin高阶单步法时域积分算法结构动力分析
Keywords:
time continuous galerkintime discontinuous galerkinhigh order single-step mothedtime step integration algorithmstructural dynamics
分类号:
TU311.3;TU311.4
DOI:
10.13197/j.eeev.2017.03.80.xujj.008
摘要:
本文简要综述了时域连续Galerkin(TCG),改进TCG,以及时域间断Galerkin(TDG)以及高阶单步法等几种典型的高阶时域积分算法。若采用p阶多项式对基本未知量进行插值近似,采用单场格式的常规TCG算法、改进TCG算法、两场格式的TDG算法求得的位移和速度分别具有p、2p、2p+1阶收敛精度,在计算成本相当的情况下,改进TCG算法具有最高收敛精度。高阶单步法多为后处理的算法,大多具有4阶精度。相比最常用的二阶算法,高阶单步法操作简单,易于实施,保留二阶算法无条件稳定、计算效率高等优点,可对二阶算法进行误差估计,并可根据精度需求,指导时间步长自适应调整。
Abstract:
In this paper, several typical high-order time step integration algorithms such as Time Continuous Galerkin (TCG), improved TCG, Time Discontinuous Galerkin (TDG) and high-order single-step method are briefly introduced. The displacement and velocity calculated by conventional TCG algorithm with single-field formulation, the improved TCG algorithm and the TDG algorithm with two-field formulation have the convergence accuracy of p, 2p, 2p+1 order, respectively. In the case of equivalent cost, the improved TCG algorithm has the highest convergence accuracy among these three algorithms. High-order single-step method mostly achieve accuracy of four order based on post-processing algorithms. Compared with the most commonly used second-order algorithm, the high-order single-step method has the advantages of simple operation, easy implementation, unconditionally stability and high computational efficiency, and can estimate the error of the second-order algorithm and guide the time step adaptive adjustment for goal-oriented computing.

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备注/Memo

备注/Memo:
收稿日期:2017-3-10;改回日期:2017-4-21。
基金项目:国家科技支撑计划课题(2015BAK17B02);中国地震局工程力学研究所基本科研业务费专项资助项目(2016A05);国家自然科学基金项目(51508529)
作者简介:徐俊杰(1984-),男,副研究员,博士,主要从事结构工程研究.E-mail:xujj@iem.ac.cn
更新日期/Last Update: 1900-01-01