结构动力方程的显式级数积分格式

英文篇名：Explicit integral method with Taylor series for structural dynamic equation
中文刊名：地震工程与工程振动
英文刊名：Journal of Earthquake Engineering and Engineering Vibration
作者：郭泽英 ; 李青宁
英文作者：GUO Zeying1 ; 2 ; LI Qingning2(1.School of Engineering ; Shanxi Normal University ; Linfen 041004 ; China ; 2.School of Civil Engineering ; Xi'an University of Architecture and Technology ; Xi'an 710055 ; China)
中文关键词：结构动力方程 ; 常平均加速度法 ; 精细算法 ; Taylor级数 ; 稳定性
英文关键词：structural dynamic equation ; constant average acceleration method ; precise exponential matrix calculation ; Taylor series ; stability
出版日期：2009-08-15
机构：山西师范大学工程学院;西安建筑科技大学土木工程学院;
年：2009
期：04
出版单位：地震工程与工程振动

摘要

将Newmark-β法中常平均加速度法的基本假定与精细指数算法结合,根据指数矩阵的Taylor级数展开式,提出了动力方程的显式级数解,并设计了相应的时程积分算法。该算法的精度可根据Taylor级数展开式的项数进行灵活控制。算例的结果表明:在满足稳定性条件的前提下,随着时间步长的增加,其精度优于传统的时程积分法。通过稳定性的分析,指出其稳定性条件是显然满足的。
Combining the precise exponential matrix calculation with the basic assumptions of constant average acceleration method of the Newmark family,explicit integral method with Taylor series and its algorithm are put forward.The accuracy of the algorithm can be controlled by choosing the number of Taylor series expansion.Results of the example show that the accuracy of the algorithm is better than that of traditional scheme with the increase of time step depending on the stable conditions.The analysis of stability shows the stable conditions are obviously satisfied.

引文

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