A-stable two-step time integration methods with controllable numerical dissipation for structural dynamics
A-stable two-step time integration methods with controllable numerical dissipation for structural dynamics
复制标题
结构动力学可控数值耗散的稳定两步时间积分方法
DOI：
10.1002/nme.6188
复制
发表时间：
2020
影响因子：
2.9
通讯作者：
Jie Zhang
中科院分区：
文献类型：
--
作者：
Jie Zhang
本文对用于结构动力学分析的A稳定线性两步时间积分方法进行了全面的研究。提出了一种最优的A稳定线性两步时间积分方法，该方法在低频精度和高频数值耗散性能上都具有良好的性能。对结构动力学的二阶方程采用直接积分的方式实现了OALTS时间积分方法；是隐式的，A稳定的，并且在位移，速度和加速度上同时是二阶精确的；容易启动；且数值耗散是否可控。OALTS时间积分方法在谱半径分布、耗散和色散误差以及超调行为等方面表现出较好的性能，并对文献中几种典型算法的结果进行了比较。通过有/无物理阻尼的基准算例验证了OALTS时间积分方法的精度、稳定性和效率。
A comprehensive study of A‐stable linear two‐step time integration methods for structural dynamics analysis is presented in this paper. An optimal A‐stable linear two‐step (OALTS) time integration method is revealed with desirable performance on low‐frequency accuracy and high‐frequency numerical dissipation properties. The OALTS time integration method is implemented in a direct integration manner for the second‐order equations of structural dynamics; is implicit, A‐stable, and second‐order accurate in displacement, velocity, and acceleration, simultaneously; is easily started; and is numerical dissipation controllable. The OALTS time integration method shows desirable performance on spectral radius distribution, dissipation and dispersion errors, and overshooting behavior, where the results of some typical algorithms in the literature are also compared. Benchmark examples with/without physical damping are performed to validate the accuracy, stability, and efficiency of the OALTS time integration method.