@Article{cmes.2021.014244,
AUTHOR = {Yi Ji, Yufeng Xing},
TITLE = {An Improved Higher-Order Time Integration Algorithm for Structural Dynamics},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {126},
YEAR = {2021},
NUMBER = {2},
PAGES = {549--575},
URL = {http://www.techscience.com/CMES/v126n2/41281},
ISSN = {1526-1506},
ABSTRACT = {Based on the weighted residual method, a single-step time integration algorithm with higher-order accuracy and
unconditional stability has been proposed, which is superior to the second-order accurate algorithms in tracking
long-term dynamics. For improving such a higher-order accurate algorithm, this paper proposes a two sub-step
higher-order algorithm with unconditional stability and controllable dissipation. In the proposed algorithm, a time
step interval [<i>tk</i>, <i>tk</i> + <i>h</i>] where h stands for the size of a time step is divided into two sub-steps [<i>tk</i>, <i>tk</i> + <i>γh</i>] and
[<i>tk</i> + <i>γh</i>, <i>tk</i> + <i>h</i>]. A non-dissipative fourth-order algorithm is used in the rst sub-step to ensure low-frequency
accuracy and a dissipative third-order algorithm is employed in the second sub-step to lter out the contribution of
high-frequency modes. Besides, two approaches are used to design the algorithm parameter <i>γ</i>. The rst approach
determines <i>γ</i> by maximizing low-frequency accuracy and the other determines <i>γ</i> for quickly damping out highfrequency modes. The present algorithm uses ρ∞ to exactly control the degree of numerical dissipation, and it
is third-order accurate when 0 ≤ <i>ρ</i><sub>∞</sub> < 1 and fourth-order accurate when <i>ρ</i><sub>∞</sub> = 1. Furthermore, the proposed
algorithm is self-starting and easy to implement. Some illustrative linear and nonlinear examples are solved to
check the performances of the proposed two sub-step higher-order algorithm.},
DOI = {10.32604/cmes.2021.014244}
}