@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 [tk, tk + h] where h stands for the size of a time step is divided into two sub-steps [tk, tk + γh] and [tk + γh, tk + h]. 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 γ. The rst approach determines γ by maximizing low-frequency accuracy and the other determines γ 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 ≤ ρ < 1 and fourth-order accurate when ρ = 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} }