An Improved Higher-Order Time Integration Algorithm for Structural Dynamics

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, th...

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Bibliographic Details
Published in:Computer modeling in engineering & sciences Vol. 126; no. 2; pp. 549 - 575
Main Authors: Ji, Yi, Xing, Yufeng
Format: Journal Article
Language:English
Published: Henderson Tech Science Press 01.01.2021
Subjects:
Accuracy
Algorithms
Control stability
Controllable Dissipation
Damping
Design parameters
Higher-Order Accuracy
Numerical dissipation
Time integration
Time Integration Algorithm
Two-Sub-Step
Unconditional Stability
ISSN:1526-1492, 1526-1506, 1526-1506
Online Access:Get full text
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Summary: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 first sub-step to ensure low-frequency accuracy and a dissipative third-order algorithm is employed in the second sub-step to filter out the contribution of high-frequency modes. Besides, two approaches are used to design the algorithm parameter γ. The first approach determines γ by maximizing low-frequency accuracy and the other determines γ for quickly damping out high-frequency 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.
Bibliography:1526-1492(20210210)126:2L.549;1-
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ISSN:1526-1492
1526-1506
1526-1506
DOI:10.32604/cmes.2021.014244