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A three-parameter single-step time integration method for structural dynamic analysis

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Abstract

The existing three-parameter single-step time integration methods, such as the Generalized-\(\alpha \) method, improve numerical dissipation by modifying equilibrium equation at time points, which cause them to lose accuracy due to the interpolation of load vectors. Moreover, these three-parameter methods do not present an available formulation applied to a general second-order nonlinear differential equation. To solve these problems, this paper proposes an innovative three-parameter single-step method by introducing an additional variable into update equations. Although the present method is spectrally identical to the Generalized-\(\alpha \) method for undamped systems, it possesses higher accuracy since it strictly satisfies the equilibrium equation at time points, and can be readily used to solve nonlinear equations. By the analysis of accuracy, stability, numerical dissipation and dispersion, the optimal second-order implicit and explicit schemes are generated, which can maximize low-frequency accuracy when high-frequency dissipation is specified. To check the performance of the proposed method, several numerical experiments are conducted and the proposed method is compared with a few up-to-date methods.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (11672019, 11372021, and 37686003).

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  1. Institute of Solid Mechanics, Beihang University (BUAA), Beijing, 100083, China

    Huimin Zhang & Yufeng Xing

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  1. Huimin Zhang
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  2. Yufeng Xing
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Correspondence to Yufeng Xing.

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Zhang, H., Xing, Y. A three-parameter single-step time integration method for structural dynamic analysis. Acta Mech. Sin. 35, 112–128 (2019). https://doi.org/10.1007/s10409-018-0775-y

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