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Improved two-stage implicit time integration methods with unconventionally determined parameters for analyses of linear and nonlinear structural dynamics

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Abstract

In this article, a simple way to determine algorithmic parameters included in time approximations of two-stage implicit time schemes is presented. To be specific, algorithmic parameters of time approximations are mathematically determined to give higher-order total energy convergence rates for conservative nonlinear problems while satisfying traditional linear accuracy requirements. Due to the use of newly proposed algorithmic parameters, two-stage implicit time schemes can possess enhanced total energy conserving capabilities for conservative nonlinear problems while providing improved linear performances when compared with those of the existing two-stage time schemes. Enhanced total energy conserving capabilities achieved through the use of newly proposed algorithmic parameters do not require any additional computational efforts when compared with the existing two-stage schemes. This article also explains that a certain standard type of two-stage implicit time schemes can reduce computational time and effort in linear analyses if effective coefficient matrices of the first and second stages are constructed identically. For the verification of improved numerical performances, linear and nonlinear benchmark problems are solved, and their numerical results are investigated to support the main discussions of this article.

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Data Availability

The data that supports the findings of this study is available from the corresponding author [Wooram Kim], upon reasonable request.

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Acknowledgements

The author deeply appreciates supports from Ra-Kyoung Yoon, Dal-Soo Yoon, and Seung-Im Paek.

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This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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  1. Department of Mechanical Engineering, Korea Army Academy at Yeongcheon, Yeongcheon-si, Gyeongsangbuk-do, 38900, Korea

    Wooram Kim

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  1. Wooram Kim
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Kim, W. Improved two-stage implicit time integration methods with unconventionally determined parameters for analyses of linear and nonlinear structural dynamics. Nonlinear Dyn 112, 1221–1259 (2024). https://doi.org/10.1007/s11071-023-09101-6

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