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A truly self-starting implicit family of integration algorithms with dissipation control for nonlinear dynamics

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Abstract

In this paper, a novel implicit family of composite two sub-step algorithms with controllable dissipations is developed to effectively solve nonlinear structural dynamic problems. The primary superiority of the present method over other existing integration methods lies that it is truly self-starting and so the computation of initial acceleration vector is avoided, but the second-order accurate acceleration responses can be provided. Besides, the present method also achieves other desired numerical characteristics, such as the second-order accuracy of three primary variables, unconditional stability and no overshoots. Particularly, the novel method achieves adjustable numerical dissipations in the low and high frequency by controlling its two algorithmic parameters (\( \gamma \) and \( \rho _{\infty }\)). The classical dissipative parameter \( \rho _{\infty }\) determines numerical dissipations in the high-frequency while \( \gamma \) adjusts numerical dissipations in the low-frequency. Linear and nonlinear numerical examples are given to show the superiority of the novel method over existing integration methods with respect to accuracy and overshoot.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11372084). The helpful and constructive comments by the referees have led to the improvements of this paper; the authors gratefully acknowledge this assistance.

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  1. Department of Astronautic Science and Mechanics, Harbin Institute of Technology, No.92 West Dazhi Street, Harbin, 150001, China

    Jinze Li & Kaiping Yu

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  1. Jinze Li
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Correspondence to Kaiping Yu.

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Li, J., Yu, K. A truly self-starting implicit family of integration algorithms with dissipation control for nonlinear dynamics. Nonlinear Dyn 102, 2503–2530 (2020). https://doi.org/10.1007/s11071-020-06101-8

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