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Development of a family of explicit algorithms for structural dynamics with unconditional stability

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Abstract

A new family of explicit integration algorithms is developed based on discrete control theory for solving the dynamic equations of motion. The proposed algorithms are explicit for both displacement and velocity and require no factorisation of the damping matrix and the stiffness matrix. Therefore, for a system with nonlinear damping and stiffness, the proposed algorithms are more efficient than the common explicit algorithms that provide only explicit displacement. Accuracy and stability properties of the proposed algorithms are analysed theoretically and verified numerically. Certain subfamilies are found to be unconditionally stable for any system state (linear elastic, stiffness softening or stiffness hardening) that may occur in earthquake engineering of a practical structure. With dual explicit expression and excellent stability property, the proposed family of algorithms can potentially solve complicated nonlinear dynamic problems.

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Acknowledgments

This research is financially supported by the National Natural Science Foundation of China (Nos. 51179093, 91215301 and 41274106) and the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20130002110032). The authors express their sincerest gratitude for these supports.

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Authors and Affiliations

  1. State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing , 100084, China

    Yao Gui, Jin-Ting Wang, Feng Jin & Meng-Xia Zhou

  2. School of Engineering, San Francisco State University, San Francisco, CA , 94132, USA

    Cheng Chen

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  1. Yao Gui
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  2. Jin-Ting Wang
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  3. Feng Jin
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  4. Cheng Chen
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  5. Meng-Xia Zhou
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Correspondence to Feng Jin.

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Gui, Y., Wang, JT., Jin, F. et al. Development of a family of explicit algorithms for structural dynamics with unconditional stability. Nonlinear Dyn 77, 1157–1170 (2014). https://doi.org/10.1007/s11071-014-1368-3

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  • DOI: https://doi.org/10.1007/s11071-014-1368-3

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