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New Insights into a Three-Sub-Step Composite Method and Its Performance on Multibody Systems

Author

Listed:
  • Yi Ji

    (MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China)

  • Huan Zhang

    (MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China)

  • Yufeng Xing

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

Abstract

This paper develops a new implicit solution procedure for multibody systems based on a three-sub-step composite method, named TTBIF (trapezoidal–trapezoidal backward interpolation formula). The TTBIF is second-order accurate, and the effective stiffness matrices of the first two sub-steps are the same. In this work, the algorithmic parameters of the TTBIF are further optimized to minimize its local truncation error. Theoretical analysis shows that for both undamped and damped systems, this optimized TTBIF is unconditionally stable, controllably dissipative, third-order accurate, and has no overshoots. Additionally, the effective stiffness matrices of all three sub-steps are the same, leading to the effective stiffness matrix being factorized only once in a step for linear systems. Then, the implementation procedure of the present optimized TTBIF for multibody systems is presented, in which the position constraint equation is strictly satisfied. The advantages in accuracy, stability, and energy conservation of the optimized TTBIF are validated by some benchmark multibody dynamic problems.

Suggested Citation

  • Yi Ji & Huan Zhang & Yufeng Xing, 2022. "New Insights into a Three-Sub-Step Composite Method and Its Performance on Multibody Systems," Mathematics, MDPI, vol. 10(14), pages 1-28, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2375-:d:856968
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    References listed on IDEAS

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    1. Jinyue Zhang & Lei Shi & Tianhao Liu & De Zhou & Weibin Wen, 2021. "Performance of a Three-Substep Time Integration Method on Structural Nonlinear Seismic Analysis," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-20, December.
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    Cited by:

    1. Yi Ji & Yufeng Xing, 2023. "Highly Accurate and Efficient Time Integration Methods with Unconditional Stability and Flexible Numerical Dissipation," Mathematics, MDPI, vol. 11(3), pages 1-36, January.

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    1. Yi Ji & Yufeng Xing, 2023. "Highly Accurate and Efficient Time Integration Methods with Unconditional Stability and Flexible Numerical Dissipation," Mathematics, MDPI, vol. 11(3), pages 1-36, January.

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