A novel family of composite sub-step algorithms with desired numerical dissipations for structural dynamics

  • Jinze Li
  • Kaiping YuEmail author


A novel family of composite sub-step algorithms with controllable numerical dissipations is proposed in this paper to obtain reliable numerical responses in structural dynamics. The new scheme is a self-starting, unconditionally stable and second-order-accurate two-sub-step algorithm with the same computational cost as the Bathe algorithm. The new algorithm can control continuously numerical dissipations in the high-frequency range in an intuitive way, and the ability of numerical dissipations can range from the non-dissipative trapezoidal rule to the asymptotic annihilating Bathe algorithm. Besides, the new algorithm only involves one free parameter and always achieves the identical effective stiffness matrices inside two sub-steps, which is not always achieved in three Bathe-type algorithms, to reduce the computational cost in the analysis of linear systems. Some numerical examples are given to show the superiority of the new algorithm over the Bathe algorithm and the CH-\(\alpha \) algorithm.


Sub-step algorithm Bathe algorithm Implicit integration algorithm Controllable numerical dissipation 



This work is supported by the National Natural Science Foundation of China (Grant No. 11372084). This support is gratefully acknowledged. 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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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Astronautic Science and MechanicsHarbin Institute of TechnologyHarbinChina

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