Nonlinear Dynamics

, Volume 96, Issue 4, pp 2475–2507 | Cite as

A novel family of controllably dissipative composite integration algorithms for structural dynamic analysis

  • Jinze Li
  • Kaiping YuEmail author
  • Xiangyang Li
Original Paper


In this paper, a new family of controllably dissipative composite algorithms is developed to obtain reliable numerical response of structural dynamic problems. The proposed algorithm is a self-starting, unconditionally stable and second-order accurate three sub-step composite algorithm. The new method includes two optimal sub-families of algorithms, both of which can control numerical dissipations in the high-frequency range by an intuitive way, and their numerical dissipations can range from the non-dissipative case to the asymptotic annihilating case. Besides, they actually involve only one free parameter and always share the identical effective stiffness matrices inside three sub-step to save the computational cost, which does not hold in some existing sub-step algorithms. Some numerical examples are given to show the superiority of the new algorithm with respect to controllable numerical dissipations and the ability of capturing the free-play nonlinearity.


Composite algorithm Bathe algorithm Structural dynamics Three sub-step algorithm Controllable numerical dissipations 



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.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this manuscript.


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© Springer Nature B.V. 2019

Authors and Affiliations

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

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