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

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-startin...

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Bibliographic Details
Published in:Nonlinear dynamics Vol. 102; no. 4; pp. 2503 - 2530
Main Authors: Li, Jinze, Yu, Kaiping
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2020
Springer Nature B.V
Subjects:
Algorithms
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Mechanical Engineering
Nonlinear control
Nonlinear dynamics
Original Paper
Parameters
Stability
Vibration
Structural dynamics
Two sub-step scheme
Truly self-starting
Implicit integration algorithm
Controllable dissipation
ISSN:0924-090X, 1573-269X
Online Access:Get full text
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Summary: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 ( γ and ρ ∞ ). The classical dissipative parameter ρ ∞ determines numerical dissipations in the high-frequency while γ 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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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-06101-8