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

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 meth...

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Bibliographic Details
Published in:Nonlinear dynamics Vol. 96; no. 4; pp. 2475 - 2507
Main Authors: Li, Jinze, Yu, Kaiping, Li, Xiangyang
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.06.2019
Springer Nature B.V
Subjects:
Algorithms
Automotive Engineering
Classical Mechanics
Control
Controllability
Dissipation
Dynamical Systems
Engineering
Frequency ranges
Mechanical Engineering
Original Paper
Stiffness matrix
Vibration
Composite algorithm
Structural dynamics
Controllable numerical dissipations
Three sub-step algorithm
Bathe algorithm
ISSN:0924-090X, 1573-269X
Online Access:Get full text
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Summary: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.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-019-04936-4