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

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 c...

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Bibliographic Details
Published in:Archive of applied mechanics (1991) Vol. 90; no. 4; pp. 737 - 772
Main Authors: Li, Jinze, Yu, Kaiping
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2020
Springer Nature B.V
Subjects:
Algorithms
Classical Mechanics
Computational efficiency
Computing costs
Cost analysis
Engineering
Frequency ranges
Linear systems
Original
Stability
Stiffness matrix
Theoretical and Applied Mechanics
Sub-step algorithm
Controllable numerical dissipation
Implicit integration algorithm
Bathe algorithm
ISSN:0939-1533, 1432-0681
Online Access:Get full text
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Summary: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- α algorithm.
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ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-019-01637-7