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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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
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Abstract	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.
AbstractList	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. 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.
Author	Li, Jinze Yu, Kaiping
Author_xml	– sequence: 1 givenname: Jinze surname: Li fullname: Li, Jinze organization: Department of Astronautic Science and Mechanics, Harbin Institute of Technology – sequence: 2 givenname: Kaiping surname: Yu fullname: Yu, Kaiping email: yukp@hit.edu.cn organization: Department of Astronautic Science and Mechanics, Harbin Institute of Technology
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Snippet	A novel family of composite sub-step algorithms with controllable numerical dissipations is proposed in this paper to obtain reliable numerical responses in...
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SubjectTerms	Algorithms Classical Mechanics Computational efficiency Computing costs Cost analysis Engineering Frequency ranges Linear systems Original Stability Stiffness matrix Theoretical and Applied Mechanics
Title	A novel family of composite sub-step algorithms with desired numerical dissipations for structural dynamics
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