An improved implicit time integration algorithm: The generalized composite time integration algorithm

•The algorithm can be applied to nonlinear structural dynamics in a consistent manner.•The algorithm includes one free parameter which controls algorithmic dissipation.•The effective stiffness matrices of the first and second sub-steps become identical in linear analyses.•The algorithm provided impr...

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Vydáno v:	Computers & structures Ročník 196; s. 341 - 354
Hlavní autoři:	Kim, Wooram, Choi, Su Yeon
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Elsevier Ltd 01.02.2018 Elsevier BV
Témata:	Accuracy Algorithms Bathe method Composite time integration Linear and non-linear structural dynamics Mathematical analysis Matrix Matrix methods Nonlinear analysis Optimization Parameters Step-by-step implicit time integration method Stiffness matrix Time finite element method Time integration Weighted residual method Linear and non-linear structural dynamics Composite time integration Bathe method Time finite element method Step-by-step implicit time integration method Weighted residual method
ISSN:	0045-7949, 1879-2243
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Abstract	•The algorithm can be applied to nonlinear structural dynamics in a consistent manner.•The algorithm includes one free parameter which controls algorithmic dissipation.•The effective stiffness matrices of the first and second sub-steps become identical in linear analyses.•The algorithm provided improved solutions compared with those obtained from the Bathe method. The weighted residual method is employed to develop one- and two-step time integration schemes. Newly developed time integration schemes are combined to obtain a new second-order accurate implicit time integration algorithm whose computational structure is similar to the Bathe method (Bathe and Noh, 2012). The newly developed algorithm can control algorithmic dissipation in the high frequency limit through the optimized weighting parameters. It contains only one free parameter, and always provides an identical effective stiffness matrix to the first and second sub-steps in linear analyses, which is not provided in the algorithm proposed by Kim and Reddy (2016). Various nonlinear test problems are used to investigate performance of the new algorithm in nonlinear analyses.
AbstractList	The weighted residual method is employed to develop one- and two-step time integration schemes. Newly developed time integration schemes are combined to obtain a new second-order accurate implicit time integration algorithm whose computational structure is similar to the Bathe method (Bathe and Noh, 2012). The newly developed algorithm can control algorithmic dissipation in the high frequency limit through the optimized weighting parameters. It contains only one free parameter, and always provides an identical effective stiffness matrix to the first and second sub-steps in linear analyses, which is not provided in the algorithm proposed by Kim and Reddy (2016). Various nonlinear test problems are used to investigate performance of the new algorithm in nonlinear analyses. •The algorithm can be applied to nonlinear structural dynamics in a consistent manner.•The algorithm includes one free parameter which controls algorithmic dissipation.•The effective stiffness matrices of the first and second sub-steps become identical in linear analyses.•The algorithm provided improved solutions compared with those obtained from the Bathe method. The weighted residual method is employed to develop one- and two-step time integration schemes. Newly developed time integration schemes are combined to obtain a new second-order accurate implicit time integration algorithm whose computational structure is similar to the Bathe method (Bathe and Noh, 2012). The newly developed algorithm can control algorithmic dissipation in the high frequency limit through the optimized weighting parameters. It contains only one free parameter, and always provides an identical effective stiffness matrix to the first and second sub-steps in linear analyses, which is not provided in the algorithm proposed by Kim and Reddy (2016). Various nonlinear test problems are used to investigate performance of the new algorithm in nonlinear analyses.
Author	Choi, Su Yeon Kim, Wooram
Author_xml	– sequence: 1 givenname: Wooram surname: Kim fullname: Kim, Wooram email: c14445@naver.com – sequence: 2 givenname: Su Yeon orcidid: 0000-0003-3385-6967 surname: Choi fullname: Choi, Su Yeon
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Keywords	Linear and non-linear structural dynamics Composite time integration Bathe method Time finite element method Step-by-step implicit time integration method Weighted residual method
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Snippet	•The algorithm can be applied to nonlinear structural dynamics in a consistent manner.•The algorithm includes one free parameter which controls algorithmic... The weighted residual method is employed to develop one- and two-step time integration schemes. Newly developed time integration schemes are combined to obtain...
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SubjectTerms	Accuracy Algorithms Bathe method Composite time integration Linear and non-linear structural dynamics Mathematical analysis Matrix Matrix methods Nonlinear analysis Optimization Parameters Step-by-step implicit time integration method Stiffness matrix Time finite element method Time integration Weighted residual method
Title	An improved implicit time integration algorithm: The generalized composite time integration algorithm
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