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Article: Precise integration methods based on the Chebyshev polynomial of the first kind

TitlePrecise integration methods based on the Chebyshev polynomial of the first kind
Authors
KeywordsChebyshev polynomial of the first kind
Homogenized initial system method
Integral formula method
Structural dynamics
The Crout decomposed method
Issue Date2008
PublisherMultidisciplinary Center for Earthquake Engineering Research. The Journal's web site is located at http://mceer.buffalo.edu/eeev
Citation
Earthquake Engineering And Engineering Vibration, 2008, v. 7 n. 2, p. 207-216 How to Cite?
AbstractThis paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method (IFM) and the homogenized initial system method (HISM). In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods. © 2008 Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH.
Persistent Identifierhttp://hdl.handle.net/10722/71588
ISSN
2015 Impact Factor: 0.814
2015 SCImago Journal Rankings: 0.475
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorWang, Men_HK
dc.contributor.authorAu, FTKen_HK
dc.date.accessioned2010-09-06T06:33:21Z-
dc.date.available2010-09-06T06:33:21Z-
dc.date.issued2008en_HK
dc.identifier.citationEarthquake Engineering And Engineering Vibration, 2008, v. 7 n. 2, p. 207-216en_HK
dc.identifier.issn1671-3664en_HK
dc.identifier.urihttp://hdl.handle.net/10722/71588-
dc.description.abstractThis paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method (IFM) and the homogenized initial system method (HISM). In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods. © 2008 Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH.en_HK
dc.languageengen_HK
dc.publisherMultidisciplinary Center for Earthquake Engineering Research. The Journal's web site is located at http://mceer.buffalo.edu/eeeven_HK
dc.relation.ispartofEarthquake Engineering and Engineering Vibrationen_HK
dc.subjectChebyshev polynomial of the first kinden_HK
dc.subjectHomogenized initial system methoden_HK
dc.subjectIntegral formula methoden_HK
dc.subjectStructural dynamicsen_HK
dc.subjectThe Crout decomposed methoden_HK
dc.titlePrecise integration methods based on the Chebyshev polynomial of the first kinden_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1671-3664&volume=7&issue=2&spage=207&epage=216&date=2008&atitle=Precise+integration+methods+based+on+the+Chebyshev+polynomial+of+the+first+kinden_HK
dc.identifier.emailAu, FTK:francis.au@hku.hken_HK
dc.identifier.authorityAu, FTK=rp00083en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s11803-008-0837-4en_HK
dc.identifier.scopuseid_2-s2.0-46449129474en_HK
dc.identifier.hkuros147569en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-46449129474&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume7en_HK
dc.identifier.issue2en_HK
dc.identifier.spage207en_HK
dc.identifier.epage216en_HK
dc.identifier.isiWOS:000257328100008-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridWang, M=7407801843en_HK
dc.identifier.scopusauthoridAu, FTK=7005204072en_HK
dc.identifier.citeulike3638146-

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