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Article: Precise integration methods based on Lagrange piecewise interpolation polynomials

TitlePrecise integration methods based on Lagrange piecewise interpolation polynomials
Authors
KeywordsHomogenized initial system method
Integral formula method
Lagrange piecewise interpolation polynomial
Structural dynamics
Zeros of the first Chebyshev polynomial
Issue Date2009
PublisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/1430
Citation
International Journal For Numerical Methods In Engineering, 2009, v. 77 n. 7, p. 998-1014 How to Cite?
AbstractThis paper introduces two new types of precise integration methods for dynamic response analysis of structures, namely, the integral formula method and the homogenized initial system method. The applied loading vectors in the two algorithms are simulated by the Lagrange piecewise interpolation polynomials based on the zeros of the first Chebyshev polynomial. Developed on the basis of the integral formula and the Lagrange piecewise interpolation polynomial and combined with the recurrence relationship of some key parameters in the integral computation suggested in this paper with the solving process of linear algebraic equations, the integral formula method has been set up. On the basis of the Lagrange piecewise interpolation polynomial, and transforming the non-homogenous initial system into the homogeneous dynamic system, the homogenized initial system method without dimensional expanding is presented; this homogenized initial system method avoids the matrix inversion operation and is a general homogenized high-precision direct integration scheme. The accuracy of the presented time integration schemes is studied and is compared with those of other commonly used schemes; the presented time integration schemes have arbitrary order of accuracy, wider application and are less time consuming. Two numerical examples are also presented to demonstrate the applicability of these new methods. Copyright © 2008 John Wiley & Sons, Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/58499
ISSN
2015 Impact Factor: 2.1
2015 SCImago Journal Rankings: 2.007
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorWang, MFen_HK
dc.contributor.authorAu, FTKen_HK
dc.date.accessioned2010-05-31T03:31:30Z-
dc.date.available2010-05-31T03:31:30Z-
dc.date.issued2009en_HK
dc.identifier.citationInternational Journal For Numerical Methods In Engineering, 2009, v. 77 n. 7, p. 998-1014en_HK
dc.identifier.issn0029-5981en_HK
dc.identifier.urihttp://hdl.handle.net/10722/58499-
dc.description.abstractThis paper introduces two new types of precise integration methods for dynamic response analysis of structures, namely, the integral formula method and the homogenized initial system method. The applied loading vectors in the two algorithms are simulated by the Lagrange piecewise interpolation polynomials based on the zeros of the first Chebyshev polynomial. Developed on the basis of the integral formula and the Lagrange piecewise interpolation polynomial and combined with the recurrence relationship of some key parameters in the integral computation suggested in this paper with the solving process of linear algebraic equations, the integral formula method has been set up. On the basis of the Lagrange piecewise interpolation polynomial, and transforming the non-homogenous initial system into the homogeneous dynamic system, the homogenized initial system method without dimensional expanding is presented; this homogenized initial system method avoids the matrix inversion operation and is a general homogenized high-precision direct integration scheme. The accuracy of the presented time integration schemes is studied and is compared with those of other commonly used schemes; the presented time integration schemes have arbitrary order of accuracy, wider application and are less time consuming. Two numerical examples are also presented to demonstrate the applicability of these new methods. Copyright © 2008 John Wiley & Sons, Ltd.en_HK
dc.languageengen_HK
dc.publisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/1430en_HK
dc.relation.ispartofInternational Journal for Numerical Methods in Engineeringen_HK
dc.rightsInternational Journal for Numerical Methods in Engineering. Copyright © John Wiley & Sons Ltd.en_HK
dc.subjectHomogenized initial system methoden_HK
dc.subjectIntegral formula methoden_HK
dc.subjectLagrange piecewise interpolation polynomialen_HK
dc.subjectStructural dynamicsen_HK
dc.subjectZeros of the first Chebyshev polynomialen_HK
dc.titlePrecise integration methods based on Lagrange piecewise interpolation polynomialsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0029-5981&volume=77&issue=7&spage=998&epage=1014&date=2009&atitle=Precise+integration+methods+based+on+Lagrange+piecewise+interpolation+polynomialsen_HK
dc.identifier.emailAu, FTK:francis.au@hku.hken_HK
dc.identifier.authorityAu, FTK=rp00083en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1002/nme.2444en_HK
dc.identifier.scopuseid_2-s2.0-60949106646en_HK
dc.identifier.hkuros158949en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-60949106646&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume77en_HK
dc.identifier.issue7en_HK
dc.identifier.spage998en_HK
dc.identifier.epage1014en_HK
dc.identifier.eissn1097-0207-
dc.identifier.isiWOS:000263227200004-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridWang, MF=7407801843en_HK
dc.identifier.scopusauthoridAu, FTK=7005204072en_HK

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