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Article: The fractal finite element method for unbounded problems

TitleThe fractal finite element method for unbounded problems
Authors
KeywordsConcentrated load
Elastic half space
Fractal finite element
Ring load
Stress intensity factor
Unbounded problem
Issue Date2004
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, 2004, v. 61 n. 7, p. 990-1008 How to Cite?
AbstractThe fractal finite element method, previously developed for stress intensity factor calculation for crack problems in fracture mechanics, is extended to analyse some unbounded problems in half space. The concepts of geometrical similarity and two-level finite element mesh are applied to generate an infinite number of self-similar layers in the far field with a similarity ratio bigger than one; that is, one layer is bigger than the next in size but of the same shape. Only conventional finite elements are used and no new elements are generated. The global interpolating functions in the form of a truncated infinite series are employed to transform the infinite number of nodal variables to a small number of unknown coefficients associated with the global interpolating functions. Taking the advantage of geometrical similarity, transformation for one layer is enough because the relevant entries of the transformed matrix after assembling all layers are infinite geometric series of the similarity ratio and can be summed analytically. Accurate nodal displacements are obtained as shown in the numerical examples. © 2004 John Wiley and Sons, Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/71013
ISSN
2015 Impact Factor: 2.1
2015 SCImago Journal Rankings: 2.007
ISI Accession Number ID
References
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DC FieldValueLanguage
dc.contributor.authorLeung, AYTen_HK
dc.contributor.authorDai, Hen_HK
dc.contributor.authorFok, SLen_HK
dc.contributor.authorSu, RKLen_HK
dc.date.accessioned2010-09-06T06:28:08Z-
dc.date.available2010-09-06T06:28:08Z-
dc.date.issued2004en_HK
dc.identifier.citationInternational Journal For Numerical Methods In Engineering, 2004, v. 61 n. 7, p. 990-1008en_HK
dc.identifier.issn0029-5981en_HK
dc.identifier.urihttp://hdl.handle.net/10722/71013-
dc.description.abstractThe fractal finite element method, previously developed for stress intensity factor calculation for crack problems in fracture mechanics, is extended to analyse some unbounded problems in half space. The concepts of geometrical similarity and two-level finite element mesh are applied to generate an infinite number of self-similar layers in the far field with a similarity ratio bigger than one; that is, one layer is bigger than the next in size but of the same shape. Only conventional finite elements are used and no new elements are generated. The global interpolating functions in the form of a truncated infinite series are employed to transform the infinite number of nodal variables to a small number of unknown coefficients associated with the global interpolating functions. Taking the advantage of geometrical similarity, transformation for one layer is enough because the relevant entries of the transformed matrix after assembling all layers are infinite geometric series of the similarity ratio and can be summed analytically. Accurate nodal displacements are obtained as shown in the numerical examples. © 2004 John Wiley and 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.subjectConcentrated loaden_HK
dc.subjectElastic half spaceen_HK
dc.subjectFractal finite elementen_HK
dc.subjectRing loaden_HK
dc.subjectStress intensity factoren_HK
dc.subjectUnbounded problemen_HK
dc.titleThe fractal finite element method for unbounded problemsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0029-5981&volume=61&issue=7&spage=990&epage=1008&date=2004&atitle=The+fractal+finite+element+method+for+unbounded+problemsen_HK
dc.identifier.emailSu, RKL:klsu@hkucc.hku.hken_HK
dc.identifier.authoritySu, RKL=rp00072en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1002/nme.1097en_HK
dc.identifier.scopuseid_2-s2.0-6344280795en_HK
dc.identifier.hkuros96778en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-6344280795&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume61en_HK
dc.identifier.issue7en_HK
dc.identifier.spage990en_HK
dc.identifier.epage1008en_HK
dc.identifier.isiWOS:000224603200003-
dc.publisher.placeUnited Kingdomen_HK
dc.relation.projectInteraction of multiple branched cracks-
dc.identifier.scopusauthoridLeung, AYT=7403012564en_HK
dc.identifier.scopusauthoridDai, H=25822111000en_HK
dc.identifier.scopusauthoridFok, SL=7005182786en_HK
dc.identifier.scopusauthoridSu, RKL=7102627096en_HK

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