A C k continuous generalized finite element formulation applied to laminated Kirchhoff plate model
Identifieur interne : 000166 ( Istex/Corpus ); précédent : 000165; suivant : 000167A C k continuous generalized finite element formulation applied to laminated Kirchhoff plate model
Auteurs : Clovis Sperb De Barcellos ; Paulo De Tarso R. Mendonça ; Carlos A. DuarteSource :
- Computational Mechanics [ 0178-7675 ] ; 2009-08-01.
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Abstract
Abstract: A generalized finite element method based on a partition of unity (POU) with smooth approximation functions is investigated in this paper for modeling laminated plates under Kirchhoff hypothesis. The shape functions are built from the product of a Shepard POU and enrichment functions. The Shepard functions have a smoothness degree directly related to the weight functions adopted for their evaluation. The weight functions at a point are built as products of C ∞ edge functions of the distance of such a point to each of the cloud boundaries. Different edge functions are investigated to generate C k functions. The POU together with polynomial global enrichment functions build the approximation subspace. The formulation implemented in this paper is aimed at the general case of laminated plates composed of anisotropic layers. A detailed convergence analysis is presented and the integrability of these functions is also discussed.
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DOI: 10.1007/s00466-009-0376-5
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The shape functions are built from the product of a Shepard POU and enrichment functions. The Shepard functions have a smoothness degree directly related to the weight functions adopted for their evaluation. The weight functions at a point are built as products of C ∞ edge functions of the distance of such a point to each of the cloud boundaries. Different edge functions are investigated to generate C k functions. The POU together with polynomial global enrichment functions build the approximation subspace. The formulation implemented in this paper is aimed at the general case of laminated plates composed of anisotropic layers. A detailed convergence analysis is presented and the integrability of these functions is also discussed.</div></front></TEI><istex><corpusName>springer-journals</corpusName><author><json:item><name>Clovis Sperb de Barcellos</name><affiliations><json:string>Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900, Florianópolis, SC, Brazil</json:string><json:string>E-mail: clovis@grante.ufsc.br</json:string></affiliations></json:item><json:item><name>Paulo de Tarso R. Mendonça</name><affiliations><json:string>Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900, Florianópolis, SC, Brazil</json:string><json:string>E-mail: mendonca@grante.ufsc.br</json:string></affiliations></json:item><json:item><name>Carlos A. 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laminated Kirchhoff plate model</ArticleTitle><ArticleCategory>Original Paper</ArticleCategory><ArticleFirstPage>377</ArticleFirstPage><ArticleLastPage>393</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2009</Year><Month>2</Month><Day>3</Day></RegistrationDate><Received><Year>2008</Year><Month>12</Month><Day>5</Day></Received><Accepted><Year>2009</Year><Month>1</Month><Day>30</Day></Accepted><OnlineDate><Year>2009</Year><Month>3</Month><Day>10</Day></OnlineDate></ArticleHistory><ArticleCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName><CopyrightYear>2009</CopyrightYear></ArticleCopyright><ArticleGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ArticleGrants></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1" CorrespondingAffiliationID="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Clovis</GivenName><GivenName>Sperb</GivenName><Particle>de</Particle><FamilyName>Barcellos</FamilyName></AuthorName><Contact><Email>clovis@grante.ufsc.br</Email></Contact></Author><Author AffiliationIDS="Aff1" CorrespondingAffiliationID="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Paulo</GivenName><Particle>de</Particle><FamilyName>Tarso R. Mendonça</FamilyName></AuthorName><Contact><Email>mendonca@grante.ufsc.br</Email></Contact></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Carlos</GivenName><GivenName>A.</GivenName><FamilyName>Duarte</FamilyName></AuthorName><Contact><Email>caduarte@uiuc.edu</Email></Contact></Author><Affiliation ID="Aff1"><OrgDivision>Mechanical Engineering Department</OrgDivision><OrgName>Federal University of Santa Catarina</OrgName><OrgAddress><Postcode>88040-900</Postcode><City>Florianópolis</City><State>SC</State><Country Code="BR">Brazil</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgDivision>2122 Newmark Civil Engineering Laboratory</OrgDivision><OrgName>University of Illinois at Urbana-Champaign</OrgName><OrgAddress><Street>205 North Mathews Ave.</Street><City>Urbana</City><State>IL</State><Postcode>62801-2352</Postcode><Country Code="US">USA</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para TextBreak="No">A generalized finite element method based on a partition of unity (POU) with smooth approximation functions is investigated in this paper for modeling laminated plates under Kirchhoff hypothesis. The shape functions are built from the product of a Shepard POU and enrichment functions. The Shepard functions have a smoothness degree directly related to the weight functions adopted for their evaluation. The weight functions at a point are built as products of <Emphasis Type="Italic">C</Emphasis><Superscript>∞</Superscript> edge functions of the distance of such a point to each of the cloud boundaries. Different edge functions are investigated to generate <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">k</Emphasis></Superscript> functions. The POU together with polynomial global enrichment functions build the approximation subspace. The formulation implemented in this paper is aimed at the general case of laminated plates composed of anisotropic layers. A detailed convergence analysis is presented and the integrability of these functions is also discussed.</Para></Abstract><KeywordGroup Language="En"><Heading>Keywords</Heading><Keyword>Generalized finite element method</Keyword><Keyword>Partition of unity method</Keyword><Keyword>Kirchhoff plate FEM</Keyword><Keyword><Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">k</Emphasis></Superscript> continuous approximation functions</Keyword></KeywordGroup></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A C k continuous generalized finite element formulation applied to laminated Kirchhoff plate model</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>A C k continuous generalized finite element formulation applied to laminated Kirchhoff plate model</title></titleInfo><name type="personal" displayLabel="corresp"><namePart type="given">Clovis</namePart><namePart type="given">Sperb</namePart><namePart type="family">de Barcellos</namePart><affiliation>Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900, Florianópolis, SC, Brazil</affiliation><affiliation>E-mail: clovis@grante.ufsc.br</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal" displayLabel="corresp"><namePart type="given">Paulo</namePart><namePart type="family">de Tarso R. Mendonça</namePart><affiliation>Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900, Florianópolis, SC, Brazil</affiliation><affiliation>E-mail: mendonca@grante.ufsc.br</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Carlos</namePart><namePart type="given">A.</namePart><namePart type="family">Duarte</namePart><affiliation>2122 Newmark Civil Engineering Laboratory, University of Illinois at Urbana-Champaign, 205 North Mathews Ave., 62801-2352, Urbana, IL, USA</affiliation><affiliation>E-mail: caduarte@uiuc.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer-Verlag</publisher><place><placeTerm type="text">Berlin/Heidelberg</placeTerm></place><dateCreated encoding="w3cdtf">2008-12-05</dateCreated><dateIssued encoding="w3cdtf">2009-08-01</dateIssued><copyrightDate encoding="w3cdtf">2009</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: A generalized finite element method based on a partition of unity (POU) with smooth approximation functions is investigated in this paper for modeling laminated plates under Kirchhoff hypothesis. The shape functions are built from the product of a Shepard POU and enrichment functions. The Shepard functions have a smoothness degree directly related to the weight functions adopted for their evaluation. The weight functions at a point are built as products of C ∞ edge functions of the distance of such a point to each of the cloud boundaries. Different edge functions are investigated to generate C k functions. The POU together with polynomial global enrichment functions build the approximation subspace. The formulation implemented in this paper is aimed at the general case of laminated plates composed of anisotropic layers. A detailed convergence analysis is presented and the integrability of these functions is also discussed.</abstract><note>Original Paper</note><subject lang="en"><genre>Keywords</genre><topic>Generalized finite element method</topic><topic>Partition of unity method</topic><topic>Kirchhoff plate FEM</topic><topic>C k continuous approximation functions</topic></subject><relatedItem type="host"><titleInfo><title>Computational Mechanics</title><subTitle>Solids, Fluids, Structures, Fluid-Structure Interactions, Biomechanics, Micromechanics, Multiscale Mechanics, Materials, Constitutive Modeling, Nonlinear Mechanics, Aerodynamics</subTitle></titleInfo><titleInfo type="abbreviated"><title>Comput Mech</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><originInfo><publisher>Springer</publisher><dateIssued encoding="w3cdtf">2009-06-03</dateIssued><copyrightDate encoding="w3cdtf">2009</copyrightDate></originInfo><subject><genre>Engineering</genre><topic>Mechanics, Fluids, Thermodynamics</topic><topic>Computational Science and Engineering</topic><topic>Theoretical and Applied Mechanics</topic></subject><identifier type="ISSN">0178-7675</identifier><identifier type="eISSN">1432-0924</identifier><identifier type="JournalID">466</identifier><identifier type="JournalSPIN">30021159</identifier><identifier type="IssueArticleCount">11</identifier><identifier type="VolumeIssueCount">6</identifier><part><date>2009</date><detail type="volume"><number>44</number><caption>vol.</caption></detail><detail type="issue"><number>3</number><caption>no.</caption></detail><extent unit="pages"><start>377</start><end>393</end></extent></part><recordInfo><recordOrigin>Springer-Verlag, 2009</recordOrigin></recordInfo></relatedItem><identifier type="istex">ADFC6D5B14BB09729DE4E55999D87271C3A4F882</identifier><identifier type="ark">ark:/67375/VQC-3MPLRFXZ-M</identifier><identifier type="DOI">10.1007/s00466-009-0376-5</identifier><identifier type="ArticleID">376</identifier><identifier type="ArticleID">s00466-009-0376-5</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 2009</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</recordContentSource><recordOrigin>Springer-Verlag, 2009</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/ADFC6D5B14BB09729DE4E55999D87271C3A4F882/metadata/json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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