Dynamic stability of finite dimensional linearly elastic systems with unilateral contact and Coulomb friction
Identifieur interne : 001075 ( Main/Corpus ); précédent : 001074; suivant : 001076Dynamic stability of finite dimensional linearly elastic systems with unilateral contact and Coulomb friction
Auteurs : J. A. C. Martins ; S. Barbarin ; M. Raous ; A. Pinto Da CostaSource :
- Computer Methods in Applied Mechanics and Engineering [ 0045-7825 ] ; 1997.
Abstract
Necessary and sufficient conditions are established for the occurrence of dynamic instabilities in finite dimensional linearly elastic systems in unilateral frictional contact with a rigid flat surface. These conditions apply, in particular, to the systems that result from the finite element discretization of linearly elastic bodies. From a numerical point of view, these conditions lead to studying eigenproblems relative to a non-symmetric (tangent) stiffness matrix that incorporates the effect of the current state of the contract candidate particles. Illustrative small-sized examples are presented, together with an application to the case of an experimentally tested block of polyurethane, where friction induced instability phenomena were observed.
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DOI: 10.1016/S0045-7825(98)00386-7
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Civil and Inst. Construção, Instituto Superior Técnico, 1096 Lisboa Codex, Portugal</mods:affiliation></affiliation><affiliation><mods:affiliation>Corresponding author.</mods:affiliation></affiliation></author><author><name sortKey="Barbarin, S" sort="Barbarin, S" uniqKey="Barbarin S" first="S." last="Barbarin">S. Barbarin</name><affiliation><mods:affiliation>Laboratoire de Mécanique et d'Acoustique, CNRS, 13402 Marseille Cedex 20, France</mods:affiliation></affiliation></author><author><name sortKey="Raous, M" sort="Raous, M" uniqKey="Raous M" first="M." last="Raous">M. Raous</name><affiliation><mods:affiliation>Laboratoire de Mécanique et d'Acoustique, CNRS, 13402 Marseille Cedex 20, France</mods:affiliation></affiliation></author><author><name sortKey="Pinto Da Costa, A" sort="Pinto Da Costa, A" uniqKey="Pinto Da Costa A" first="A." last="Pinto Da Costa">A. Pinto Da Costa</name><affiliation><mods:affiliation>Dept. Eng. Civil and Inst. 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These conditions apply, in particular, to the systems that result from the finite element discretization of linearly elastic bodies. From a numerical point of view, these conditions lead to studying eigenproblems relative to a non-symmetric (tangent) stiffness matrix that incorporates the effect of the current state of the contract candidate particles. Illustrative small-sized examples are presented, together with an application to the case of an experimentally tested block of polyurethane, where friction induced instability phenomena were observed.</div></front></TEI><istex><corpusName>elsevier</corpusName><author><json:item><name>J.A.C. Martins</name><affiliations><json:string>Dept. Eng. Civil and Inst. Construção, Instituto Superior Técnico, 1096 Lisboa Codex, Portugal</json:string><json:string>Corresponding author.</json:string></affiliations></json:item><json:item><name>S. Barbarin</name><affiliations><json:string>Laboratoire de Mécanique et d'Acoustique, CNRS, 13402 Marseille Cedex 20, France</json:string></affiliations></json:item><json:item><name>M. Raous</name><affiliations><json:string>Laboratoire de Mécanique et d'Acoustique, CNRS, 13402 Marseille Cedex 20, France</json:string></affiliations></json:item><json:item><name>A. Pinto da Costa</name><affiliations><json:string>Dept. Eng. Civil and Inst. 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From a numerical point of view, these conditions lead to studying eigenproblems relative to a non-symmetric (tangent) stiffness matrix that incorporates the effect of the current state of the contract candidate particles. Illustrative small-sized examples are presented, together with an application to the case of an experimentally tested block of polyurethane, where friction induced instability phenomena were observed.</abstract><qualityIndicators><score>6.248</score><pdfVersion>1.3</pdfVersion><pdfPageSize>548 x 771 pts</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>1</keywordCount><abstractCharCount>758</abstractCharCount><pdfWordCount>18735</pdfWordCount><pdfCharCount>92941</pdfCharCount><pdfPageCount>40</pdfPageCount><abstractWordCount>104</abstractWordCount></qualityIndicators><title>Dynamic stability of finite dimensional linearly elastic systems with unilateral contact and Coulomb friction</title><pii><json:string>S0045-7825(98)00386-7</json:string></pii><genre><json:string>research-article</json:string></genre><serie><language><json:string>unknown</json:string></language><title>Int. 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Eng. Civil and Inst. Construção, Instituto Superior Técnico, 1096 Lisboa Codex, Portugal</affiliation><affiliation>Corresponding author.</affiliation></author><author><persName><forename type="first">S.</forename><surname>Barbarin</surname></persName><affiliation>Laboratoire de Mécanique et d'Acoustique, CNRS, 13402 Marseille Cedex 20, France</affiliation></author><author><persName><forename type="first">M.</forename><surname>Raous</surname></persName><affiliation>Laboratoire de Mécanique et d'Acoustique, CNRS, 13402 Marseille Cedex 20, France</affiliation></author><author><persName><forename type="first">A.</forename><surname>Pinto da Costa</surname></persName><affiliation>Dept. Eng. Civil and Inst. Construção, Instituto Superior Técnico, 1096 Lisboa Codex, Portugal</affiliation></author></analytic><monogr><title level="j">Computer Methods in Applied Mechanics and Engineering</title><title level="j" type="abbrev">CMA</title><idno type="pISSN">0045-7825</idno><idno type="PII">S0045-7825(00)X0533-6</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1997"></date><biblScope unit="volume">177</biblScope><biblScope unit="issue">3–4</biblScope><biblScope unit="page" from="289">289</biblScope><biblScope unit="page" to="328">328</biblScope></imprint></monogr><idno type="istex">7CD10A9F6F84BA187370BBE50C4C4332F7BCDA0B</idno><idno type="DOI">10.1016/S0045-7825(98)00386-7</idno><idno type="PII">S0045-7825(98)00386-7</idno><idno type="ArticleID">98003867</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1999</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Necessary and sufficient conditions are established for the occurrence of dynamic instabilities in finite dimensional linearly elastic systems in unilateral frictional contact with a rigid flat surface. These conditions apply, in particular, to the systems that result from the finite element discretization of linearly elastic bodies. From a numerical point of view, these conditions lead to studying eigenproblems relative to a non-symmetric (tangent) stiffness matrix that incorporates the effect of the current state of the contract candidate particles. Illustrative small-sized examples are presented, together with an application to the case of an experimentally tested block of polyurethane, where friction induced instability phenomena were observed.</p></abstract><textClass><keywords scheme="keyword"><list><head>Article category</head><item><term>Special issue: Computational modeling of contact and friction</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1997-04-14">Received</change><change when="1998-02-09">Modified</change><change when="1997">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><original>false</original><mimetype>text/plain</mimetype><extension>txt</extension><uri>https://api.istex.fr/document/7CD10A9F6F84BA187370BBE50C4C4332F7BCDA0B/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier doc found" wicri:toSee="Elsevier, no converted or simple article"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 5.0.1//EN//XML" URI="art501.dtd" name="istex:docType"></istex:docType><istex:document><article version="5.0" xml:lang="en" docsubtype="fla"><item-info><jid>CMA</jid><aid>98003867</aid><ce:pii>S0045-7825(98)00386-7</ce:pii><ce:doi>10.1016/S0045-7825(98)00386-7</ce:doi><ce:copyright type="unknown" year="1999">Elsevier Science S.A. All rights reserved</ce:copyright><ce:doctopics><ce:doctopic><ce:text>Special issue: Computational modeling of contact and friction</ce:text></ce:doctopic></ce:doctopics></item-info><head><ce:title>Dynamic stability of finite dimensional linearly elastic systems with unilateral contact and Coulomb friction</ce:title><ce:author-group><ce:author><ce:given-name>J.A.C.</ce:given-name><ce:surname>Martins</ce:surname><ce:cross-ref refid="aff1"><ce:sup>a</ce:sup></ce:cross-ref><ce:cross-ref refid="cor1"><ce:sup>*</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>S.</ce:given-name><ce:surname>Barbarin</ce:surname><ce:cross-ref refid="aff2"><ce:sup>b</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>M.</ce:given-name><ce:surname>Raous</ce:surname><ce:cross-ref refid="aff2"><ce:sup>b</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>A.</ce:given-name><ce:surname>Pinto da Costa</ce:surname><ce:cross-ref refid="aff1"><ce:sup>a</ce:sup></ce:cross-ref></ce:author><ce:affiliation id="aff1"><ce:label>a</ce:label><ce:textfn>Dept. Eng. Civil and Inst. Construção, Instituto Superior Técnico, 1096 Lisboa Codex, Portugal</ce:textfn></ce:affiliation><ce:affiliation id="aff2"><ce:label>b</ce:label><ce:textfn>Laboratoire de Mécanique et d'Acoustique, CNRS, 13402 Marseille Cedex 20, France</ce:textfn></ce:affiliation><ce:correspondence id="cor1"><ce:label>*</ce:label><ce:text>Corresponding author.</ce:text></ce:correspondence></ce:author-group><ce:date-received day="14" month="4" year="1997"></ce:date-received><ce:date-revised day="9" month="2" year="1998"></ce:date-revised><ce:abstract id="ab1" class="author" xml:lang="en"><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>Necessary and sufficient conditions are established for the occurrence of dynamic instabilities in finite dimensional linearly elastic systems in unilateral frictional contact with a rigid flat surface. These conditions apply, in particular, to the systems that result from the finite element discretization of linearly elastic bodies. From a numerical point of view, these conditions lead to studying eigenproblems relative to a non-symmetric (tangent) stiffness matrix that incorporates the effect of the current state of the contract candidate particles. Illustrative small-sized examples are presented, together with an application to the case of an experimentally tested block of polyurethane, where friction induced instability phenomena were observed.</ce:simple-para></ce:abstract-sec></ce:abstract></head><tail><ce:bibliography><ce:section-title>References</ce:section-title><ce:bibliography-sec><ce:bib-reference id="bib1"><ce:label>[1]</ce:label><sb:reference><sb:contribution langtype="iso" xml:lang="fr"><sb:authors><sb:author><ce:given-name>S.</ce:given-name><ce:surname>Barbarin</ce:surname></sb:author><sb:author><ce:given-name>J.A.C.</ce:given-name><ce:surname>Martins</ce:surname></sb:author><sb:author><ce:given-name>M.</ce:given-name><ce:surname>Raous</ce:surname></sb:author><sb:author><ce:given-name>B.</ce:given-name><ce:surname>Villechaise</ce:surname></sb:author><sb:author><ce:given-name>T.</ce:given-name><ce:surname>Zeghloul</ce:surname></sb:author></sb:authors><sb:title><sb:maintitle>Ondes de contraintes dans un contact glissant, modélisation et analyse experimentale</sb:maintitle></sb:title></sb:contribution><sb:host><sb:edited-book><sb:title><sb:maintitle>Actes du 8ème Colloque National MECAMAT</sb:maintitle></sb:title><sb:conference>Aussois, France</sb:conference><sb:date>1995</sb:date></sb:edited-book></sb:host></sb:reference></ce:bib-reference><ce:bib-reference id="bib2"><ce:label>[2]</ce:label><sb:reference><sb:contribution langtype="en"><sb:authors><sb:author><ce:given-name>Z.</ce:given-name><ce:surname>Bazant</ce:surname></sb:author><sb:author><ce:given-name>L.</ce:given-name><ce:surname>Cedolin</ce:surname></sb:author></sb:authors><sb:title><sb:maintitle>Stability of Structures</sb:maintitle></sb:title></sb:contribution><sb:host><sb:book><sb:date>1991</sb:date><sb:publisher><sb:name>Oxford University Press</sb:name><sb:location>Rome</sb:location></sb:publisher></sb:book></sb:host></sb:reference></ce:bib-reference><ce:bib-reference id="bib3"><ce:label>[3]</ce:label><sb:reference><sb:contribution langtype="en"><sb:authors><sb:author><ce:given-name>P.</ce:given-name><ce:surname>Chabrand</ce:surname></sb:author><sb:author><ce:given-name>F.</ce:given-name><ce:surname>Dubois</ce:surname></sb:author><sb:author><ce:given-name>M.</ce:given-name><ce:surname>Raous</ce:surname></sb:author></sb:authors><sb:title><sb:maintitle>Comparison of various numerical methods for solving unilateral contact problems with friction</sb:maintitle></sb:title></sb:contribution><sb:host><sb:issue><sb:series><sb:title><sb:maintitle>Math. 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Eng. Civil and Inst. Construção, Instituto Superior Técnico, 1096 Lisboa Codex, Portugal</affiliation><affiliation>Corresponding author.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">S.</namePart><namePart type="family">Barbarin</namePart><affiliation>Laboratoire de Mécanique et d'Acoustique, CNRS, 13402 Marseille Cedex 20, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Raous</namePart><affiliation>Laboratoire de Mécanique et d'Acoustique, CNRS, 13402 Marseille Cedex 20, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Pinto da Costa</namePart><affiliation>Dept. Eng. Civil and Inst. Construção, Instituto Superior Técnico, 1096 Lisboa Codex, Portugal</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">1999</dateIssued><dateModified encoding="w3cdtf">1998-02-09</dateModified><copyrightDate encoding="w3cdtf">1999</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Necessary and sufficient conditions are established for the occurrence of dynamic instabilities in finite dimensional linearly elastic systems in unilateral frictional contact with a rigid flat surface. These conditions apply, in particular, to the systems that result from the finite element discretization of linearly elastic bodies. From a numerical point of view, these conditions lead to studying eigenproblems relative to a non-symmetric (tangent) stiffness matrix that incorporates the effect of the current state of the contract candidate particles. Illustrative small-sized examples are presented, together with an application to the case of an experimentally tested block of polyurethane, where friction induced instability phenomena were observed.</abstract><subject><genre>article-category</genre><topic>Special issue: Computational modeling of contact and friction</topic></subject><relatedItem type="host"><titleInfo><title>Computer Methods in Applied Mechanics and Engineering</title></titleInfo><titleInfo type="abbreviated"><title>CMA</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">19990720</dateIssued></originInfo><identifier type="ISSN">0045-7825</identifier><identifier type="PII">S0045-7825(00)X0533-6</identifier><part><date>19990720</date><detail type="volume"><number>177</number><caption>vol.</caption></detail><detail type="issue"><number>3–4</number><caption>no.</caption></detail><extent unit="issue pages"><start>163</start><end>468</end></extent><extent unit="pages"><start>289</start><end>328</end></extent></part></relatedItem><identifier type="istex">7CD10A9F6F84BA187370BBE50C4C4332F7BCDA0B</identifier><identifier type="DOI">10.1016/S0045-7825(98)00386-7</identifier><identifier type="PII">S0045-7825(98)00386-7</identifier><identifier type="ArticleID">98003867</identifier><accessCondition type="use and reproduction" contentType="">© 1999Elsevier Science S.A. 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