Four-node Hu–Washizu elements based on skew coordinates and contravariant assumed strain
Mixed 4-node elements based on the Hu–Washizu (HW) functional are developed for the representation of the assumed strain in the natural basis at the element’s center, i.e. for the contravariant transformation rule. In other aspects, the formulation is identical as in our previous paper [9], to which...
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| Veröffentlicht in: | Computers & structures 2010-11, Vol.88 (21), p.1278-1284 |
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| creator | Wisniewski, K. Wagner, W. Turska, E. Gruttmann, F. |
| description | Mixed 4-node elements based on the Hu–Washizu (HW) functional are developed for the representation of the assumed strain in the natural basis at the element’s center, i.e. for the contravariant transformation rule. In other aspects, the formulation is identical as in our previous paper
[9], to which this note is an addendum.
Two mixed HW elements based on the 5-parameter stress are developed; they use either the 7-parameter or 9-parameter strain representation. The stress and strain representations are assumed in terms of skew coordinates, see
[10]. The numerical tests involving coarse distorted meshes are used to assess the effects of using the contravariant strain representation.
The tests show that both elements pass the discrete
inf-sup test. Accuracy of the element based on the 9-parameter strain, designated as HW14-S and selected as the best in
[9], remains unaffected. Accuracy of the element based on the 7-parameter strain is significantly improved. |
| doi_str_mv | 10.1016/j.compstruc.2010.07.008 |
| format | Article |
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[9], to which this note is an addendum.
Two mixed HW elements based on the 5-parameter stress are developed; they use either the 7-parameter or 9-parameter strain representation. The stress and strain representations are assumed in terms of skew coordinates, see
[10]. The numerical tests involving coarse distorted meshes are used to assess the effects of using the contravariant strain representation.
The tests show that both elements pass the discrete
inf-sup test. Accuracy of the element based on the 9-parameter strain, designated as HW14-S and selected as the best in
[9], remains unaffected. Accuracy of the element based on the 7-parameter strain is significantly improved.</description><identifier>ISSN: 0045-7949</identifier><identifier>EISSN: 1879-2243</identifier><identifier>DOI: 10.1016/j.compstruc.2010.07.008</identifier><language>eng</language><publisher>Kidlington: Elsevier Ltd</publisher><subject>Accuracy ; Computer simulation ; Contravariant assumed strain ; Distortion ; Exact sciences and technology ; Four-node finite elements ; Fundamental areas of phenomenology (including applications) ; Hu–Washizu functional ; Mathematical models ; Mathematics ; Methods of scientific computing (including symbolic computation, algebraic computation) ; Mixed elements ; Numerical analysis. Scientific computation ; Physics ; Plane stress ; Representations ; Sciences and techniques of general use ; Skew coordinates ; Solid mechanics ; Strain ; Stresses ; Structural and continuum mechanics ; Transformations</subject><ispartof>Computers & structures, 2010-11, Vol.88 (21), p.1278-1284</ispartof><rights>2010 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c377t-c52679392e64c695e95a46af962097adc37f13154dd96f86e4387b966b9b907f3</citedby><cites>FETCH-LOGICAL-c377t-c52679392e64c695e95a46af962097adc37f13154dd96f86e4387b966b9b907f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.compstruc.2010.07.008$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3548,27923,27924,45994</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23292947$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Wisniewski, K.</creatorcontrib><creatorcontrib>Wagner, W.</creatorcontrib><creatorcontrib>Turska, E.</creatorcontrib><creatorcontrib>Gruttmann, F.</creatorcontrib><title>Four-node Hu–Washizu elements based on skew coordinates and contravariant assumed strain</title><title>Computers & structures</title><description>Mixed 4-node elements based on the Hu–Washizu (HW) functional are developed for the representation of the assumed strain in the natural basis at the element’s center, i.e. for the contravariant transformation rule. In other aspects, the formulation is identical as in our previous paper
[9], to which this note is an addendum.
Two mixed HW elements based on the 5-parameter stress are developed; they use either the 7-parameter or 9-parameter strain representation. The stress and strain representations are assumed in terms of skew coordinates, see
[10]. The numerical tests involving coarse distorted meshes are used to assess the effects of using the contravariant strain representation.
The tests show that both elements pass the discrete
inf-sup test. Accuracy of the element based on the 9-parameter strain, designated as HW14-S and selected as the best in
[9], remains unaffected. Accuracy of the element based on the 7-parameter strain is significantly improved.</description><subject>Accuracy</subject><subject>Computer simulation</subject><subject>Contravariant assumed strain</subject><subject>Distortion</subject><subject>Exact sciences and technology</subject><subject>Four-node finite elements</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Hu–Washizu functional</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Methods of scientific computing (including symbolic computation, algebraic computation)</subject><subject>Mixed elements</subject><subject>Numerical analysis. Scientific computation</subject><subject>Physics</subject><subject>Plane stress</subject><subject>Representations</subject><subject>Sciences and techniques of general use</subject><subject>Skew coordinates</subject><subject>Solid mechanics</subject><subject>Strain</subject><subject>Stresses</subject><subject>Structural and continuum mechanics</subject><subject>Transformations</subject><issn>0045-7949</issn><issn>1879-2243</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNqFkMFu1DAQhi1EJZbCM5AL4pTFsR07PlYVpUiVegEhcbFm7YnwktiLJykqJ96hb9gnqauteuU0mtH3_zPzM_au49uOd_rjfuvzfKClrH4reJ1ys-V8eME23WBsK4SSL9mGc9W3xir7ir0m2nPOteJ8w35c5LW0KQdsLtf7f3ffgX7Gv2uDE86YFmp2QBianBr6hX8an3MJMcGC1EAKtU9LgRsoEdLSANE6V7oeAzG9YScjTIRvn-op-3bx6ev5ZXt1_fnL-dlV66UxS-t7oY2VVqBWXtsebQ9Kw2i14NZAqNTYya5XIVg9DhqVHMzOar2zO8vNKE_Zh6PvoeTfK9Li5kgepwkS5pXcMFR32UlVSXMkfclEBUd3KHGGcus67h7DdHv3HKZ7DNNx42qYVfn-aQeQh2kskHykZ7mQwgqrTOXOjhzWh28iFkc-YvIYYkG_uJDjf3c9ADAnkNQ</recordid><startdate>20101101</startdate><enddate>20101101</enddate><creator>Wisniewski, K.</creator><creator>Wagner, W.</creator><creator>Turska, E.</creator><creator>Gruttmann, F.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20101101</creationdate><title>Four-node Hu–Washizu elements based on skew coordinates and contravariant assumed strain</title><author>Wisniewski, K. ; Wagner, W. ; Turska, E. ; Gruttmann, F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c377t-c52679392e64c695e95a46af962097adc37f13154dd96f86e4387b966b9b907f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Accuracy</topic><topic>Computer simulation</topic><topic>Contravariant assumed strain</topic><topic>Distortion</topic><topic>Exact sciences and technology</topic><topic>Four-node finite elements</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Hu–Washizu functional</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Methods of scientific computing (including symbolic computation, algebraic computation)</topic><topic>Mixed elements</topic><topic>Numerical analysis. Scientific computation</topic><topic>Physics</topic><topic>Plane stress</topic><topic>Representations</topic><topic>Sciences and techniques of general use</topic><topic>Skew coordinates</topic><topic>Solid mechanics</topic><topic>Strain</topic><topic>Stresses</topic><topic>Structural and continuum mechanics</topic><topic>Transformations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wisniewski, K.</creatorcontrib><creatorcontrib>Wagner, W.</creatorcontrib><creatorcontrib>Turska, E.</creatorcontrib><creatorcontrib>Gruttmann, F.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computers & structures</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wisniewski, K.</au><au>Wagner, W.</au><au>Turska, E.</au><au>Gruttmann, F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Four-node Hu–Washizu elements based on skew coordinates and contravariant assumed strain</atitle><jtitle>Computers & structures</jtitle><date>2010-11-01</date><risdate>2010</risdate><volume>88</volume><issue>21</issue><spage>1278</spage><epage>1284</epage><pages>1278-1284</pages><issn>0045-7949</issn><eissn>1879-2243</eissn><abstract>Mixed 4-node elements based on the Hu–Washizu (HW) functional are developed for the representation of the assumed strain in the natural basis at the element’s center, i.e. for the contravariant transformation rule. In other aspects, the formulation is identical as in our previous paper
[9], to which this note is an addendum.
Two mixed HW elements based on the 5-parameter stress are developed; they use either the 7-parameter or 9-parameter strain representation. The stress and strain representations are assumed in terms of skew coordinates, see
[10]. The numerical tests involving coarse distorted meshes are used to assess the effects of using the contravariant strain representation.
The tests show that both elements pass the discrete
inf-sup test. Accuracy of the element based on the 9-parameter strain, designated as HW14-S and selected as the best in
[9], remains unaffected. Accuracy of the element based on the 7-parameter strain is significantly improved.</abstract><cop>Kidlington</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.compstruc.2010.07.008</doi><tpages>7</tpages></addata></record> |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Accuracy Computer simulation Contravariant assumed strain Distortion Exact sciences and technology Four-node finite elements Fundamental areas of phenomenology (including applications) Hu–Washizu functional Mathematical models Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Mixed elements Numerical analysis. Scientific computation Physics Plane stress Representations Sciences and techniques of general use Skew coordinates Solid mechanics Strain Stresses Structural and continuum mechanics Transformations |
| title | Four-node Hu–Washizu elements based on skew coordinates and contravariant assumed strain |
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