A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements
This paper presents a new finite element solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of the classical bilinear or trilinear Lagrangian elements. It solves the primal variable displacement in the strain–div formulation and can handle both displacement and t...
Gespeichert in:
| Veröffentlicht in: | Computers & mathematics with applications (1987) 2020-09, Vol.80 (6), p.1578-1595 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1595 |
|---|---|
| container_issue | 6 |
| container_start_page | 1578 |
| container_title | Computers & mathematics with applications (1987) |
| container_volume | 80 |
| creator | Harper, Graham Wang, Ruishu Liu, Jiangguo Tavener, Simon Zhang, Ran |
| description | This paper presents a new finite element solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of the classical bilinear or trilinear Lagrangian elements. It solves the primal variable displacement in the strain–div formulation and can handle both displacement and traction boundary conditions. It is a locking-free solver based on conforming finite elements. The solver has second order accuracy in displacement and first order accuracy in stress and dilation (divergence of displacement), as validated by theoretical analysis and illustrated by numerical experiments on benchmarks. deal.II implementation is also discussed. |
| doi_str_mv | 10.1016/j.camwa.2020.07.014 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2505413905</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0898122120302807</els_id><sourcerecordid>2505413905</sourcerecordid><originalsourceid>FETCH-LOGICAL-c376t-cb665bade80c3815307033b8cfc213080c1f7913f5f8530710d7a67704d57c303</originalsourceid><addsrcrecordid>eNp9kMtOwzAQRS0EEuXxBWwssU4Yx02cLlggxEuqxAbW1tQety6pDXbKY8G_k1DWrEYz994ZzWHsTEApQDQX69Lg5gPLCiooQZUgpntsIlolC9U07T6bQDtrC1FV4pAd5bwGgKmsYMK-r3gXzYsPy8IlIp5j906Ju5h45wNh4tRh7r3x_RePgb9t0SbfYU8JO47B8hV94ors2G4oryjzBWayo5lC8ma1odDz6PgclwnD0uMgdDRO8wk7cNhlOv2rx-z59ubp-r6YP949XF_NCyNV0xdm0TT1Ai21YGQragkKpFy0xplKSBimwqmZkK527SgKsAobpWBqa2UkyGN2vtv7muLblnKv13GbwnBSVzXUUyFnUA8uuXOZFHNO5PRr8htMX1qAHjnrtf7lrEfOGpQeOA-py12KhgfePSWdjadgyPpEptc2-n_zPx2AiDg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2505413905</pqid></control><display><type>article</type><title>A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements</title><source>ScienceDirect Journals (5 years ago - present)</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>Harper, Graham ; Wang, Ruishu ; Liu, Jiangguo ; Tavener, Simon ; Zhang, Ran</creator><creatorcontrib>Harper, Graham ; Wang, Ruishu ; Liu, Jiangguo ; Tavener, Simon ; Zhang, Ran</creatorcontrib><description>This paper presents a new finite element solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of the classical bilinear or trilinear Lagrangian elements. It solves the primal variable displacement in the strain–div formulation and can handle both displacement and traction boundary conditions. It is a locking-free solver based on conforming finite elements. The solver has second order accuracy in displacement and first order accuracy in stress and dilation (divergence of displacement), as validated by theoretical analysis and illustrated by numerical experiments on benchmarks. deal.II implementation is also discussed.</description><identifier>ISSN: 0898-1221</identifier><identifier>EISSN: 1873-7668</identifier><identifier>DOI: 10.1016/j.camwa.2020.07.014</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Boundary conditions ; Deal.II implementation ; Displacement ; Divergence ; Elasticity ; Enrichment of Lagrangian elements ; Hexahedral meshes ; Linear elasticity ; Locking ; Locking-free ; Mathematical analysis ; Quadrilateral meshes ; Quadrilaterals ; Solvers</subject><ispartof>Computers & mathematics with applications (1987), 2020-09, Vol.80 (6), p.1578-1595</ispartof><rights>2020 Elsevier Ltd</rights><rights>Copyright Elsevier BV Sep 15, 2020</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c376t-cb665bade80c3815307033b8cfc213080c1f7913f5f8530710d7a67704d57c303</citedby><cites>FETCH-LOGICAL-c376t-cb665bade80c3815307033b8cfc213080c1f7913f5f8530710d7a67704d57c303</cites><orcidid>0000-0002-2188-5157 ; 0000-0001-9298-5588</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.camwa.2020.07.014$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3548,27922,27923,45993</link.rule.ids></links><search><creatorcontrib>Harper, Graham</creatorcontrib><creatorcontrib>Wang, Ruishu</creatorcontrib><creatorcontrib>Liu, Jiangguo</creatorcontrib><creatorcontrib>Tavener, Simon</creatorcontrib><creatorcontrib>Zhang, Ran</creatorcontrib><title>A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements</title><title>Computers & mathematics with applications (1987)</title><description>This paper presents a new finite element solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of the classical bilinear or trilinear Lagrangian elements. It solves the primal variable displacement in the strain–div formulation and can handle both displacement and traction boundary conditions. It is a locking-free solver based on conforming finite elements. The solver has second order accuracy in displacement and first order accuracy in stress and dilation (divergence of displacement), as validated by theoretical analysis and illustrated by numerical experiments on benchmarks. deal.II implementation is also discussed.</description><subject>Boundary conditions</subject><subject>Deal.II implementation</subject><subject>Displacement</subject><subject>Divergence</subject><subject>Elasticity</subject><subject>Enrichment of Lagrangian elements</subject><subject>Hexahedral meshes</subject><subject>Linear elasticity</subject><subject>Locking</subject><subject>Locking-free</subject><subject>Mathematical analysis</subject><subject>Quadrilateral meshes</subject><subject>Quadrilaterals</subject><subject>Solvers</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEuXxBWwssU4Yx02cLlggxEuqxAbW1tQety6pDXbKY8G_k1DWrEYz994ZzWHsTEApQDQX69Lg5gPLCiooQZUgpntsIlolC9U07T6bQDtrC1FV4pAd5bwGgKmsYMK-r3gXzYsPy8IlIp5j906Ju5h45wNh4tRh7r3x_RePgb9t0SbfYU8JO47B8hV94ors2G4oryjzBWayo5lC8ma1odDz6PgclwnD0uMgdDRO8wk7cNhlOv2rx-z59ubp-r6YP949XF_NCyNV0xdm0TT1Ai21YGQragkKpFy0xplKSBimwqmZkK527SgKsAobpWBqa2UkyGN2vtv7muLblnKv13GbwnBSVzXUUyFnUA8uuXOZFHNO5PRr8htMX1qAHjnrtf7lrEfOGpQeOA-py12KhgfePSWdjadgyPpEptc2-n_zPx2AiDg</recordid><startdate>20200915</startdate><enddate>20200915</enddate><creator>Harper, Graham</creator><creator>Wang, Ruishu</creator><creator>Liu, Jiangguo</creator><creator>Tavener, Simon</creator><creator>Zhang, Ran</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-2188-5157</orcidid><orcidid>https://orcid.org/0000-0001-9298-5588</orcidid></search><sort><creationdate>20200915</creationdate><title>A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements</title><author>Harper, Graham ; Wang, Ruishu ; Liu, Jiangguo ; Tavener, Simon ; Zhang, Ran</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c376t-cb665bade80c3815307033b8cfc213080c1f7913f5f8530710d7a67704d57c303</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Boundary conditions</topic><topic>Deal.II implementation</topic><topic>Displacement</topic><topic>Divergence</topic><topic>Elasticity</topic><topic>Enrichment of Lagrangian elements</topic><topic>Hexahedral meshes</topic><topic>Linear elasticity</topic><topic>Locking</topic><topic>Locking-free</topic><topic>Mathematical analysis</topic><topic>Quadrilateral meshes</topic><topic>Quadrilaterals</topic><topic>Solvers</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Harper, Graham</creatorcontrib><creatorcontrib>Wang, Ruishu</creatorcontrib><creatorcontrib>Liu, Jiangguo</creatorcontrib><creatorcontrib>Tavener, Simon</creatorcontrib><creatorcontrib>Zhang, Ran</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering 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 & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Harper, Graham</au><au>Wang, Ruishu</au><au>Liu, Jiangguo</au><au>Tavener, Simon</au><au>Zhang, Ran</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2020-09-15</date><risdate>2020</risdate><volume>80</volume><issue>6</issue><spage>1578</spage><epage>1595</epage><pages>1578-1595</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>This paper presents a new finite element solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of the classical bilinear or trilinear Lagrangian elements. It solves the primal variable displacement in the strain–div formulation and can handle both displacement and traction boundary conditions. It is a locking-free solver based on conforming finite elements. The solver has second order accuracy in displacement and first order accuracy in stress and dilation (divergence of displacement), as validated by theoretical analysis and illustrated by numerical experiments on benchmarks. deal.II implementation is also discussed.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.camwa.2020.07.014</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0002-2188-5157</orcidid><orcidid>https://orcid.org/0000-0001-9298-5588</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0898-1221 |
| ispartof | Computers & mathematics with applications (1987), 2020-09, Vol.80 (6), p.1578-1595 |
| issn | 0898-1221 1873-7668 |
| language | eng |
| recordid | cdi_proquest_journals_2505413905 |
| source | ScienceDirect Journals (5 years ago - present); EZB-FREE-00999 freely available EZB journals |
| subjects | Boundary conditions Deal.II implementation Displacement Divergence Elasticity Enrichment of Lagrangian elements Hexahedral meshes Linear elasticity Locking Locking-free Mathematical analysis Quadrilateral meshes Quadrilaterals Solvers |
| title | A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T12%3A03%3A59IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20locking-free%20solver%20for%20linear%20elasticity%20on%20quadrilateral%20and%20hexahedral%20meshes%20based%20on%20enrichment%20of%20Lagrangian%20elements&rft.jtitle=Computers%20&%20mathematics%20with%20applications%20(1987)&rft.au=Harper,%20Graham&rft.date=2020-09-15&rft.volume=80&rft.issue=6&rft.spage=1578&rft.epage=1595&rft.pages=1578-1595&rft.issn=0898-1221&rft.eissn=1873-7668&rft_id=info:doi/10.1016/j.camwa.2020.07.014&rft_dat=%3Cproquest_cross%3E2505413905%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2505413905&rft_id=info:pmid/&rft_els_id=S0898122120302807&rfr_iscdi=true |