Efficient modeling of internal cracks for Laplace problem by XFEM using Joukowski mapping
Summary In this study, the extended finite element method (XFEM) is applied to the two‐dimensional Laplace equation with an internal discontinuity. The real part of a complex velocity potential from potential flow theory is used to represent the enrichment function in this technique. The Joukowski m...
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| Veröffentlicht in: | International journal for numerical methods in engineering 2019-07, Vol.119 (1), p.1-17 |
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| container_title | International journal for numerical methods in engineering |
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| creator | Nakasumi, Shogo Schweitzer, Marc Alexander |
| description | Summary
In this study, the extended finite element method (XFEM) is applied to the two‐dimensional Laplace equation with an internal discontinuity. The real part of a complex velocity potential from potential flow theory is used to represent the enrichment function in this technique. The Joukowski mapping, which maps a circle to a line, is mainly used to obtain a solution around an airfoil in two‐dimensional potential flow; here, we extend that solution to model magnetic flux around an internal crack. The effectiveness of the proposed method is verified using numerical examples of single and multiple cracks. The L2 error norm is used to evaluate the accuracy of the proposed method in comparison with XFEM using previously proposed enrichment functions (Heaviside and analytical forms for a single crack tip). The proposed method gives better results than those of the existing XFEM in the case of a coarse mesh. |
| doi_str_mv | 10.1002/nme.6039 |
| format | Article |
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In this study, the extended finite element method (XFEM) is applied to the two‐dimensional Laplace equation with an internal discontinuity. The real part of a complex velocity potential from potential flow theory is used to represent the enrichment function in this technique. The Joukowski mapping, which maps a circle to a line, is mainly used to obtain a solution around an airfoil in two‐dimensional potential flow; here, we extend that solution to model magnetic flux around an internal crack. The effectiveness of the proposed method is verified using numerical examples of single and multiple cracks. The L2 error norm is used to evaluate the accuracy of the proposed method in comparison with XFEM using previously proposed enrichment functions (Heaviside and analytical forms for a single crack tip). The proposed method gives better results than those of the existing XFEM in the case of a coarse mesh.</description><identifier>ISSN: 0029-5981</identifier><identifier>EISSN: 1097-0207</identifier><identifier>DOI: 10.1002/nme.6039</identifier><language>eng</language><publisher>Bognor Regis: Wiley Subscription Services, Inc</publisher><subject>Crack tips ; Cracks ; elliptic ; extended finite element method ; Finite element method ; finite element methods ; Flow theory ; inverse problem ; Laplace equation ; Magnetic flux ; Mapping ; Mathematical analysis ; partial differential equations ; partition‐of‐unity ; Potential flow</subject><ispartof>International journal for numerical methods in engineering, 2019-07, Vol.119 (1), p.1-17</ispartof><rights>2019 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3599-a221c48b69e1646ffa00fd77f7510eb32276a5c4c1122704bea54420dc6403d93</citedby><cites>FETCH-LOGICAL-c3599-a221c48b69e1646ffa00fd77f7510eb32276a5c4c1122704bea54420dc6403d93</cites><orcidid>0000-0002-9626-9156</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnme.6039$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnme.6039$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Nakasumi, Shogo</creatorcontrib><creatorcontrib>Schweitzer, Marc Alexander</creatorcontrib><title>Efficient modeling of internal cracks for Laplace problem by XFEM using Joukowski mapping</title><title>International journal for numerical methods in engineering</title><description>Summary
In this study, the extended finite element method (XFEM) is applied to the two‐dimensional Laplace equation with an internal discontinuity. The real part of a complex velocity potential from potential flow theory is used to represent the enrichment function in this technique. The Joukowski mapping, which maps a circle to a line, is mainly used to obtain a solution around an airfoil in two‐dimensional potential flow; here, we extend that solution to model magnetic flux around an internal crack. The effectiveness of the proposed method is verified using numerical examples of single and multiple cracks. The L2 error norm is used to evaluate the accuracy of the proposed method in comparison with XFEM using previously proposed enrichment functions (Heaviside and analytical forms for a single crack tip). The proposed method gives better results than those of the existing XFEM in the case of a coarse mesh.</description><subject>Crack tips</subject><subject>Cracks</subject><subject>elliptic</subject><subject>extended finite element method</subject><subject>Finite element method</subject><subject>finite element methods</subject><subject>Flow theory</subject><subject>inverse problem</subject><subject>Laplace equation</subject><subject>Magnetic flux</subject><subject>Mapping</subject><subject>Mathematical analysis</subject><subject>partial differential equations</subject><subject>partition‐of‐unity</subject><subject>Potential flow</subject><issn>0029-5981</issn><issn>1097-0207</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kMtOwzAQRS0EEqUg8QmW2LBJGT-S1EtUhZda2IAEK8txbOQ2iYPdqOrfk9BuWc1o5szo6iB0TWBGAOhd25hZBkycoAkBkSdAIT9Fk2ElklTMyTm6iHENQEgKbIK-Cmuddqbd4sZXpnbtN_YWu3ZrQqtqrIPSm4itD3ipulppg7vgy9o0uNzjz4dihfs4Hr34fuN3ceNwo7pumFyiM6vqaK6OdYo-Hor3xVOyfHt8XtwvE81SIRJFKdF8XmbCkIxn1ioAW-W5zVMCpmSU5plKNdeEDC3w0qiUcwqVzjiwSrApujn8HXL99CZu5dr3Y_YoKWUsZ6ONgbo9UDr4GIOxsguuUWEvCchRnBzEySOaHNCdq83-X06-roo__hdQhG21</recordid><startdate>20190706</startdate><enddate>20190706</enddate><creator>Nakasumi, Shogo</creator><creator>Schweitzer, Marc Alexander</creator><general>Wiley Subscription Services, Inc</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/0000-0002-9626-9156</orcidid></search><sort><creationdate>20190706</creationdate><title>Efficient modeling of internal cracks for Laplace problem by XFEM using Joukowski mapping</title><author>Nakasumi, Shogo ; Schweitzer, Marc Alexander</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3599-a221c48b69e1646ffa00fd77f7510eb32276a5c4c1122704bea54420dc6403d93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Crack tips</topic><topic>Cracks</topic><topic>elliptic</topic><topic>extended finite element method</topic><topic>Finite element method</topic><topic>finite element methods</topic><topic>Flow theory</topic><topic>inverse problem</topic><topic>Laplace equation</topic><topic>Magnetic flux</topic><topic>Mapping</topic><topic>Mathematical analysis</topic><topic>partial differential equations</topic><topic>partition‐of‐unity</topic><topic>Potential flow</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nakasumi, Shogo</creatorcontrib><creatorcontrib>Schweitzer, Marc Alexander</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>International journal for numerical methods in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nakasumi, Shogo</au><au>Schweitzer, Marc Alexander</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Efficient modeling of internal cracks for Laplace problem by XFEM using Joukowski mapping</atitle><jtitle>International journal for numerical methods in engineering</jtitle><date>2019-07-06</date><risdate>2019</risdate><volume>119</volume><issue>1</issue><spage>1</spage><epage>17</epage><pages>1-17</pages><issn>0029-5981</issn><eissn>1097-0207</eissn><abstract>Summary
In this study, the extended finite element method (XFEM) is applied to the two‐dimensional Laplace equation with an internal discontinuity. The real part of a complex velocity potential from potential flow theory is used to represent the enrichment function in this technique. The Joukowski mapping, which maps a circle to a line, is mainly used to obtain a solution around an airfoil in two‐dimensional potential flow; here, we extend that solution to model magnetic flux around an internal crack. The effectiveness of the proposed method is verified using numerical examples of single and multiple cracks. The L2 error norm is used to evaluate the accuracy of the proposed method in comparison with XFEM using previously proposed enrichment functions (Heaviside and analytical forms for a single crack tip). The proposed method gives better results than those of the existing XFEM in the case of a coarse mesh.</abstract><cop>Bognor Regis</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/nme.6039</doi><tpages>17</tpages><orcidid>https://orcid.org/0000-0002-9626-9156</orcidid></addata></record> |
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| subjects | Crack tips Cracks elliptic extended finite element method Finite element method finite element methods Flow theory inverse problem Laplace equation Magnetic flux Mapping Mathematical analysis partial differential equations partition‐of‐unity Potential flow |
| title | Efficient modeling of internal cracks for Laplace problem by XFEM using Joukowski mapping |
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