Grid-based volume integration for elasticity: Traction boundary integral equation
•For nonlinear elasticity, the traction boundary integral equation has a volume term.•This volume integral is evaluated using just a regular cell grid covering the domain.•For fracture analysis, the volume integration can simply ignores the fracture surface.•Test calculations have demonstrated the c...
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| Veröffentlicht in: | Engineering fracture mechanics 2017-05, Vol.176, p.74-82 |
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| container_title | Engineering fracture mechanics |
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| creator | Lumsden, Ian Gray, L.J. Ye, Wenjing |
| description | •For nonlinear elasticity, the traction boundary integral equation has a volume term.•This volume integral is evaluated using just a regular cell grid covering the domain.•For fracture analysis, the volume integration can simply ignores the fracture surface.•Test calculations have demonstrated the correctness of the implementation.
A volume integral algorithm for the non-homogeneous 3D elasticity traction boundary integral equation is presented. The body force volume integral is exactly split into a relatively simple boundary integral, together with a remainder volume integral that can be evaluated using a regular grid of cuboid cells covering the problem domain. Of particular importance for (inelastic) fracture analysis is that the volume integral over the regular grid is computed without explicit knowledge of the domain boundary, including the fracture surface. A Galerkin approximation is employed, and the numerical implementation is validated by solving body force elasticity problems with known solutions. |
| doi_str_mv | 10.1016/j.engfracmech.2017.02.009 |
| format | Article |
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A volume integral algorithm for the non-homogeneous 3D elasticity traction boundary integral equation is presented. The body force volume integral is exactly split into a relatively simple boundary integral, together with a remainder volume integral that can be evaluated using a regular grid of cuboid cells covering the problem domain. Of particular importance for (inelastic) fracture analysis is that the volume integral over the regular grid is computed without explicit knowledge of the domain boundary, including the fracture surface. A Galerkin approximation is employed, and the numerical implementation is validated by solving body force elasticity problems with known solutions.</description><identifier>ISSN: 0013-7944</identifier><identifier>EISSN: 1873-7315</identifier><identifier>DOI: 10.1016/j.engfracmech.2017.02.009</identifier><language>eng</language><publisher>New York: Elsevier Ltd</publisher><subject>Elasticity ; Elasticity body forces ; Fracture mechanics ; Galerkin method ; Integral equations ; Regular grid ; Traction ; Traction boundary integral equation ; Volume integral</subject><ispartof>Engineering fracture mechanics, 2017-05, Vol.176, p.74-82</ispartof><rights>2017 Elsevier Ltd</rights><rights>Copyright Elsevier BV May 1, 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c349t-245b248b625dc41e6a9b42a7aec160460692cc8a89ac0ae69bbcd250663fe2873</citedby><cites>FETCH-LOGICAL-c349t-245b248b625dc41e6a9b42a7aec160460692cc8a89ac0ae69bbcd250663fe2873</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0013794416306300$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Lumsden, Ian</creatorcontrib><creatorcontrib>Gray, L.J.</creatorcontrib><creatorcontrib>Ye, Wenjing</creatorcontrib><title>Grid-based volume integration for elasticity: Traction boundary integral equation</title><title>Engineering fracture mechanics</title><description>•For nonlinear elasticity, the traction boundary integral equation has a volume term.•This volume integral is evaluated using just a regular cell grid covering the domain.•For fracture analysis, the volume integration can simply ignores the fracture surface.•Test calculations have demonstrated the correctness of the implementation.
A volume integral algorithm for the non-homogeneous 3D elasticity traction boundary integral equation is presented. The body force volume integral is exactly split into a relatively simple boundary integral, together with a remainder volume integral that can be evaluated using a regular grid of cuboid cells covering the problem domain. Of particular importance for (inelastic) fracture analysis is that the volume integral over the regular grid is computed without explicit knowledge of the domain boundary, including the fracture surface. A Galerkin approximation is employed, and the numerical implementation is validated by solving body force elasticity problems with known solutions.</description><subject>Elasticity</subject><subject>Elasticity body forces</subject><subject>Fracture mechanics</subject><subject>Galerkin method</subject><subject>Integral equations</subject><subject>Regular grid</subject><subject>Traction</subject><subject>Traction boundary integral equation</subject><subject>Volume integral</subject><issn>0013-7944</issn><issn>1873-7315</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNqNUF1LwzAUDaLgnP6His-tN2maNr7J0CkMRJjPIU1vZ8rWbEk72L83cwo--nQv3PNxzyHklkJGgYr7LsN-1XptNmg-Mwa0zIBlAPKMTGhV5mmZ0-KcTABo3CXnl-QqhA4ASlHBhLzPvW3SWgdskr1bjxtMbD_gyuvBuj5pnU9wrcNgjR0OD8kyOn0fajf2jfaHX_Q6wd34zbkmF61eB7z5mVPy8fy0nL2ki7f56-xxkZqcyyFlvKgZr2rBisZwikLLmjNdajRUABcgJDOm0pXUBjQKWdemYQUIkbfIYrIpuTvpbr3bjRgG1bnR99FSUZkzWspS0oiSJ5TxLgSPrdp6u4mPKwrq2KDq1J8G1bFBBUzFBiN3duJijLG36FUwFnuDjfVoBtU4-w-VL7OFgKs</recordid><startdate>20170501</startdate><enddate>20170501</enddate><creator>Lumsden, Ian</creator><creator>Gray, L.J.</creator><creator>Ye, Wenjing</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>7TB</scope><scope>8BQ</scope><scope>8FD</scope><scope>FR3</scope><scope>JG9</scope><scope>KR7</scope></search><sort><creationdate>20170501</creationdate><title>Grid-based volume integration for elasticity: Traction boundary integral equation</title><author>Lumsden, Ian ; Gray, L.J. ; Ye, Wenjing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c349t-245b248b625dc41e6a9b42a7aec160460692cc8a89ac0ae69bbcd250663fe2873</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Elasticity</topic><topic>Elasticity body forces</topic><topic>Fracture mechanics</topic><topic>Galerkin method</topic><topic>Integral equations</topic><topic>Regular grid</topic><topic>Traction</topic><topic>Traction boundary integral equation</topic><topic>Volume integral</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lumsden, Ian</creatorcontrib><creatorcontrib>Gray, L.J.</creatorcontrib><creatorcontrib>Ye, Wenjing</creatorcontrib><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Materials Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>Engineering fracture mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lumsden, Ian</au><au>Gray, L.J.</au><au>Ye, Wenjing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Grid-based volume integration for elasticity: Traction boundary integral equation</atitle><jtitle>Engineering fracture mechanics</jtitle><date>2017-05-01</date><risdate>2017</risdate><volume>176</volume><spage>74</spage><epage>82</epage><pages>74-82</pages><issn>0013-7944</issn><eissn>1873-7315</eissn><abstract>•For nonlinear elasticity, the traction boundary integral equation has a volume term.•This volume integral is evaluated using just a regular cell grid covering the domain.•For fracture analysis, the volume integration can simply ignores the fracture surface.•Test calculations have demonstrated the correctness of the implementation.
A volume integral algorithm for the non-homogeneous 3D elasticity traction boundary integral equation is presented. The body force volume integral is exactly split into a relatively simple boundary integral, together with a remainder volume integral that can be evaluated using a regular grid of cuboid cells covering the problem domain. Of particular importance for (inelastic) fracture analysis is that the volume integral over the regular grid is computed without explicit knowledge of the domain boundary, including the fracture surface. A Galerkin approximation is employed, and the numerical implementation is validated by solving body force elasticity problems with known solutions.</abstract><cop>New York</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.engfracmech.2017.02.009</doi><tpages>9</tpages></addata></record> |
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| ispartof | Engineering fracture mechanics, 2017-05, Vol.176, p.74-82 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Elasticity Elasticity body forces Fracture mechanics Galerkin method Integral equations Regular grid Traction Traction boundary integral equation Volume integral |
| title | Grid-based volume integration for elasticity: Traction boundary integral equation |
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