B-spline finite element method based on node moving adaptive refinement strategy
In this paper, an adaptive refinement procedure in conjunction with the B-spline finite element method is presented for the effective and efficient analysis of Euler–Bernoulli beam and planar elasticity problems. The B-spline plays a key role in the construction of stable wavelet on the interval, an...
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Veröffentlicht in: | Finite elements in analysis and design 2014-11, Vol.91, p.84-94 |
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description | In this paper, an adaptive refinement procedure in conjunction with the B-spline finite element method is presented for the effective and efficient analysis of Euler–Bernoulli beam and planar elasticity problems. The B-spline plays a key role in the construction of stable wavelet on the interval, and there is actually no limitation for the interval. The spline elements are constructed in practical domain in this paper, and the spline bases concerns nodes distributed on the interval. As a result, the B-spline finite element method can be reconsidered as a meshless method. By repositioning the nodes of the spline bases, the accuracy of the method can be improved, and a simple node moving strategy is proposed to displace the nodal points to the areas indicated by the higher values of the error indicator. The efficiency and effectiveness of proposed B-spline finite element method and adaptive refinement technique are tested on some benchmark examples with the available analytical solutions and the results are presented.
•A spline element method constructed in practical domain can be dealt with as a meshless method.•A simple node moving strategy is proposed to refine the nodal distribution.•The Euler–Bernoulli beam and planar elasticity problems have been solved efficiently. |
doi_str_mv | 10.1016/j.finel.2014.07.007 |
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•A spline element method constructed in practical domain can be dealt with as a meshless method.•A simple node moving strategy is proposed to refine the nodal distribution.•The Euler–Bernoulli beam and planar elasticity problems have been solved efficiently.</description><identifier>ISSN: 0168-874X</identifier><identifier>EISSN: 1872-6925</identifier><identifier>DOI: 10.1016/j.finel.2014.07.007</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Adaptive refinement ; B-spline finite element method ; Construction ; Design engineering ; Elasticity problems ; Euler-Bernoulli beams ; Finite element method ; Intervals ; Mathematical analysis ; Node moving strategy ; Splines ; Strategy</subject><ispartof>Finite elements in analysis and design, 2014-11, Vol.91, p.84-94</ispartof><rights>2014 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c336t-8d51dd54d7525f57998c0639fea0c78d85cba378367e38e650c648018336a2f03</citedby><cites>FETCH-LOGICAL-c336t-8d51dd54d7525f57998c0639fea0c78d85cba378367e38e650c648018336a2f03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.finel.2014.07.007$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Shen, Li</creatorcontrib><creatorcontrib>Liu, Zhangyi</creatorcontrib><creatorcontrib>Wu, Jiu Hui</creatorcontrib><title>B-spline finite element method based on node moving adaptive refinement strategy</title><title>Finite elements in analysis and design</title><description>In this paper, an adaptive refinement procedure in conjunction with the B-spline finite element method is presented for the effective and efficient analysis of Euler–Bernoulli beam and planar elasticity problems. The B-spline plays a key role in the construction of stable wavelet on the interval, and there is actually no limitation for the interval. The spline elements are constructed in practical domain in this paper, and the spline bases concerns nodes distributed on the interval. As a result, the B-spline finite element method can be reconsidered as a meshless method. By repositioning the nodes of the spline bases, the accuracy of the method can be improved, and a simple node moving strategy is proposed to displace the nodal points to the areas indicated by the higher values of the error indicator. The efficiency and effectiveness of proposed B-spline finite element method and adaptive refinement technique are tested on some benchmark examples with the available analytical solutions and the results are presented.
•A spline element method constructed in practical domain can be dealt with as a meshless method.•A simple node moving strategy is proposed to refine the nodal distribution.•The Euler–Bernoulli beam and planar elasticity problems have been solved efficiently.</description><subject>Adaptive refinement</subject><subject>B-spline finite element method</subject><subject>Construction</subject><subject>Design engineering</subject><subject>Elasticity problems</subject><subject>Euler-Bernoulli beams</subject><subject>Finite element method</subject><subject>Intervals</subject><subject>Mathematical analysis</subject><subject>Node moving strategy</subject><subject>Splines</subject><subject>Strategy</subject><issn>0168-874X</issn><issn>1872-6925</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAQhi0EEqXwC1g8siTYSfyRgQEqvqRKMIDEZrn2pbhK4mK7lfrvcVtmplue5727F6FrSkpKKL9dlZ0boS8rQpuSiJIQcYImVIqq4G3FTtEkU7KQovk6RxcxrgghrOLNBL0_FHHdZxnnBJcAQw8DjAkPkL69xQsdwWI_4tFbwIPfunGJtdXr5LaAA-z3HviYgk6w3F2is073Ea7-5hR9Pj1-zF6K-dvz6-x-Xpi65qmQllFrWWMFq1jHRNtKQ3jddqCJEdJKZha6FrLmAmoJnBHDG0mozLauOlJP0c0xdx38zwZiUoOLBvpej-A3UVEuKGNNS0VG6yNqgo8x36zWwQ067BQlat-fWqlDf2rfnyJC5f6ydXe0IH-xdRBUNA5GA9YFMElZ7_71fwHTDHnr</recordid><startdate>20141115</startdate><enddate>20141115</enddate><creator>Shen, Li</creator><creator>Liu, Zhangyi</creator><creator>Wu, Jiu Hui</creator><general>Elsevier B.V</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></search><sort><creationdate>20141115</creationdate><title>B-spline finite element method based on node moving adaptive refinement strategy</title><author>Shen, Li ; Liu, Zhangyi ; Wu, Jiu Hui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c336t-8d51dd54d7525f57998c0639fea0c78d85cba378367e38e650c648018336a2f03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Adaptive refinement</topic><topic>B-spline finite element method</topic><topic>Construction</topic><topic>Design engineering</topic><topic>Elasticity problems</topic><topic>Euler-Bernoulli beams</topic><topic>Finite element method</topic><topic>Intervals</topic><topic>Mathematical analysis</topic><topic>Node moving strategy</topic><topic>Splines</topic><topic>Strategy</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shen, Li</creatorcontrib><creatorcontrib>Liu, Zhangyi</creatorcontrib><creatorcontrib>Wu, Jiu Hui</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>Finite elements in analysis and design</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shen, Li</au><au>Liu, Zhangyi</au><au>Wu, Jiu Hui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>B-spline finite element method based on node moving adaptive refinement strategy</atitle><jtitle>Finite elements in analysis and design</jtitle><date>2014-11-15</date><risdate>2014</risdate><volume>91</volume><spage>84</spage><epage>94</epage><pages>84-94</pages><issn>0168-874X</issn><eissn>1872-6925</eissn><abstract>In this paper, an adaptive refinement procedure in conjunction with the B-spline finite element method is presented for the effective and efficient analysis of Euler–Bernoulli beam and planar elasticity problems. The B-spline plays a key role in the construction of stable wavelet on the interval, and there is actually no limitation for the interval. The spline elements are constructed in practical domain in this paper, and the spline bases concerns nodes distributed on the interval. As a result, the B-spline finite element method can be reconsidered as a meshless method. By repositioning the nodes of the spline bases, the accuracy of the method can be improved, and a simple node moving strategy is proposed to displace the nodal points to the areas indicated by the higher values of the error indicator. The efficiency and effectiveness of proposed B-spline finite element method and adaptive refinement technique are tested on some benchmark examples with the available analytical solutions and the results are presented.
•A spline element method constructed in practical domain can be dealt with as a meshless method.•A simple node moving strategy is proposed to refine the nodal distribution.•The Euler–Bernoulli beam and planar elasticity problems have been solved efficiently.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.finel.2014.07.007</doi><tpages>11</tpages></addata></record> |
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subjects | Adaptive refinement B-spline finite element method Construction Design engineering Elasticity problems Euler-Bernoulli beams Finite element method Intervals Mathematical analysis Node moving strategy Splines Strategy |
title | B-spline finite element method based on node moving adaptive refinement strategy |
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