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Article: A refined nonconforming quadrilateral element for couple stress/strain gradient elasticity
Title | A refined nonconforming quadrilateral element for couple stress/strain gradient elasticity | ||||||
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Authors | |||||||
Keywords | C0-1 patch test Couple stress theory Finite element method Strain gradient theory | ||||||
Issue Date | 2011 | ||||||
Publisher | John Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/1430 | ||||||
Citation | International Journal For Numerical Methods In Engineering, 2011, v. 85 n. 3, p. 269-288 How to Cite? | ||||||
Abstract | C0-1 patch test (Int. J. Numer. Meth. Engng 2004; 61:433-454) proposed by Soh and Chen is a reliable method to ensure convergence of nonconforming finite element for the couple stress/strain gradient elasticity. The C0-1 patch test function is a complete quadratic polynomial that satisfies the equilibrium equations. To pass the C0-1 patch test, the element displacement functions used to calculate strains must satisfy C0 continuity (or weak C0 continuity) and quadratic completeness. In this paper, a 24-DOF (degrees of freedom) quadrilateral element (CQ12+RDKQ) for the couple stress/strain gradient elasticity is developed by combining the refined thin plate element RDKQ and the nonconforming element CQ12. The element RDKQ, which satisfies weak C1 continuity, is used to calculate strain gradients, whereas strains are computed by the element CQ12, which is established based on an extended variational functional and satisfies weak C0 continuity and quadratic completeness. Numerical examples show that the element (CQ12+RDKQ) passes the C0-1 patch test and it is also more efficient than the existing available triangular and quadrilateral elements in stress concentration problems with size effects. © 2010 John Wiley & Sons, Ltd. | ||||||
Persistent Identifier | http://hdl.handle.net/10722/139095 | ||||||
ISSN | 2023 Impact Factor: 2.7 2023 SCImago Journal Rankings: 1.019 | ||||||
ISI Accession Number ID |
Funding Information: This work was support by the National Natural Sciences Foundation of China (No. 10672032) and China Postdoctoral Science Foundation (No. 20100470069). | ||||||
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Zhao, J | en_HK |
dc.contributor.author | Chen, WJ | en_HK |
dc.contributor.author | Lo, SH | en_HK |
dc.date.accessioned | 2011-09-23T05:44:54Z | - |
dc.date.available | 2011-09-23T05:44:54Z | - |
dc.date.issued | 2011 | en_HK |
dc.identifier.citation | International Journal For Numerical Methods In Engineering, 2011, v. 85 n. 3, p. 269-288 | en_HK |
dc.identifier.issn | 0029-5981 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/139095 | - |
dc.description.abstract | C0-1 patch test (Int. J. Numer. Meth. Engng 2004; 61:433-454) proposed by Soh and Chen is a reliable method to ensure convergence of nonconforming finite element for the couple stress/strain gradient elasticity. The C0-1 patch test function is a complete quadratic polynomial that satisfies the equilibrium equations. To pass the C0-1 patch test, the element displacement functions used to calculate strains must satisfy C0 continuity (or weak C0 continuity) and quadratic completeness. In this paper, a 24-DOF (degrees of freedom) quadrilateral element (CQ12+RDKQ) for the couple stress/strain gradient elasticity is developed by combining the refined thin plate element RDKQ and the nonconforming element CQ12. The element RDKQ, which satisfies weak C1 continuity, is used to calculate strain gradients, whereas strains are computed by the element CQ12, which is established based on an extended variational functional and satisfies weak C0 continuity and quadratic completeness. Numerical examples show that the element (CQ12+RDKQ) passes the C0-1 patch test and it is also more efficient than the existing available triangular and quadrilateral elements in stress concentration problems with size effects. © 2010 John Wiley & Sons, Ltd. | en_HK |
dc.language | eng | en_US |
dc.publisher | John Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/1430 | en_HK |
dc.relation.ispartof | International Journal for Numerical Methods in Engineering | en_HK |
dc.rights | International Journal for Numerical Methods in Engineering. Copyright © John Wiley & Sons Ltd. | en_US |
dc.subject | C0-1 patch test | en_HK |
dc.subject | Couple stress theory | en_HK |
dc.subject | Finite element method | en_HK |
dc.subject | Strain gradient theory | en_HK |
dc.title | A refined nonconforming quadrilateral element for couple stress/strain gradient elasticity | en_HK |
dc.type | Article | en_HK |
dc.identifier.email | Lo, SH:hreclsh@hkucc.hku.hk | en_HK |
dc.identifier.authority | Lo, SH=rp00223 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1002/nme.2962 | en_HK |
dc.identifier.scopus | eid_2-s2.0-78650582368 | en_HK |
dc.identifier.hkuros | 195789 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-78650582368&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 85 | en_HK |
dc.identifier.issue | 3 | en_HK |
dc.identifier.spage | 269 | en_HK |
dc.identifier.epage | 288 | en_HK |
dc.identifier.eissn | 1097-0207 | - |
dc.identifier.isi | WOS:000285933500001 | - |
dc.publisher.place | United Kingdom | en_HK |
dc.identifier.scopusauthorid | Zhao, J=36761792700 | en_HK |
dc.identifier.scopusauthorid | Chen, WJ=16021219300 | en_HK |
dc.identifier.scopusauthorid | Lo, SH=7401542444 | en_HK |
dc.identifier.issnl | 0029-5981 | - |