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Article: A refined nonconforming quadrilateral element for couple stress/strain gradient elasticity

TitleA refined nonconforming quadrilateral element for couple stress/strain gradient elasticity
Authors
KeywordsC0-1 patch test
Couple stress theory
Finite element method
Strain gradient theory
Issue Date2011
PublisherJohn 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 Identifierhttp://hdl.handle.net/10722/139095
ISSN
2013 Impact Factor: 1.961
ISI Accession Number ID
Funding AgencyGrant Number
National Natural Sciences Foundation of China10672032
China Postdoctoral Science Foundation20100470069
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 FieldValueLanguage
dc.contributor.authorZhao, Jen_HK
dc.contributor.authorChen, WJen_HK
dc.contributor.authorLo, SHen_HK
dc.date.accessioned2011-09-23T05:44:54Z-
dc.date.available2011-09-23T05:44:54Z-
dc.date.issued2011en_HK
dc.identifier.citationInternational Journal For Numerical Methods In Engineering, 2011, v. 85 n. 3, p. 269-288en_HK
dc.identifier.issn0029-5981en_HK
dc.identifier.urihttp://hdl.handle.net/10722/139095-
dc.description.abstractC0-1 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.languageengen_US
dc.publisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/1430en_HK
dc.relation.ispartofInternational Journal for Numerical Methods in Engineeringen_HK
dc.rightsInternational Journal for Numerical Methods in Engineering. Copyright © John Wiley & Sons Ltd.en_US
dc.subjectC0-1 patch testen_HK
dc.subjectCouple stress theoryen_HK
dc.subjectFinite element methoden_HK
dc.subjectStrain gradient theoryen_HK
dc.titleA refined nonconforming quadrilateral element for couple stress/strain gradient elasticityen_HK
dc.typeArticleen_HK
dc.identifier.emailLo, SH:hreclsh@hkucc.hku.hken_HK
dc.identifier.authorityLo, SH=rp00223en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1002/nme.2962en_HK
dc.identifier.scopuseid_2-s2.0-78650582368en_HK
dc.identifier.hkuros195789en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-78650582368&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume85en_HK
dc.identifier.issue3en_HK
dc.identifier.spage269en_HK
dc.identifier.epage288en_HK
dc.identifier.eissn1097-0207-
dc.identifier.isiWOS:000285933500001-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridZhao, J=36761792700en_HK
dc.identifier.scopusauthoridChen, WJ=16021219300en_HK
dc.identifier.scopusauthoridLo, SH=7401542444en_HK

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