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Article: A refined nonconforming quadrilateral element for couple stress/strain gradient elasticity
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TitleA refined nonconforming quadrilateral element for couple stress/strain gradient elasticity
 
AuthorsZhao, J1
Chen, WJ1 3
Lo, SH2
 
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
 
CitationInternational Journal For Numerical Methods In Engineering, 2011, v. 85 n. 3, p. 269-288 [How to Cite?]
DOI: http://dx.doi.org/10.1002/nme.2962
 
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.
 
ISSN0029-5981
2012 Impact Factor: 2.056
2012 SCImago Journal Rankings: 2.365
 
DOIhttp://dx.doi.org/10.1002/nme.2962
 
ISI Accession Number IDWOS:000285933500001
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).

 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorZhao, J
 
dc.contributor.authorChen, WJ
 
dc.contributor.authorLo, SH
 
dc.date.accessioned2011-09-23T05:44:54Z
 
dc.date.available2011-09-23T05:44:54Z
 
dc.date.issued2011
 
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.
 
dc.description.natureLink_to_subscribed_fulltext
 
dc.identifier.citationInternational Journal For Numerical Methods In Engineering, 2011, v. 85 n. 3, p. 269-288 [How to Cite?]
DOI: http://dx.doi.org/10.1002/nme.2962
 
dc.identifier.doihttp://dx.doi.org/10.1002/nme.2962
 
dc.identifier.eissn1097-0207
 
dc.identifier.epage288
 
dc.identifier.hkuros195789
 
dc.identifier.isiWOS:000285933500001
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).

 
dc.identifier.issn0029-5981
2012 Impact Factor: 2.056
2012 SCImago Journal Rankings: 2.365
 
dc.identifier.issue3
 
dc.identifier.scopuseid_2-s2.0-78650582368
 
dc.identifier.spage269
 
dc.identifier.urihttp://hdl.handle.net/10722/139095
 
dc.identifier.volume85
 
dc.languageeng
 
dc.publisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/1430
 
dc.publisher.placeUnited Kingdom
 
dc.relation.ispartofInternational Journal for Numerical Methods in Engineering
 
dc.relation.referencesReferences in Scopus
 
dc.rightsInternational Journal for Numerical Methods in Engineering. Copyright © John Wiley & Sons Ltd.
 
dc.subjectC0-1 patch test
 
dc.subjectCouple stress theory
 
dc.subjectFinite element method
 
dc.subjectStrain gradient theory
 
dc.titleA refined nonconforming quadrilateral element for couple stress/strain gradient elasticity
 
dc.typeArticle
 
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Author Affiliations
  1. Dalian University of Technology
  2. The University of Hong Kong
  3. Shenyang Institute of Aeronautical Engineering