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Article: Four‐node tetrahedral elements for gradient‐elasticity analysis

TitleFour‐node tetrahedral elements for gradient‐elasticity analysis
Authors
KeywordsC1
discrete Kirchhoff
gradient‐elasticity
hybrid formulation
strain‐gradient
Issue Date2020
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, 2020, v. 121 n. 16, p. 3660-3679 How to Cite?
AbstractComputational analyses of gradient‐elasticity often require the trial solution to be C1 yet constructing simple C1 finite elements is not trivial. This article develops two 48‐dof 4‐node tetrahedral elements for 3D gradient‐elasticity analyses by generalizing the discrete Kirchhoff method and a relaxed hybrid‐stress method. Displacement and displacement‐gradient are the only nodal dofs. Both methods start with the derivation of a C0 quadratic‐complete displacement interpolation from which the strain is derived. In the first element, displacement‐gradient at the mid‐edge points are approximated and then interpolated together with those at the nodes whilst the strain‐gradient is derived from the displacement‐gradient interpolation. In the second element, the assumed constant double‐stress modes are employed to enforce the continuity of the normal derivative of the displacement. The whole formulation can be viewed as if the strain‐gradient matrix derived from the displacement interpolation matrix is refined by a constant matrix. Both elements are validated by the individual element patch test and other numerical benchmark tests. To the best knowledge of the authors, the proposed elements are probably the first nonmixed/penalty 3D elements which employ only displacement and displacement‐gradient as the nodal dofs for gradient‐elasticity analyses.
Persistent Identifierhttp://hdl.handle.net/10722/290189
ISSN
2023 Impact Factor: 2.7
2023 SCImago Journal Rankings: 1.019
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorSze, KY-
dc.contributor.authorYuan, WC-
dc.contributor.authorZhou, YX-
dc.date.accessioned2020-10-22T08:23:18Z-
dc.date.available2020-10-22T08:23:18Z-
dc.date.issued2020-
dc.identifier.citationInternational Journal for Numerical Methods in Engineering, 2020, v. 121 n. 16, p. 3660-3679-
dc.identifier.issn0029-5981-
dc.identifier.urihttp://hdl.handle.net/10722/290189-
dc.description.abstractComputational analyses of gradient‐elasticity often require the trial solution to be C1 yet constructing simple C1 finite elements is not trivial. This article develops two 48‐dof 4‐node tetrahedral elements for 3D gradient‐elasticity analyses by generalizing the discrete Kirchhoff method and a relaxed hybrid‐stress method. Displacement and displacement‐gradient are the only nodal dofs. Both methods start with the derivation of a C0 quadratic‐complete displacement interpolation from which the strain is derived. In the first element, displacement‐gradient at the mid‐edge points are approximated and then interpolated together with those at the nodes whilst the strain‐gradient is derived from the displacement‐gradient interpolation. In the second element, the assumed constant double‐stress modes are employed to enforce the continuity of the normal derivative of the displacement. The whole formulation can be viewed as if the strain‐gradient matrix derived from the displacement interpolation matrix is refined by a constant matrix. Both elements are validated by the individual element patch test and other numerical benchmark tests. To the best knowledge of the authors, the proposed elements are probably the first nonmixed/penalty 3D elements which employ only displacement and displacement‐gradient as the nodal dofs for gradient‐elasticity analyses.-
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.relation.ispartofInternational Journal for Numerical Methods in Engineering-
dc.rightsThis is the peer reviewed version of the following article: International Journal for Numerical Methods in Engineering, 2020, v. 121 n. 16, p. 3660-3679, which has been published in final form at https://doi.org/10.1002/nme.6375. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.-
dc.subjectC1-
dc.subjectdiscrete Kirchhoff-
dc.subjectgradient‐elasticity-
dc.subjecthybrid formulation-
dc.subjectstrain‐gradient-
dc.titleFour‐node tetrahedral elements for gradient‐elasticity analysis-
dc.typeArticle-
dc.identifier.emailSze, KY: kysze@hku.hk-
dc.identifier.authoritySze, KY=rp00171-
dc.description.naturepostprint-
dc.identifier.doi10.1002/nme.6375-
dc.identifier.scopuseid_2-s2.0-85085562696-
dc.identifier.hkuros316960-
dc.identifier.volume121-
dc.identifier.issue16-
dc.identifier.spage3660-
dc.identifier.epage3679-
dc.identifier.isiWOS:000535756000001-
dc.publisher.placeUnited Kingdom-
dc.identifier.issnl0029-5981-

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