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8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity

Yan Shang, Chenfeng Li Orcid Logo, Kang‐Yu Jia

International Journal for Numerical Methods in Engineering, Volume: 121, Issue: 12, Pages: 2683 - 2700

Swansea University Author: Chenfeng Li Orcid Logo

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DOI (Published version): 10.1002/nme.6325

Abstract

A new C0 8‐node 48‐DOF hexahedral element is developed for analysis of size‐dependent problems in the context of the modified couple stress theory by extending the methodology proposed in our recent work (Shang et al., Int J Numer Methods Eng 119(9): 807‐825, 2019) to the three‐dimensional (3D) case...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa54099
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spelling 2020-06-04T17:36:44.3332859 v2 54099 2020-05-01 8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity 82fe170d5ae2c840e538a36209e5a3ac 0000-0003-0441-211X Chenfeng Li Chenfeng Li true false 2020-05-01 CIVL A new C0 8‐node 48‐DOF hexahedral element is developed for analysis of size‐dependent problems in the context of the modified couple stress theory by extending the methodology proposed in our recent work (Shang et al., Int J Numer Methods Eng 119(9): 807‐825, 2019) to the three‐dimensional (3D) cases. There are two major innovations in the present formulation. First, the independent nodal rotation degrees of freedom (DOFs) are employed to enhance the standard 3D isoparametric interpolation for obtaining the displacement and strain test functions, as well as to approximatively design the physical rotation field for deriving the curvature test function. Second, the equilibrium stress functions instead of the analytical functions are used to formulate the stress trial function whilst the couple stress trial function is directly obtained from the curvature test function by using the constitutive relationship. Besides, the penalty function is introduced into the virtual work principle for enforcing the C1 continuity condition in weak sense. Several benchmark examples are examined and the numerical results demonstrate that the element can simulate the size‐dependent mechanical behaviors well, exhibiting satisfactory accuracy and low susceptibility to mesh distortion. Journal Article International Journal for Numerical Methods in Engineering 121 12 2683 2700 Wiley 0029-5981 1097-0207 hexahedral element, modified couple stress theory, rotation degree of freedom, size-dependent, unsymmetric FEM 30 6 2020 2020-06-30 10.1002/nme.6325 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2020-06-04T17:36:44.3332859 2020-05-01T12:03:50.3893308 Yan Shang 1 Chenfeng Li 0000-0003-0441-211X 2 Kang‐Yu Jia 3 54099__17198__8342533af2514acf9c0b9b02eab311b5.pdf 54099.pdf 2020-05-07T09:58:32.2021800 Output 1073950 application/pdf Accepted Manuscript true 2021-02-05T00:00:00.0000000 true eng
title 8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity
spellingShingle 8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity
Chenfeng Li
title_short 8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity
title_full 8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity
title_fullStr 8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity
title_full_unstemmed 8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity
title_sort 8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity
author_id_str_mv 82fe170d5ae2c840e538a36209e5a3ac
author_id_fullname_str_mv 82fe170d5ae2c840e538a36209e5a3ac_***_Chenfeng Li
author Chenfeng Li
author2 Yan Shang
Chenfeng Li
Kang‐Yu Jia
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 121
container_issue 12
container_start_page 2683
publishDate 2020
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.6325
publisher Wiley
document_store_str 1
active_str 0
description A new C0 8‐node 48‐DOF hexahedral element is developed for analysis of size‐dependent problems in the context of the modified couple stress theory by extending the methodology proposed in our recent work (Shang et al., Int J Numer Methods Eng 119(9): 807‐825, 2019) to the three‐dimensional (3D) cases. There are two major innovations in the present formulation. First, the independent nodal rotation degrees of freedom (DOFs) are employed to enhance the standard 3D isoparametric interpolation for obtaining the displacement and strain test functions, as well as to approximatively design the physical rotation field for deriving the curvature test function. Second, the equilibrium stress functions instead of the analytical functions are used to formulate the stress trial function whilst the couple stress trial function is directly obtained from the curvature test function by using the constitutive relationship. Besides, the penalty function is introduced into the virtual work principle for enforcing the C1 continuity condition in weak sense. Several benchmark examples are examined and the numerical results demonstrate that the element can simulate the size‐dependent mechanical behaviors well, exhibiting satisfactory accuracy and low susceptibility to mesh distortion.
published_date 2020-06-30T04:08:36Z
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score 10.899228