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Penalty C0 8-node quadrilateral and 20-node hexahedral elements for consistent couple stress elasticity based on the unsymmetric finite element method

Huan-Pu Wu, Yan Shang, Song Cen, Chenfeng Li Orcid Logo

Engineering Analysis with Boundary Elements, Volume: 147, Pages: 302 - 319

Swansea University Author: Chenfeng Li Orcid Logo

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DOI (Published version): 10.1016/j.enganabound.2022.12.008

Abstract

In this paper, the penalty unsymmetric finite element framework for the consistent couple stress theory is derived from the virtual work principle. The C1 continuity requirement is satisfied in weak form by using the penalty function method to constrain the independently introduced rotations for app...

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Published in: Engineering Analysis with Boundary Elements
ISSN: 0955-7997
Published: Elsevier BV 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa62201
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spelling 2023-01-16T09:48:23.6975139 v2 62201 2022-12-22 Penalty C0 8-node quadrilateral and 20-node hexahedral elements for consistent couple stress elasticity based on the unsymmetric finite element method 82fe170d5ae2c840e538a36209e5a3ac 0000-0003-0441-211X Chenfeng Li Chenfeng Li true false 2022-12-22 CIVL In this paper, the penalty unsymmetric finite element framework for the consistent couple stress theory is derived from the virtual work principle. The C1 continuity requirement is satisfied in weak form by using the penalty function method to constrain the independently introduced rotations for approximating the mechanical rotations, enabling the utilization of C° continuous interpolations for designing the element displacement without the loss of convergence property. Within the proposed framework, 8-node quadrilateral element and 20-node hexahedral solid element are constructed for analyzing the size-dependent mechanical responses of consistent couple stress elasticity materials. In these developments, the quadratic serendipity isoparametric shape functions are enriched by the rotation degrees of freedom for determining the test functions, whilst the metric stress functions that are derived from the concerned equilibrium equations are used to design the trial functions. A series of numerical benchmarks are examined for verifying their effectiveness and accuracy. It is shown that the elements can efficiently capture the size dependences, exhibiting good accuracy and low susceptibility to mesh distortion. Journal Article Engineering Analysis with Boundary Elements 147 302 319 Elsevier BV 0955-7997 Unsymmetric FEM; Consistent couple stress theory; Size dependence; Mesh distortion; Penalty function 1 2 2023 2023-02-01 10.1016/j.enganabound.2022.12.008 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2023-01-16T09:48:23.6975139 2022-12-22T10:54:55.7028484 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Huan-Pu Wu 1 Yan Shang 2 Song Cen 3 Chenfeng Li 0000-0003-0441-211X 4 Under embargo Under embargo 2023-01-16T09:46:27.4634928 Output 1895944 application/pdf Accepted Manuscript true 2023-12-19T00:00:00.0000000 ©2022 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Penalty C0 8-node quadrilateral and 20-node hexahedral elements for consistent couple stress elasticity based on the unsymmetric finite element method
spellingShingle Penalty C0 8-node quadrilateral and 20-node hexahedral elements for consistent couple stress elasticity based on the unsymmetric finite element method
Chenfeng Li
title_short Penalty C0 8-node quadrilateral and 20-node hexahedral elements for consistent couple stress elasticity based on the unsymmetric finite element method
title_full Penalty C0 8-node quadrilateral and 20-node hexahedral elements for consistent couple stress elasticity based on the unsymmetric finite element method
title_fullStr Penalty C0 8-node quadrilateral and 20-node hexahedral elements for consistent couple stress elasticity based on the unsymmetric finite element method
title_full_unstemmed Penalty C0 8-node quadrilateral and 20-node hexahedral elements for consistent couple stress elasticity based on the unsymmetric finite element method
title_sort Penalty C0 8-node quadrilateral and 20-node hexahedral elements for consistent couple stress elasticity based on the unsymmetric finite element method
author_id_str_mv 82fe170d5ae2c840e538a36209e5a3ac
author_id_fullname_str_mv 82fe170d5ae2c840e538a36209e5a3ac_***_Chenfeng Li
author Chenfeng Li
author2 Huan-Pu Wu
Yan Shang
Song Cen
Chenfeng Li
format Journal article
container_title Engineering Analysis with Boundary Elements
container_volume 147
container_start_page 302
publishDate 2023
institution Swansea University
issn 0955-7997
doi_str_mv 10.1016/j.enganabound.2022.12.008
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 0
active_str 0
description In this paper, the penalty unsymmetric finite element framework for the consistent couple stress theory is derived from the virtual work principle. The C1 continuity requirement is satisfied in weak form by using the penalty function method to constrain the independently introduced rotations for approximating the mechanical rotations, enabling the utilization of C° continuous interpolations for designing the element displacement without the loss of convergence property. Within the proposed framework, 8-node quadrilateral element and 20-node hexahedral solid element are constructed for analyzing the size-dependent mechanical responses of consistent couple stress elasticity materials. In these developments, the quadratic serendipity isoparametric shape functions are enriched by the rotation degrees of freedom for determining the test functions, whilst the metric stress functions that are derived from the concerned equilibrium equations are used to design the trial functions. A series of numerical benchmarks are examined for verifying their effectiveness and accuracy. It is shown that the elements can efficiently capture the size dependences, exhibiting good accuracy and low susceptibility to mesh distortion.
published_date 2023-02-01T04:21:38Z
_version_ 1763754428247048192
score 11.013104

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