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A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory

Yan Shang, Zheng‐Hua Qian, Song Cen, Chen‐Feng Li, Chenfeng Li Orcid Logo

International Journal for Numerical Methods in Engineering

Swansea University Author: Chenfeng Li Orcid Logo

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DOI (Published version): 10.1002/nme.6073

Abstract

In this work, the recently proposed unsymmetric 4‐node 12‐DOF (degree‐of‐freedom) membrane element (Shang and Ouyang, Int J Numer Methods Eng 113(10): 1589‐1606, 2018), which has demonstrated excellent performance for the classical elastic problems, is further extended for the modified couple stress...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa50186
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spelling 2019-07-17T17:42:37.5117612 v2 50186 2019-05-01 A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory 82fe170d5ae2c840e538a36209e5a3ac 0000-0003-0441-211X Chenfeng Li Chenfeng Li true false 2019-05-01 CIVL In this work, the recently proposed unsymmetric 4‐node 12‐DOF (degree‐of‐freedom) membrane element (Shang and Ouyang, Int J Numer Methods Eng 113(10): 1589‐1606, 2018), which has demonstrated excellent performance for the classical elastic problems, is further extended for the modified couple stress theory, to account for the size effect of materials. This is achieved via two formulation developments. Firstly, by using the penalty function method, the kinematic relations between the element's nodal drilling DOFs and the true physical rotations are enforced. Consequently, the continuity requirement for the modified couple stress theory is satisfied in weak sense, and the symmetric curvature test function can be easily derived from the gradients of the drilling DOFs. Secondly, the couple stress field that satisfies a priori the related equilibrium equations is adopted as the energy conjugate trial function to formulate the element for the modified couple stress theory. As demonstrated by a series of benchmark tests, the new element can efficiently capture the size‐dependent responses of materials and is robust to mesh distortions. Moreover, as the new element uses only three conventional DOFs per node, it can be readily incorporated into the standard finite element program framework and commonly available finite element programs. Journal Article International Journal for Numerical Methods in Engineering 0029-5981 1097-0207 31 12 2019 2019-12-31 10.1002/nme.6073 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2019-07-17T17:42:37.5117612 2019-05-01T11:08:11.6734127 College of Engineering Engineering Yan Shang 1 Zheng‐Hua Qian 2 Song Cen 3 Chen‐Feng Li 4 Chenfeng Li 0000-0003-0441-211X 5 0050186-01052019152549.pdf shang2019.pdf 2019-05-01T15:25:49.1430000 Output 1560811 application/pdf Accepted Manuscript true 2020-03-27T00:00:00.0000000 true eng
title A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory
spellingShingle A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory
Chenfeng Li
title_short A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory
title_full A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory
title_fullStr A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory
title_full_unstemmed A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory
title_sort A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory
author_id_str_mv 82fe170d5ae2c840e538a36209e5a3ac
author_id_fullname_str_mv 82fe170d5ae2c840e538a36209e5a3ac_***_Chenfeng Li
author Chenfeng Li
author2 Yan Shang
Zheng‐Hua Qian
Song Cen
Chen‐Feng Li
Chenfeng Li
format Journal article
container_title International Journal for Numerical Methods in Engineering
publishDate 2019
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.6073
college_str College of Engineering
hierarchytype
hierarchy_top_id collegeofengineering
hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
document_store_str 1
active_str 0
description In this work, the recently proposed unsymmetric 4‐node 12‐DOF (degree‐of‐freedom) membrane element (Shang and Ouyang, Int J Numer Methods Eng 113(10): 1589‐1606, 2018), which has demonstrated excellent performance for the classical elastic problems, is further extended for the modified couple stress theory, to account for the size effect of materials. This is achieved via two formulation developments. Firstly, by using the penalty function method, the kinematic relations between the element's nodal drilling DOFs and the true physical rotations are enforced. Consequently, the continuity requirement for the modified couple stress theory is satisfied in weak sense, and the symmetric curvature test function can be easily derived from the gradients of the drilling DOFs. Secondly, the couple stress field that satisfies a priori the related equilibrium equations is adopted as the energy conjugate trial function to formulate the element for the modified couple stress theory. As demonstrated by a series of benchmark tests, the new element can efficiently capture the size‐dependent responses of materials and is robust to mesh distortions. Moreover, as the new element uses only three conventional DOFs per node, it can be readily incorporated into the standard finite element program framework and commonly available finite element programs.
published_date 2019-12-31T04:03:31Z
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score 10.896665