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Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory

Yan Shang, Yu-Hao Mao, Song Cen, Chenfeng Li Orcid Logo

Engineering Analysis with Boundary Elements, Volume: 125, Pages: 46 - 58

Swansea University Author: Chenfeng Li Orcid Logo

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DOI (Published version): 10.1016/j.enganabound.2021.01.007

Abstract

In this work, a new displacement-based Trefftz plate element is developed for size-dependent bending analysis of the thin plate structures in the context of the modified couple stress theory. This is achieved via two steps. First, the Trefftz functions, that are derived by introducing the thin plate...

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Published in: Engineering Analysis with Boundary Elements
ISSN: 0955-7997
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa56142
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spelling 2021-02-16T13:53:45.5635937 v2 56142 2021-01-28 Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory 82fe170d5ae2c840e538a36209e5a3ac 0000-0003-0441-211X Chenfeng Li Chenfeng Li true false 2021-01-28 CIVL In this work, a new displacement-based Trefftz plate element is developed for size-dependent bending analysis of the thin plate structures in the context of the modified couple stress theory. This is achieved via two steps. First, the Trefftz functions, that are derived by introducing the thin plate bending assumptions into the three-dimensional governing equations of the modified couple stress elasticity, are adopted as the basis functions for designing the element's displacement interpolations. Second, the generalized conforming theory is employed to meet the interelement compatibility requirements in weak sense for ensuring the convergence property. The resulting 4-node displacement-based plate element performs like nonconforming models on coarse meshes and gradually converges into a conforming one with the mesh refinement. Numerical tests reveal that the new element can efficiently capture the size-dependent mechanical responses of thin microplates and exhibits satisfactory numerical accuracy and distortion tolerance. Moreover, as the element has only three degrees of freedom (DOF) per node, it can be easily incorporated into the commonly available finite element programs. Journal Article Engineering Analysis with Boundary Elements 125 46 58 Elsevier BV 0955-7997 Trefftz finite element, Thin plate, Generalized conforming theory, Size effect, Modified couple stress theory 1 4 2021 2021-04-01 10.1016/j.enganabound.2021.01.007 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2021-02-16T13:53:45.5635937 2021-01-28T10:08:58.6427906 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Yan Shang 1 Yu-Hao Mao 2 Song Cen 3 Chenfeng Li 0000-0003-0441-211X 4 56142__19232__cc9009f9015d47efb1dbf3a36491be61.pdf 56142.pdf 2021-02-04T10:35:25.6939525 Output 761452 application/pdf Accepted Manuscript true 2022-01-23T00:00:00.0000000 ©2021. 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 http://creativecommons.org/licenses/by-nc-nd/4.0/
title Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory
spellingShingle Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory
Chenfeng Li
title_short Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory
title_full Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory
title_fullStr Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory
title_full_unstemmed Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory
title_sort Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory
author_id_str_mv 82fe170d5ae2c840e538a36209e5a3ac
author_id_fullname_str_mv 82fe170d5ae2c840e538a36209e5a3ac_***_Chenfeng Li
author Chenfeng Li
author2 Yan Shang
Yu-Hao Mao
Song Cen
Chenfeng Li
format Journal article
container_title Engineering Analysis with Boundary Elements
container_volume 125
container_start_page 46
publishDate 2021
institution Swansea University
issn 0955-7997
doi_str_mv 10.1016/j.enganabound.2021.01.007
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 1
active_str 0
description In this work, a new displacement-based Trefftz plate element is developed for size-dependent bending analysis of the thin plate structures in the context of the modified couple stress theory. This is achieved via two steps. First, the Trefftz functions, that are derived by introducing the thin plate bending assumptions into the three-dimensional governing equations of the modified couple stress elasticity, are adopted as the basis functions for designing the element's displacement interpolations. Second, the generalized conforming theory is employed to meet the interelement compatibility requirements in weak sense for ensuring the convergence property. The resulting 4-node displacement-based plate element performs like nonconforming models on coarse meshes and gradually converges into a conforming one with the mesh refinement. Numerical tests reveal that the new element can efficiently capture the size-dependent mechanical responses of thin microplates and exhibits satisfactory numerical accuracy and distortion tolerance. Moreover, as the element has only three degrees of freedom (DOF) per node, it can be easily incorporated into the commonly available finite element programs.
published_date 2021-04-01T04:10:52Z
_version_ 1763753751066181632
score 11.037056

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