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High-performance geometric nonlinear analysis with the unsymmetric 4-node, 8-DOF plane element US-ATFQ4

Zhi Li, Song Cen, Cheng-Jin Wu, Yan Shang, 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.5771

Abstract

A recent unsymmetric 4-node, 8-DOF plane element US-ATFQ4, which exhibits excellent precision and distortion-resistance for linear elastic problems, is extended to geometric nonlinear analysis. Since the original linear element US-ATFQ4 contains the analytical solutions for plane pure bending, how t...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 00295981
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa38853
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first_indexed 2018-02-22T19:51:39Z
last_indexed 2018-04-23T19:30:19Z
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spelling 2018-04-23T15:18:03.0152660 v2 38853 2018-02-22 High-performance geometric nonlinear analysis with the unsymmetric 4-node, 8-DOF plane element US-ATFQ4 82fe170d5ae2c840e538a36209e5a3ac 0000-0003-0441-211X Chenfeng Li Chenfeng Li true false 2018-02-22 CIVL A recent unsymmetric 4-node, 8-DOF plane element US-ATFQ4, which exhibits excellent precision and distortion-resistance for linear elastic problems, is extended to geometric nonlinear analysis. Since the original linear element US-ATFQ4 contains the analytical solutions for plane pure bending, how to modify such formulae into incremental forms for nonlinear applications and design an appropriate updated algorithm become the key of the whole job. First, the analytical trial functions should be updated at each iterative step in the framework of updated Lagrangian formulation that takes the configuration at the beginning of an incremental step as the reference configuration during that step. Second, an appropriate stress update algorithm in which the Cauchy stresses are updated by the Hughes-Winget method is adopted to estimate current stress fields. Numerical examples show that the new nonlinear element US-ATFQ4 also possesses amazing performance for geometric nonlinear analysis, no matter whether regular or distorted meshes are used. It again demonstrates the advantages of the unsymmetric finite element method with analytical trial functions. Journal Article International Journal for Numerical Methods in Engineering 00295981 analytical trial function; finite element; geometric nonlinear analysis; mesh distortion; UL formulation; unsymmetric 4-node plane element 31 12 2018 2018-12-31 10.1002/nme.5771 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2018-04-23T15:18:03.0152660 2018-02-22T16:08:16.6113351 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Zhi Li 1 Song Cen 2 Cheng-Jin Wu 3 Yan Shang 4 Chen-Feng Li 5 Chenfeng Li 0000-0003-0441-211X 6 0038853-23022018103745.pdf li2018.pdf 2018-02-23T10:37:45.7430000 Output 3505233 application/pdf Accepted Manuscript true 2019-02-13T00:00:00.0000000 true eng
title High-performance geometric nonlinear analysis with the unsymmetric 4-node, 8-DOF plane element US-ATFQ4
spellingShingle High-performance geometric nonlinear analysis with the unsymmetric 4-node, 8-DOF plane element US-ATFQ4
Chenfeng Li
title_short High-performance geometric nonlinear analysis with the unsymmetric 4-node, 8-DOF plane element US-ATFQ4
title_full High-performance geometric nonlinear analysis with the unsymmetric 4-node, 8-DOF plane element US-ATFQ4
title_fullStr High-performance geometric nonlinear analysis with the unsymmetric 4-node, 8-DOF plane element US-ATFQ4
title_full_unstemmed High-performance geometric nonlinear analysis with the unsymmetric 4-node, 8-DOF plane element US-ATFQ4
title_sort High-performance geometric nonlinear analysis with the unsymmetric 4-node, 8-DOF plane element US-ATFQ4
author_id_str_mv 82fe170d5ae2c840e538a36209e5a3ac
author_id_fullname_str_mv 82fe170d5ae2c840e538a36209e5a3ac_***_Chenfeng Li
author Chenfeng Li
author2 Zhi Li
Song Cen
Cheng-Jin Wu
Yan Shang
Chen-Feng Li
Chenfeng Li
format Journal article
container_title International Journal for Numerical Methods in Engineering
publishDate 2018
institution Swansea University
issn 00295981
doi_str_mv 10.1002/nme.5771
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 A recent unsymmetric 4-node, 8-DOF plane element US-ATFQ4, which exhibits excellent precision and distortion-resistance for linear elastic problems, is extended to geometric nonlinear analysis. Since the original linear element US-ATFQ4 contains the analytical solutions for plane pure bending, how to modify such formulae into incremental forms for nonlinear applications and design an appropriate updated algorithm become the key of the whole job. First, the analytical trial functions should be updated at each iterative step in the framework of updated Lagrangian formulation that takes the configuration at the beginning of an incremental step as the reference configuration during that step. Second, an appropriate stress update algorithm in which the Cauchy stresses are updated by the Hughes-Winget method is adopted to estimate current stress fields. Numerical examples show that the new nonlinear element US-ATFQ4 also possesses amazing performance for geometric nonlinear analysis, no matter whether regular or distorted meshes are used. It again demonstrates the advantages of the unsymmetric finite element method with analytical trial functions.
published_date 2018-12-31T03:48:12Z
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score 10.928156