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Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate

Song Cen, Yan Shang, Chen-Feng Li, Hong-Guang Li, Chenfeng Li Orcid Logo

International Journal for Numerical Methods in Engineering, Volume: 98, Issue: 3, Pages: 203 - 234

Swansea University Author: Chenfeng Li Orcid Logo

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DOI (Published version): 10.1002/nme.4632

Abstract

In order to develop robust finite element models for analysis of thin and moderately thick plates, a simple hybrid displacement function element method is presented. First, the variational functional of complementary energy for Mindlin–Reissner plates is modified to be expressed by a displacement fu...

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Published in: International Journal for Numerical Methods in Engineering
Published: 2014
URI: https://cronfa.swan.ac.uk/Record/cronfa21434
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spelling 2018-04-14T12:08:01.7407389 v2 21434 2015-05-15 Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate 82fe170d5ae2c840e538a36209e5a3ac 0000-0003-0441-211X Chenfeng Li Chenfeng Li true false 2015-05-15 CIVL In order to develop robust finite element models for analysis of thin and moderately thick plates, a simple hybrid displacement function element method is presented. First, the variational functional of complementary energy for Mindlin–Reissner plates is modified to be expressed by a displacement function F, which can be used to derive displacement components satisfying all governing equations. Second, the assumed element resultant force fields, which can satisfy all related governing equations, are derived from the fundamental analytical solutions of F. Third, the displacements and shear strains along each element boundary are determined by the locking-free formulae based on the Timoshenko's beam theory. Finally, by applying the principle of minimum complementary energy, the element stiffness matrix related to the conventional nodal displacement DOFs is obtained. Because the trial functions of the domain stress approximations a priori satisfy governing equations, this method is consistent with the hybrid-Trefftz stress element method. As an example, a 4-node, 12-DOF quadrilateral plate bending element, HDF-P4-11 β, is formulated. Numerical benchmark examples have proved that the new model possesses excellent precision. It is also a shape-free element that performs very well even when a severely distorted mesh containing concave quadrilateral and degenerated triangular elements is employed. Journal Article International Journal for Numerical Methods in Engineering 98 3 203 234 20 4 2014 2014-04-20 10.1002/nme.4632 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2018-04-14T12:08:01.7407389 2015-05-15T11:27:59.5526912 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Song Cen 1 Yan Shang 2 Chen-Feng Li 3 Hong-Guang Li 4 Chenfeng Li 0000-0003-0441-211X 5
title Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate
spellingShingle Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate
Chenfeng Li
title_short Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate
title_full Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate
title_fullStr Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate
title_full_unstemmed Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate
title_sort Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate
author_id_str_mv 82fe170d5ae2c840e538a36209e5a3ac
author_id_fullname_str_mv 82fe170d5ae2c840e538a36209e5a3ac_***_Chenfeng Li
author Chenfeng Li
author2 Song Cen
Yan Shang
Chen-Feng Li
Hong-Guang Li
Chenfeng Li
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 98
container_issue 3
container_start_page 203
publishDate 2014
institution Swansea University
doi_str_mv 10.1002/nme.4632
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 order to develop robust finite element models for analysis of thin and moderately thick plates, a simple hybrid displacement function element method is presented. First, the variational functional of complementary energy for Mindlin–Reissner plates is modified to be expressed by a displacement function F, which can be used to derive displacement components satisfying all governing equations. Second, the assumed element resultant force fields, which can satisfy all related governing equations, are derived from the fundamental analytical solutions of F. Third, the displacements and shear strains along each element boundary are determined by the locking-free formulae based on the Timoshenko's beam theory. Finally, by applying the principle of minimum complementary energy, the element stiffness matrix related to the conventional nodal displacement DOFs is obtained. Because the trial functions of the domain stress approximations a priori satisfy governing equations, this method is consistent with the hybrid-Trefftz stress element method. As an example, a 4-node, 12-DOF quadrilateral plate bending element, HDF-P4-11 β, is formulated. Numerical benchmark examples have proved that the new model possesses excellent precision. It is also a shape-free element that performs very well even when a severely distorted mesh containing concave quadrilateral and degenerated triangular elements is employed.
published_date 2014-04-20T03:25:25Z
_version_ 1763750891398103040
score 11.016235

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