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Nonlocal elasticity in plates using novel trial functions

Sh. Faroughi, S.M.H. Goushegir, H. Haddad Khodaparast, M.I. Friswell, Michael Friswell, Hamed Haddad Khodaparast Orcid Logo

International Journal of Mechanical Sciences, Volume: 130, Pages: 221 - 233

Swansea University Authors: Michael Friswell, Hamed Haddad Khodaparast Orcid Logo

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DOI (Published version): 10.1016/j.ijmecsci.2017.05.034

Abstract

This study presents the Ritz formulation, which is based on boundary characteristic orthogonal polynomials (BCOPs), for the two-phase integro-differential form of the Eringen nonlocal elasticity model. This approach is named the nonlocal Ritz method (NL-RM). This feature greatly reduces the computat...

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Published in: International Journal of Mechanical Sciences
ISSN: 00207403
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa34213
first_indexed 2017-06-08T20:13:45Z
last_indexed 2018-02-09T05:24:05Z
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spelling 2017-08-08T16:56:57.9199124 v2 34213 2017-06-08 Nonlocal elasticity in plates using novel trial functions 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false f207b17edda9c4c3ea074cbb7555efc1 0000-0002-3721-4980 Hamed Haddad Khodaparast Hamed Haddad Khodaparast true false 2017-06-08 This study presents the Ritz formulation, which is based on boundary characteristic orthogonal polynomials (BCOPs), for the two-phase integro-differential form of the Eringen nonlocal elasticity model. This approach is named the nonlocal Ritz method (NL-RM). This feature greatly reduces the computational cost compared to the nonlocal finite-element method (NL-FEM). Another advantage of this approach is that, unlike NL-FEM, the nonlocal mass and stiffness matrices are independent of the mesh distribution. Here, these formulations are applied to study the static-bending and free-dynamic analyses of the Kirchhoff plate model. In this paper, novel 2D BCOPs of the plate are derived as coordinate functions. These polynomials are generated using a modified Gram-Schmidt process and satisfy the given geometrical boundary conditions as well as the natural boundary conditions. The accuracy and convergence of the presented model, demonstrated through several numerical examples, are discussed. A concise argument on the advantages of NL-RM compared to NL-FEM is also provided. Journal Article International Journal of Mechanical Sciences 130 221 233 00207403 Two-phase integro-differential formulation; Ritz Method; Boundary characteristic orthogonal polynomials; Kirchhoff plate; Static deflection; Dynamic analysis 31 12 2017 2017-12-31 10.1016/j.ijmecsci.2017.05.034 COLLEGE NANME COLLEGE CODE Swansea University 2017-08-08T16:56:57.9199124 2017-06-08T15:33:33.5774191 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Sh. Faroughi 1 S.M.H. Goushegir 2 H. Haddad Khodaparast 3 M.I. Friswell 4 Michael Friswell 5 Hamed Haddad Khodaparast 0000-0002-3721-4980 6 0034213-08062017153704.pdf faroughi2017.pdf 2017-06-08T15:37:04.2730000 Output 2572403 application/pdf Accepted Manuscript true 2018-06-08T00:00:00.0000000 true eng
title Nonlocal elasticity in plates using novel trial functions
spellingShingle Nonlocal elasticity in plates using novel trial functions
Michael Friswell
Hamed Haddad Khodaparast
title_short Nonlocal elasticity in plates using novel trial functions
title_full Nonlocal elasticity in plates using novel trial functions
title_fullStr Nonlocal elasticity in plates using novel trial functions
title_full_unstemmed Nonlocal elasticity in plates using novel trial functions
title_sort Nonlocal elasticity in plates using novel trial functions
author_id_str_mv 5894777b8f9c6e64bde3568d68078d40
f207b17edda9c4c3ea074cbb7555efc1
author_id_fullname_str_mv 5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
f207b17edda9c4c3ea074cbb7555efc1_***_Hamed Haddad Khodaparast
author Michael Friswell
Hamed Haddad Khodaparast
author2 Sh. Faroughi
S.M.H. Goushegir
H. Haddad Khodaparast
M.I. Friswell
Michael Friswell
Hamed Haddad Khodaparast
format Journal article
container_title International Journal of Mechanical Sciences
container_volume 130
container_start_page 221
publishDate 2017
institution Swansea University
issn 00207403
doi_str_mv 10.1016/j.ijmecsci.2017.05.034
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 Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description This study presents the Ritz formulation, which is based on boundary characteristic orthogonal polynomials (BCOPs), for the two-phase integro-differential form of the Eringen nonlocal elasticity model. This approach is named the nonlocal Ritz method (NL-RM). This feature greatly reduces the computational cost compared to the nonlocal finite-element method (NL-FEM). Another advantage of this approach is that, unlike NL-FEM, the nonlocal mass and stiffness matrices are independent of the mesh distribution. Here, these formulations are applied to study the static-bending and free-dynamic analyses of the Kirchhoff plate model. In this paper, novel 2D BCOPs of the plate are derived as coordinate functions. These polynomials are generated using a modified Gram-Schmidt process and satisfy the given geometrical boundary conditions as well as the natural boundary conditions. The accuracy and convergence of the presented model, demonstrated through several numerical examples, are discussed. A concise argument on the advantages of NL-RM compared to NL-FEM is also provided.
published_date 2017-12-31T19:17:17Z
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score 11.047609

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