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A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method / M. Trabelssi; S. El-Borgi; Michael Friswell

Archive of Applied Mechanics, Volume: 90, Issue: 10, Pages: 2133 - 2156

Swansea University Author: Michael, Friswell

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Abstract

The purpose of this paper is to provide a high-order finite element method (FEM) formulation of nonlocal nonlinear nonlocal graded Timoshenko based on the weak form quadrature element method (WQEM). This formulation offers the advantages and flexibility of the FEM without its limiting low-order accu...

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Published in: Archive of Applied Mechanics
ISSN: 0939-1533 1432-0681
Published: Springer Science and Business Media LLC 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa54547
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spelling 2020-09-29T14:34:14.4704424 v2 54547 2020-06-25 A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2020-06-25 EEN The purpose of this paper is to provide a high-order finite element method (FEM) formulation of nonlocal nonlinear nonlocal graded Timoshenko based on the weak form quadrature element method (WQEM). This formulation offers the advantages and flexibility of the FEM without its limiting low-order accuracy. The nanobeam theory accounts for the von Kármán geometric nonlinearity in addition to Eringen’s nonlocal constitutive models. For the sake of generality, a nonlinear foundation is included in the formulation. The proposed formulation generates high-order derivative terms that cannot be accounted for using regular first- or second-order interpolation functions. Hamilton’s principle is used to derive the variational statement which is discretized using WQEM. The results of a WQEM free vibration study are assessed using data obtained from a similar problem solved by the differential quadrature method (DQM). The study shows that WQEM can offer the same accuracy as DQM with a reduced computational cost. Currently the literature describes a small number of high-order numerical forced vibration problems, the majority of which are limited to DQM. To obtain forced vibration solutions using WQEM, the authors propose two different methods to obtain frequency response curves. The obtained results indicate that the frequency response curves generated by either method closely match their DQM counterparts obtained from the literature, and this is despite the low mesh density used for the WQEM systems. Journal Article Archive of Applied Mechanics 90 10 2133 2156 Springer Science and Business Media LLC 0939-1533 1432-0681 Functionally graded nanobeam; Nonlocal theory; Weak form quadrature element method (WQEM); Free and forced vibration; Nonlinear von’Kármán strain; Frequency response curve 1 10 2020 2020-10-01 10.1007/s00419-020-01713-3 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2020-09-29T14:34:14.4704424 2020-06-25T13:36:12.7746361 College of Engineering Engineering M. Trabelssi 1 S. El-Borgi 2 Michael Friswell 3 54547__17574__deffc1995b07432dbe0788020247c2f8.pdf 54547.pdf 2020-06-25T13:37:51.9782308 Output 652064 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution License (CC-BY). true eng
title A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method
spellingShingle A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method
Michael, Friswell
title_short A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method
title_full A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method
title_fullStr A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method
title_full_unstemmed A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method
title_sort A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method
author_id_str_mv 5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv 5894777b8f9c6e64bde3568d68078d40_***_Michael, Friswell
author Michael, Friswell
author2 M. Trabelssi
S. El-Borgi
Michael Friswell
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1432-0681
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college_str College of Engineering
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description The purpose of this paper is to provide a high-order finite element method (FEM) formulation of nonlocal nonlinear nonlocal graded Timoshenko based on the weak form quadrature element method (WQEM). This formulation offers the advantages and flexibility of the FEM without its limiting low-order accuracy. The nanobeam theory accounts for the von Kármán geometric nonlinearity in addition to Eringen’s nonlocal constitutive models. For the sake of generality, a nonlinear foundation is included in the formulation. The proposed formulation generates high-order derivative terms that cannot be accounted for using regular first- or second-order interpolation functions. Hamilton’s principle is used to derive the variational statement which is discretized using WQEM. The results of a WQEM free vibration study are assessed using data obtained from a similar problem solved by the differential quadrature method (DQM). The study shows that WQEM can offer the same accuracy as DQM with a reduced computational cost. Currently the literature describes a small number of high-order numerical forced vibration problems, the majority of which are limited to DQM. To obtain forced vibration solutions using WQEM, the authors propose two different methods to obtain frequency response curves. The obtained results indicate that the frequency response curves generated by either method closely match their DQM counterparts obtained from the literature, and this is despite the low mesh density used for the WQEM systems.
published_date 2020-10-01T04:25:10Z
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