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Nonlocal strain gradient analysis of FG GPLRC nanoscale plates based on isogeometric approach

Authors:
Phuc Phung-Van at HUTECH University
Phuc Phung-Van
  • HUTECH University
H. Nguyen-Xuan at HUTECH University
H. Nguyen-Xuan
Chien thai Hoang at Ton Duc Thang University
Chien thai Hoang
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Abstract and Figures

In this paper, a nonlocal strain gradient isogeometric model based on the higher order shear deformation theory for free vibration analysis of functionally graded graphene platelet-reinforced composites (FG GPLRC) plates is performed. Various distributed patterns of graphene platelets (GPLs) in the polymer matrix including uniform and non-uniform are considered. To capture size dependence of nanostructures, the nonlocal strain gradient theory including both nonlocal and strain gradient effects is used. Based on the modified Halpin–Tsai model, the effective Young’s modulus of the nanocomposites is expressed, while the Poisson’s ratio and density are established using the rule of mixtures. Natural frequencies of FG GPLRC nanoplates is determined using isogeometric analysis. The effects played by strain gradient parameter, distributions of GPLs, thickness-to-length ratio, and nonlocal parameter are examined, and results illustrate the interesting dynamic phenomenon. Several results are investigated and considered as benchmark results for further studies on the FG GPLRC nanoplates.
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Vol.:(0123456789)
1 3
Engineering with Computers (2023) 39:857–866
https://doi.org/10.1007/s00366-022-01689-4
ORIGINAL PAPER
Nonlocal strain gradient analysis ofFG GPLRC nanoscale plates based
onisogeometric approach
P.Phung‑Van1· H.Nguyen‑Xuan2· ChienH.Thai3,4
Received: 13 October 2021 / Accepted: 3 June 2022 / Published online: 3 July 2022
© The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022
Abstract
In this paper, a nonlocal strain gradient isogeometric model based on the higher order shear deformation theory for free
vibration analysis of functionally graded graphene platelet-reinforced composites (FG GPLRC) plates is performed. Various
distributed patterns of graphene platelets (GPLs) in the polymer matrix including uniform and non-uniform are considered.
To capture size dependence of nanostructures, the nonlocal strain gradient theory including both nonlocal and strain gradient
effects is used. Based on the modified Halpin–Tsai model, the effective Young’s modulus of the nanocomposites is expressed,
while the Poisson’s ratio and density are established using the rule of mixtures. Natural frequencies of FG GPLRC nanoplates
is determined using isogeometric analysis. The effects played by strain gradient parameter, distributions of GPLs, thickness-
to-length ratio, and nonlocal parameter are examined, and results illustrate the interesting dynamic phenomenon. Several
results are investigated and considered as benchmark results for further studies on the FG GPLRC nanoplates.
Keywords Nonlocal strain gradient theory (NSGT)· Length scale effects· NURBS basis function· Graphene platelets
(GPLs)· Nanoscale plates
* Chien H. Thai
thaihoangchien@tdtu.edu.vn
P. Phung-Van
pv.phuc86@hutech.edu.vn
1 Faculty ofCivil Engineering, HUTECH University,
HoChiMinhCity, Vietnam
2 CIRTech Institute, HUTECH University, HoChiMinhCity,
Vietnam
3 Division ofComputational Mechanics, Ton Duc Thang
University, HoChiMinhCity, Vietnam
4 Faculty ofCivil Engineering, Ton Duc Thang University,
HoChiMinhCity, Vietnam
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... Based on the nonlocal strain gradient theory, vibration responses of smallscale FG-GPLRC plates were analyzed using exponential shear deformation plate theory [12] and Kirchhoff plate model [13]. Different solution techniques, including Chebyshev-Ritz [14], isogeometric [15], meshfree [16], and spectral Chebyshev [17] approaches, were employed by researchers to compute the frequency characteristics of FG-GPLRC plates. Additionally, Muni Rami Reddy et al. [18] presented a finite element model based on the first-order shear deformation theory to obtain the natural frequencies of FG-GPLRC plates under various boundary conditions. ...
... Substituting generalized displacement solutions in Eqs. (15) into (11) and after mathematical simplifications, equations of motion can be rewritten in the form of a system of five coupled linear ordinary differential equations (ODE) as follows ...
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