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Isogeometric analysis of functionally graded CNT-reinforced composite plates based on refined plate theory

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Abstract

A simple and effective approach based on refined plate theory (RPT) is proposed to study the static and free vibration characteristics of functionally graded CNT-reinforced composite (FG-CNTRC) plates. Compared to traditional higher order shear deformation theories (HSDTs), the proposed method shows more efficient for FG-CNTRC plates analysis. To solve the C1-continuity requirement of the RPT, we used isogeometric analysis (IGA) to approximate the displacement field, which shows more advantages than the FEA, since it can construct higher-order elements without additional variables. This is an advantage for plate structural analysis because more variables make the calculation cumbersome. Finally, four types of FG-CNTRC plates were investigated and the results show the accuracy and efficiency of the proposed method.

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Abbreviations

ρ m :

Density of the matrix

ρ CNT :

Density of the matrix and the CNTs

E CNT :

Young’s moduli of the CNTs

G CNT12 :

Shear modulus of the CNTs

E m :

Young’s modulus of the matrix

G m :

Shear modulus of the matrix

n :

Efficiency parameters

V CNT :

Volume fractions of the CNTs

V m :

Volume fractions of the matrix

ε :

Strain tensor

u :

Displacement vector

m :

Mass matrix

N 0 :

Pre-buckling loads

Ni,p :

B-spline basic function

R ij :

NURBS basic function

λcr :

Bucking load parameter

K :

Global stiffness matrix

K g :

Geometric stiffness matrix

F :

Load vector

M :

Global mass matrix

\(\overline {\rm{w}} \) :

Non-dimensional central deflection

\({\overline \sigma _{xx}}\) :

Non-dimensional central axial stress

\(\overline \omega \) :

Non-dimensional frequency parameter

\(\overline {{P_{cr}}} \) :

Critical buckling load factor

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 51935009 and U1608256, in part by National Science and Technology Major Project of the Ministry of Science and Technology of China under Grant 2018ZX04020-001, and in part by the Natural Science Foundation of Zhejiang Province under Grant Y19E050078.

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Authors and Affiliations

  1. State Key Laboratory of Fluid Power & Mechatronic Systems, Zhejiang University, Hangzhou, 310027, China

    Zhenyu Liu, Chuang Wang, Guifang Duan & Jianrong Tan

Authors
  1. Zhenyu Liu
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  2. Chuang Wang
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  3. Guifang Duan
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  4. Jianrong Tan
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Corresponding author

Correspondence to Guifang Duan.

Additional information

Zhenyu Liu received the B.S. and Ph.D. in Mechanical Engineering, Zhejiang University, Hangzhou, China, in 1996 and 2002, respectively. He is currently a Professor of Mechanical Engineering and State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou, China. His current research interests include virtual prototyping, virtual-reality-based simulation, machine vision and robotics.

Chuang Wang is a student in the State Key Laboratory of Fluid Power & Mechatronic Systems of Zhejiang University. His fields of interest are in product intelligent design, numerical calculation in engineering, 4D printing.

Guifang Duan received the Doctorate in lntegrated Science and Engineering from Ritsumeikan University, Kyoto, Japan, in 2009. He is currently an Associate Professor of Engineering and Computer Graphics, Zhejiang University, Hangzhou, China. His research interests include virtual-reality-based simulation and machine learning.

Jianrong Tan is an academician of China Engineering Academy and is currently a Professor at Zhejiang University, China. His main research interests include mechanical design theory, virtual prototyping and CAX method.

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Liu, Z., Wang, C., Duan, G. et al. Isogeometric analysis of functionally graded CNT-reinforced composite plates based on refined plate theory. J Mech Sci Technol 34, 3687–3700 (2020). https://doi.org/10.1007/s12206-020-0821-0

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  • DOI: https://doi.org/10.1007/s12206-020-0821-0

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