Geometrically nonlinear large deformation of CNT-reinforced composite plates with internal column supports

2017 ◽  
Vol 1 (1) ◽  
Author(s):  
L. W. Zhang
Keyword(s):  
Large Deformation ◽  
Volume Fraction ◽  
Ritz Method ◽  
Plate Thickness ◽  
Composite Plates ◽  
Functionally Graded ◽  
Width Ratio ◽  
Various Boundary Conditions ◽  
Modified Newton Method ◽  
Element Free

AbstractThe geometrical nonlinear analysis of internally supported nanocomposite plates subjected to a uniformly distributed load is carried out. This study investigates the effects of internal point/column supports on the large deformation bending of nanocomposite plates reinforced by carbon nanotubes (CNTs) with different types of distributions, namely, uniform and two kinds of functionally graded distributions through the thickness of the plates. Two-dimensional displacement field of the plate is approximated by a set of Improved Moving Least Squares (IMLS) functions. The arc-length iterative algorithm with the modified Newton method is employed to obtain the nonlinear response of nanocomposite plates. Convergence studies indicate the validity and effectiveness of the element-free IMLS-Ritz method. The effects of plate thickness-to-width ratio, volume fraction ratio, and plate aspect ratio on the large deformation behavior of nanocomposite plates under various boundary conditions are examined. To the best of the authors’ knowledge, the problem has not been attempted in the open literature.

Bending and free vibration analyses of antisymmetrically laminated carbon nanotube-reinforced functionally graded plates

2016 ◽  
Vol 51 (22) ◽  
pp. 3111-3125 ◽  
Author(s):  
Bin Huang ◽  
Yan Guo ◽  
Ji Wang ◽  
Jianke Du ◽  
Zhenghua Qian ◽  
...  
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Functionally Graded ◽  
Width Ratio ◽  
Variable Theory ◽  
First Order ◽  
First Order Theory

In this paper, a simple four-variable first-order shear deformation theory is further applied to solve the bending and free vibration problems of antisymmetrically laminated functionally graded carbon nanotube (FG-CNT)-reinforced composite plates. The adopted four-variable theory contains only four unknowns in its displacement field which is less than the Reddy’s first-order theory. The equations of motion are derived from the Hamilton’s principle with the help of specific boundary conditions. Laminated FG-CNT-reinforced plates with different distribution types of carbon nanotube through the thickness are considered. The material properties of individual layer are estimated by using the extended rule of mixture. Analytical solutions of various simply supported antisymmetric cross-ply and angle-ply laminates are given for case study. The effects of carbon nanotube volume fraction, length to width ratio and thickness to width ratio on the non-dimensional fundamental frequency and the central deflection are investigated for antisymmetrically laminated FG-CNT-reinforced plates.

Mechanical behavior of laminated functionally graded carbon nanotube reinforced composite plates resting on elastic foundations in thermal environments

2018 ◽  
Vol 53 (9) ◽  
pp. 1159-1179 ◽  
Author(s):  
Tao Fu ◽  
Zhaobo Chen ◽  
Hongying Yu ◽  
Zhonglong Wang ◽  
Xiaoxiang Liu
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Functionally Graded ◽  
Numerical Comparison ◽  
Thermal Environments ◽  
Reinforced Composite

The present study is concerned with static and free vibration analyses of laminated functionally graded carbon nanotube reinforced composite rectangular plates on elastic foundation based on nth-order shear deformation theory. Four types of carbon nanotubes distributions along the plate thickness are considered, which include uniformly distributed and three other functionally graded distributions. Governing differential equations are derived by means of Hamilton’s principle. The differential quadrature method is developed to formulate the problem, and rapid convergence is observed in this study. A numerical comparison with available results in the literature is carried out to show the validity of the proposed theory. Furthermore, effects of the carbon nanotubes volume fraction, thickness side ratio, aspect ratio, foundation parameters, different thermal environments, the number of layers, lamination angle, boundary condition, and carbon nanotubes distribution types on the static response of laminated functionally graded carbon nanotube reinforced composite plates are also investigated.

Vibratory response and acoustic radiation behavior of laminated functionally graded composite plates in thermal environments

2019 ◽  
Vol 22 (5) ◽  
pp. 1681-1706 ◽  
Author(s):  
Tao Fu ◽  
Zhaobo Chen ◽  
Hongying Yu ◽  
Qingjun Hao ◽  
Yanzheng Zhao
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Functionally Graded ◽  
Numerical Comparison ◽  
Thermal Environments ◽  
Reinforced Composite

The present study is concerned with vibro-acoustic behavior analyses of laminated functionally graded carbon nanotube reinforced composite plates based on Reddy’s higher order shear deformation theory. Four types of carbon nanotubes distributions along the plate thickness are considered, which include uniformly distributed and three other functionally graded distributions. Governing differential equations are derived by means of Hamilton’s principle. The sound pressure and radiation efficiency are calculated with Rayleigh integral. A numerical comparison with available results in the literature is carried out to show the validity of the present model. Furthermore, effects of the carbon nanotubes volume fraction, different thermal environments, lamination angle and carbon nanotubes distribution types on the structural and acoustic response of laminated functionally graded carbon nanotube reinforced composite plates are also investigated.

scholarly journals Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

2016 ◽  
Vol 7 ◽  
pp. 511-523 ◽  
Author(s):  
Mostafa Mirzaei ◽  
Yaser Kiani
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Solution Method ◽  
Volume Fraction ◽  
Plate Theory ◽  
Ritz Method ◽  
Composite Plates ◽  
Functionally Graded ◽  
Plane Boundary

During the past five years, it has been shown that carbon nanotubes act as an exceptional reinforcement for composites. For this reason, a large number of investigations have been devoted to analysis of fundamental, structural behavior of solid structures made of carbon-nanotube-reinforced composites (CNTRC). The present research, as an extension of the available works on the vibration analysis of CNTRC structures, examines the free vibration characteristics of plates containing a cutout that are reinforced with uniform or nonuniform distribution of carbon nanotubes. The first-order shear deformation plate theory is used to estimate the kinematics of the plate. The solution method is based on the Ritz method with Chebyshev basis polynomials. Such a solution method is suitable for arbitrary in-plane and out-of-plane boundary conditions of the plate. It is shown that through a functionally graded distribution of carbon nanotubes across the thickness of the plate, the fundamental frequency of a rectangular plate with or without a cutout may be enhanced. Furthermore, the frequencies are highly dependent on the volume fraction of carbon nanotubes and may be increased upon using more carbon nanotubes as reinforcement.

Vibration Analysis of Carbon Nanotube Reinforced Composite Plates

2014 ◽  
Vol 553 ◽  
pp. 681-686 ◽  
Author(s):  
Feng Lin ◽  
Yang Xiang
Keyword(s):  
Ritz Method ◽  
Plate Thickness ◽  
Micromechanical Model ◽  
Composite Plates ◽  
Single Walled Carbon Nanotubes ◽  
Functionally Graded ◽  
Reinforced Composite ◽  
Support Conditions ◽  
Plate Vibration Problem ◽  
Walled Carbon Nanotubes

This paper presents an investigation on the free vibration of rectangular nanocomposite plates reinforced by aligned single-walled carbon nanotubes (SWCNTs). The CNT reinforcement may be uniformly distributed (UD) or functionally graded (FG) over the thickness direction of a plate. The material properties of the CNT composite are determined through a micromechanical model. The eigenvalue equation governing the plate vibration problem is derived by the p-Ritz method through minimizing the virtual strain and kinetic energies of a CNT composite plate. The influences of CNT distribution and reinforcing angle, plate thickness ratio, aspect ratio and support conditions on the vibration behaviour of the plates are discussed.

Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels with general elastic supports

2018 ◽  
Vol 5 (1) ◽  
pp. 95-115
Author(s):  
Fei Xie ◽  
Jinyuan Tang ◽  
Ailun Wang ◽  
Cijun Shuai ◽  
Qingshan Wang
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Ritz Method ◽  
Functionally Graded ◽  
Elastic Supports ◽  
Various Boundary Conditions ◽  
Reinforced Composite ◽  
Cylindrical Panels ◽  
Classical Boundary

Abstract In this paper, a unified solution for vibration analysis of the functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical panels with general elastic supports is carried out via using the Ritz method. The excellent accuracy and reliability of the present method are compared with the results of the classical boundary cases found in the literature. New results are given for vibration characteristics of FG-CNTRC cylindrical panels with various boundary conditions. The effects of the elastic restraint parameters, thickness, subtended angle and volume fraction of carbon nanotubes on the free vibration characteristic of the cylindrical panels are also reported.

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

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