• Advances in nano research
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• 제16권3호
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• pp.251-263
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• 2024

This article investigates the free vibration behavior of carbon nanotube reinforced composite (CNTRC) beams embedded using variational analytical methods and artificial neural networks (ANN). The material properties of layered functionally graded CNTRC (FG-CNTRC) beams are estimated using nonlocal parameters modified power-law with different types of CNT distributions through the thickness direction of the beam. Adopting Eringen's nonlocal elasticity theory to capture the small size effects, the nonlocal governing equations are derived and solved using the analytical method. And also, the problem was analyzed using the ANN method. The architecture of the proposed ANN model is 3-9-1. In the experiments, we used 112 different data to predict the natural frequency using ANN. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion as well as the boundary conditions of the beam are derived using Hamilton's principle. The classical beam theory is used to formulate a governing equation for predicting the free vibration of laminated CNTRC beams. According to the experimental results, the prediction ability of the ANN model is very good and the natural frequency can be predicted in ANN without attempting any experiments.

• 한국재난정보학회 논문집
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• 제17권4호
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• pp.839-847
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• 2021

연구목적: 본 연구에서는 휨을 받는 탄소 나노튜브 보강 기능경사복합재 판의 구조적 거동을 해석하였다. 이를 위해, 등기하해석과 고차전단변형이론을 결합한 수치해석 방법을 이용하였다. 연구방법: 전단보정계수를 사용하지 않고 기하학적 비선형성을 고려할 수 있는 고차전단변형이론을 통하여 휨이 작용하는 탄소 나노튜브 보강 기능경사복합재 판의 비선형 거동방정식을 유도하였으며, 수정된 Newton-Raphson 반복 기법을 사용하여 등기하해석방법에 기반한 시스템 방정식의 해를 구하였다. 연구결과: 탄소 나노튜브의 배치 양상, 폭-두께 비 및 경계조건은 휨을 받는 탄소 나노튜브 보강 기능경사복합재 판의 구조적 거동에 많은 영향을 끼침을 확인하였다. 결론: 제안된 고차전단변형이론에 근거한 등기하해석 방법은 휨을 받는 탄소 나노튜브 보강 기능경사복합재 판의 구조적 거동을 정확하고 효과적으로 해석하는 것을 알 수 있었다.

• Coupled systems mechanics
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• 제6권2호
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• pp.207-227
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• 2017

In this paper Timoshenko beam theory is employed to investigate the vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) Beams with a stiff core in thermal environment. The material characteristic of carbon nanotubes (CNT) are supposed to change in the thickness direction in a functionally graded form. They can also be calculated through a micromechanical model where the CNT efficiency parameter is determined by matching the elastic modulus of CNTRCs calculated from the rule of mixture with those gained from the molecular dynamics simulations. The differential transform method (DTM) which is established upon the Taylor series expansion is one of the effective mathematical techniques employed to the differential governing equations of sandwich beams. Effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, different thermal environment and various boundary conditions on the free vibration characteristics of FG-CNTRC sandwich beams are studied. It is observed that vibration response of FG-CNTRC sandwich beams is prominently influenced by these parameters.

• Computers and Concrete
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• 제24권6호
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• pp.499-511
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• 2019

In this paper, wave propagation of double-bonded Cooper-Naghdi micro sandwich cylindrical shells with porous core and carbon nanotube reinforced composite (CNTRC) face sheets are investigated subjected to multi-physical loadings with temperature dependent material properties. The governing equations of motion are derived by Hamilton's principle. Then, the influences of various parameters such as wave number, CNT volume fraction, temperature change, Skempton coefficient, material length scale parameter, porosity coefficient on the phase velocity of double-bonded micro sandwich shell are taken into account. It is seen that by increasing of Skempton coefficient, the phase velocity decreases for higher wave number and the results become approximately the constant. Also, by increasing of the material length scale parameter, the cut of frequency increases, because the stiffness of micro structure increases. The obtained results for this article can be used to detect, locate and quantify crack.

• Steel and Composite Structures
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• 제31권3호
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• pp.243-259
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• 2019

This study deals with the nonlinear static analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) truncated conical shells subjected to axial load based on the classical shell theory. Detailed studies for both nonlinear buckling and post-buckling behavior of truncated conical shells. The truncated conical shells are reinforced by single-walled carbon nanotubes which alter according to linear functions of the shell thickness. The nonlinear equations are solved by both the Airy stress function and Galerkin method based on the classical shell theory. In numerical results, the influences of various types of distribution and volume fractions of carbon nanotubes, geometrical parameters, elastic foundations on the nonlinear buckling and post-buckling behavior of FG-CNTRC truncated conical shells are presented. The proposed results are validated by comparing with other authors.

• Steel and Composite Structures
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• 제46권1호
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• pp.133-141
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• 2023

Based on the third-order shear deformation theory, the wave propagations in doubly curved spherical- and cylindrical- panels reinforced by carbon nanotubes (CNTs) are firstly investigated in present work. The coupled equations of wave propagation for the carbon nanotubes reinforced composite (CNTRC) doubly curved panels are established. Then, combined with the harmonic balance method, the eigenvalue technique is adopted to simulate the velocity-wave number curves of the CNTRC doubly curved panels. In the end, numerical results are showed to discuss the effects of the impact of key parameters including the volume fraction, different shell types (including spherical (R₁=R₂=R) and cylindrical (R₁=R, R₂=→∞)), wave number as well as modal number on the sensitivity of elastic waves propagating in CNTRC doubly curved shells.

• Structural Engineering and Mechanics
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• 제88권4호
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• pp.335-354
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• 2023

In this study, analysis of wave propagation characteristics for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates is performed using first-order shear deformation theory (FSDT) and nonlocal strain gradient theory. Uniform distribution (UD) and three types of functionally graded distributions of carbon nanotubes (CNTs) are assumed. The effective mechanical properties of the FG-CNTRC nanoplate are assumed to vary continuously in the thickness direction and are approximated based on the rule of mixture. Also, the governing equations of motion are derived via the extended Hamilton's principle. In numerical examples, the effects of nonlocal parameter, wavenumber, angle of wave propagation, volume fractions, and carbon nanotube distributions on the wave propagation characteristics of the FG-CNTRC nanoplate are studied. As represented in the results, it is clear that the internal length-scale parameter has a remarkable effect on the wave propagation characteristics resulting in significant changes in phase velocity and natural frequency. Furthermore, it is observed that the strain gradient theory yields a higher phase velocity and frequency compared to those obtained by the nonlocal strain gradient theory and classic theory.

• Steel and Composite Structures
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• 제29권3호
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• pp.405-422
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• 2018

In this research, experimental tensile test and manufacturing of carbon nanotube reinforced composite beam (CNTRC) is presented. Also, bending, buckling, and vibration analysis of CNTRC based on various beam theories such as Euler-Bernoulli, Timoshenko and Reddy beams are considered. At first, the experimental tensile tests are carried out for CNTRC and composite beams in order to obtain mechanical properties and then using Hamilton's principle the governing equations of motion are derived for Euler Bernoulli, Timoshenko and Reddy theories. The results have a good agreement with the obtained results by similar researches and it is shown that adding just two percent of carbon nanotubes increases dimensionless fundamental frequency and critical buckling load as well as decreases transverse deflection of composite beams. Also, the influences of different manufacturing processes such as hand layup and industrial methods using vacuum pump on composite properties are investigated. In these composite beams, glass fibers used in an epoxy matrix and for producing CNTRC, CNTs are applied as reinforcement particles. Applying two percent of CNTs leads to increase the mechanical properties and increases natural frequencies and critical buckling load and decreases deflection. The obtained natural frequencies and critical buckling load by theoretical method are higher than other methods, because there are some inevitable errors in industrial and hand layup method. Also, the minimum deflection occurs for theoretical methods, in bending analysis. In this study, Young's and shear modulli as well as density are obtained by experimental test and have not been used from the results of other researches. Then the theoretical analysis such as bending, buckling and vibration are considered by using the obtained mechanical properties of this research.

• Advances in nano research
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• 제7권6호
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• pp.405-417
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• 2019

This research is devoted to study post-buckling analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) micro plate with cut out subjected to magnetic field and resting on elastic medium. The basic formulation of plate is based on first order shear deformation theory (FSDT) and the material properties of FG-CNTRCs are presumed to be changed through the thickness direction, and are assumed based on rule of mixture; moreover, nonlocal Eringen's theory is applied to consider the size-dependent effect. It is considered that the system is embedded in elastic medium and subjected to longitudinal magnetic field. Energy approach, domain decomposition and Rayleigh-Ritz methods in conjunction with Newton-Raphson iterative technique are employed to trace the post-buckling paths of FG-CNTRC micro cut out plate. The influence of some important parameters such as small scale effect, cut out dimension, different types of FG distributions of CNTs, volume fraction of CNTs, aspect ratio of plate, magnitude of magnetic field, elastic medium and biaxial load on the post-buckling behavior of system are calculated. With respect to results, it is concluded that the aspect ratio and length of square cut out have negative effect on post-buckling response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the post-buckling behavior of plate and different distributions of CNTs in plate have diverse response. Meanwhile, nonlocal parameter and biaxial compression load on the plate has negative effect on post-buckling response. In addition, imposing magnetic field increases the post-buckling load of the microstructure.

• Steel and Composite Structures
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• 제42권2호
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• pp.243-256
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• 2022

A coupled finite element method (FEM)-boundary element method (BEM) for analyzing the hydroelastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) floating plates under moving loads is firstly introduced in this article. For that aim, the plate displacement field is described utilizing a generalized shear deformation theory (GSDT)-based FEM, meanwhile the linear water-wave theory (LWWT)-relied BEM is employed for the fluid hydrodynamic modeling. Both computational domains of the plate and fluid are coincidentally discretized into 4-node Hermite elements. Accordingly, the C1-continuous plate element model can be simply captured owing to the inherent feature of third-order Hermite polynomials. In addition, this model is also completely free from shear correction factors, although the shear deformation effects are still taken into account. While the fluid BEM can easily handle the free surface with a lower computational effort due to its boundary integral performance. Material properties through the plate thickness follow four specific CNT distributions. Outcomes gained by the present FEM-BEM are compared with those of previously released papers including analytical solutions and experimental data to validate its reliability. In addition, the influences of CNT volume fraction, different CNT configurations, water depth, and load speed on the hydroelastic behavior of FG-CNTRC plates are also examined.