• Steel and Composite Structures
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• v.30 no.6
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• pp.493-516
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• 2019

This paper is dedicated to nonlinear static and free vibration analysis of Uniform Distributed Carbon Nanotube Reinforced Composite (UD-CNTRC) structures under in-plane loading. The authors have suggested an efficient six-node triangular element. Mixed Interpolation of Tensorial Components (MITC) approach is employed to alleviate the membrane locking phenomena. Moreover, the behavior of the well-known LST element is considerably improved by applying an additional linear interpolation on the strain fields. Based on the rule of mixture, the properties of CNTRC are obtained. In this study, only the uniform distributed CNTs are employed through the thickness direction of element. To achieve the natural frequencies and shape modes, the eigenvalue problem is also solved. Using Total Lagrangian Principles, large amplitude free vibration is considered based on the first normalized mode shape of structure. Different well-known plane problem benchmarks and some proposed ones are studied to validate the accuracy and capability of authors' formulations. In addition, the effects of length to the height ratio of beam, CNT's characteristics, support conditions and normalized amplitude parameter on the linear and nonlinear vibration parameters are investigated.

• Advances in nano research
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• v.7 no.4
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• pp.277-292
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• 2019

In this present paper, a new two dimensional (2D) and quasi three dimensional (quasi-3D) nonlocal shear deformation theories are formulated for free vibration analysis of size-dependent functionally graded (FG) nanoplates. The developed theories is based on new description of displacement field which includes undetermined integral terms, the issues in using this new proposition are to reduce the number of unknowns and governing equations and exploring the effects of both thickness stretching and size-dependency on free vibration analysis of functionally graded (FG) nanoplates. The nonlocal elasticity theory of Eringen is adopted to study the size effects of FG nanoplates. Governing equations are derived from Hamilton's principle. By using Navier's method, analytical solutions for free vibration analysis are obtained through the results of eigenvalue problem. Several numerical examples are presented and compared with those predicted by other theories, to demonstrate the accuracy and efficiency of developed theories and to investigate the size effects on predicting fundamental frequencies of size-dependent functionally graded (FG) nanoplates.

• Advances in nano research
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• v.7 no.3
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• pp.157-167
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• 2019

In this paper, a classical plate model is utilized to formulate the wave propagation problem of magnetostrictive sandwich nanoplates (MSNPs) while subjected to hygrothermal loading with respect to the scale effects. Herein, magnetostriction effect is considered and controlled on the basis of a feedback control system. The nanoplate is supposed to be embedded on a visco-Pasternak substrate. The kinematic relations are derived based on the Kirchhoff plate theory; also, combining these obtained equations with Hamilton's principle, the local equations of motion are achieved. According to a nonlocal strain gradient theory (NSGT), the small scale influences are covered precisely by introducing two scale coefficients. Afterwards, the nonlocal governing equations can be derived coupling the local equations with those of the NSGT. Applying an analytical solution, the wave frequency and phase velocity of propagated waves can be gathered solving an eigenvalue problem. On the other hand, accuracy and efficiency of presented model is verified by setting a comparison between the obtained results with those of previous published researches. Effects of different variants are plotted in some figures and the highlights are discussed in detail.

• Steel and Composite Structures
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• v.31 no.5
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• pp.529-539
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• 2019

Current paper deals with thermoelastic static and free vibrational behaviors of axisymmetric thick cylinders reinforced with functionally graded (FG) randomly oriented graphene subjected to internal pressure and thermal gradient loads. The heat transfer and mechanical analyses of randomly oriented graphene-reinforced nanocomposite (GRNC) cylinders are facilitated by developing a weak form mesh-free method based on moving least squares (MLS) shape functions. Furthermore, in order to estimate the material properties of GRNC with temperature dependent components, a modified Halpin-Tsai model incorporated with two efficiency parameters is utilized. It is assumed that the distributions of graphene nano-sheets are uniform and FG along the radial direction of nanocomposite cylinders. By comparing with the exact result, the accuracy of the developed method is verified. Also, the convergence of the method is successfully confirmed. Then we investigated the effects of graphene distribution and volume fraction as well as thermo-mechanical boundary conditions on the temperature distribution, static response and natural frequency of the considered FG-GRNC thick cylinders. The results disclosed that graphene distribution has significant effects on the temperature and hoop stress distributions of FG-GRNC cylinders. However, the volume fraction of graphene has stronger effect on the natural frequencies of the considered thick cylinders than its distribution.

• Advances in nano research
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• v.10 no.4
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• pp.385-395
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• 2021

This research concentrates on the effects of distributions and volume fractions of carbon nanotubes (CNT) on the nonlinear bending behavior of deep cylindrical panels reinforced by functionally graded carbon nanotubes under thermo-mechanical loading, hitherto not reported in the literature. Assuming the effects of shear deformation and moderately high value of the radius-to-side ratio (R/a), based on the first-order shear deformation theory (FSDT) and von Karman type of geometric nonlinearity, the governing system of equations is obtained. The analytical solution of field equations is carried out using the Ritz method together with the Newton-Raphson iterative scheme. The effects of radius-to-side ratio, temperature change, and boundary conditions on the nonlinear response of the functionally graded carbon nanotubes reinforced composite deep cylindrical panel (FG-CNTRC) are investigated. It is concluded that, among the five possible distribution patterns of CNT, FG-V CNTRC deep cylindrical panel is strongest with the highest bending moment and followed by UD, X, O, and Ʌ-ones. Also, considering the present deep cylindrical panel formulation increases the accuracy of the results. Hence, according to the noticeable amount of R/a in FG-CNTRC cylindrical panels, it is mandatory to apply strain-displacement relations of deep cylindrical panels for bending analysis of FG-CNTRC which certainly is desirable for industrial application.

• Advances in nano research
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• v.13 no.6
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• pp.587-597
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• 2022

In the present study, a novel optimization method in formation control of multi -system vehicles based on the trajectory of the nearest neighbor trajectory is presented. In this regard, the state equations of each vehicle and multisystem is derived and the optimization scheme based on minimizing the differences between actual positions and desired positions of the vehicles are conducted. This formation control is a position-based decentralized model. The trajectory of the nearest neighbor are optimized based on the current position and state of the vehicle. This approach aids the whole multi-agent system to be optimized on their trajectory. Furthermore, to overcome the cumulative errors and maintain stability in the network a semi-centralized scheme is designed for the purpose of checking vehicle position to its predefined trajectory. The model is implemented in Matlab software and the results for different initial state and different trajectory definition are presented. In addition, to avoid collision avoidance and maintain the distances between vehicles agents at a predefined desired distances. In this regard, a neural fuzzy network is defined to be utilized in conjunction with the control system to avoid collision between vehicles. The outcome reveals that the model has acceptable stability and accuracy.

• Steel and Composite Structures
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• v.44 no.2
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• pp.255-270
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• 2022

This manuscript illustrates the dynamic response of nanoscale carbon nanotubes (CNTs) embedded in an elastic media under moving load using doublet mechanics theory, which not considered before. CNTs are modelled by Timoshenko beam theory (TBT) and a bottom to up modelling nano-mechanics is simulated by doublet mechanics theory to capture the size effect of CNTs. To explore the influence of the CNTs configurations on the dynamic behaviour, both armchair and zigzag configurations are considered. The governing equations of motion and the associated boundary conditions are obtained using the Hamiltonian principle. The Navier solution methodology is applied to obtain the solutions for both orientations. Free vibration and forced response under moving loads are considered. The accuracy of the developed procedure is verified by comparing the obtained results with available previous algorithms and good agreement is observed. Parametric studies are conducted to demonstrate effects of doublet length scale, CNTs configurations, moving load velocities as well as the elastic media parameters on the dynamic behaviours of CNTs. The developed procedure is supportive in the design and manufacturing of MEMS/NEMS made from CNTs.

• Advances in nano research
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• v.12 no.2
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• pp.139-150
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• 2022

This paper presents sets of explicit analytical equations that compute the static displacements of nanobeams by adopting the nonlocal elasticity theory of Eringen within the framework of Euler Bernoulli and Timoshenko beam theories. Castigliano's theorem is applied to an equivalent Virtual Local Beam (VLB) made up of linear elastic material to compute the displacements. The first derivative of the complementary energy of the VLB with respect to a virtual point load provides displacements. The displacements of the VLB are assumed equal to those of the nonlocal beam if nonlocal effects are superposed as additional stress resultants on the VLB. The illustrative equations of displacements are relevant to a few types of loadings combined with a few common boundary conditions. Several equations of displacements, thus derived, matched precisely in similar cases with the equations obtained by other analytical methods found in the literature. Furthermore, magnitudes of maximum displacements are also in excellent agreement with those computed by other numerical methods. These validated the superposition of nonlocal effects on the VLB and the accuracy of the derived equations.

• Current Optics and Photonics
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• v.6 no.1
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• pp.69-78
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• 2022

A high-resolution camera is a precise optical system. Its vibrations during transportation and launch, together with changes in temperature and gravity field in orbit, lead to different degrees of defocus of the camera. Thermal refocusing is one of the solutions to the problems related to in-orbit defocusing, but there are few relevant thermal refocusing mathematical models for systematic analysis and research. Therefore, to further research thermal refocusing systems by using the development of a high-resolution micro-nano satellite (CX6-02) super-resolution camera as an example, we established a thermal refocusing mathematical model based on the thermal elasticity theory on the basis of the secondary mirror position. The detailed design of the thermal refocusing system was carried out under the guidance of the mathematical model. Through optical-mechanical-thermal integration analysis and Zernike polynomial calculation, we found that the data error obtained was about 1%, and deformation in the secondary mirror surface conformed to the optical index, indicating the accuracy and reliability of the thermal refocusing mathematical model. In the final ground test, the thermal vacuum experimental verification data and in-orbit imaging results showed that the thermal refocusing system is consistent with the experimental data, and the performance is stable, which provides theoretical and technical support for the future development of a thermal refocusing space camera.

• Advances in nano research
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• v.14 no.3
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• pp.261-271
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• 2023

The present study follows three main goals. First, an analytical solution with high accuracy is developed to assess the effects of embedding pre-strained shape memory alloy (SMA) wires on the critical buckling temperatures of rectangular sandwich plates made of soft core and graphite fiber/epoxy (GF/EP) face sheets based on piecewise low-order shear deformation theory (PLSDT) using Brinson's model. As the second goal, this study compares the effects of SMAs on the thermal buckling of sandwich plates with those of carbon nanotubes (CNTs). The glass transition temperature is considered as a limiting factor. For each material, the effective ranges of operating temperature and thickness ratio are determined for real situations. The results indicate that depending on the geometric parameters and thermal conditions, one of the SMAs and CNTs may outperform the other. The third purpose is to study the thermal buckling of sandwich plates with advanced hybrid SMA/CNT/GF/EP composite face sheets. It is shown that in some circumstances, the co-incorporation of SMAs and CNTs leads to an astonishing enhancement in the critical buckling temperatures of sandwich plates.