• Bulletin of the Korean Chemical Society
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• 제35권1호
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• pp.253-256
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• 2014

Functionalization of zigzag graphene nanoribbon (ZGNR) segment containing 120 C atoms with pyridine (3NV-ZGNR) defects was investigated on the basis of density-functional theory (DFT) calculations, results show that edge-modified ZGNRs by Sc can adsorb multiple hydrogen molecules in a quasi-molecular fashion, thereby can be a potential candidate for hydrogen storage. The stability of Sc functionalization is dictated by a strong binding energy, suggesting a reduction of clustering of metal atoms over the metal-decorated ZGNR.

• 대한기계학회논문집A
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• 제31권1호
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• pp.121-128
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• 2007

Enhanced lower order shear deformation theory is developed in this study. Generally, lower order theories are not adequate to predict accurate deformation and stress distribution through the thickness of laminated plate. For the accurate prediction of detailed stress and deformation distributions through the thickness, higher order zigzag theories have been proposed. However, in most cases, simplified zigzag higher order theory requires $C_1$, shape functions in finite element implementation. In commercial FE softwares, $C_1$, shape functions are not so common in plate and shell analysis. Thus zigzag theories are useful for the highly accurate prediction of thick composite behaviors but they are not practical in the sense that they cannot be used conveniently in the commercial package. In practice, iso-parametric $C_0$ plate model is the standard model for the analysis and design of composite laminated plates and shells. Thus in the present study, an enhanced lower order shear deformation theory is developed. The proposed theory requires only $C_0$ shape function in FE implementation. The least-squared energy error between the lower order theory and higher order theory is minimized. An enhanced lower order shear deformation theory(ELSDT) in this paper is proposed for smart structure under complex loadings. The ELSDT is constructed by the strain energy transformation and fully coupled mechanical, electric loading cases are studied. In order to obtain accurate prediction, zigzag in-plane displacement and transverse normal deformation are considered in the deformation Held. In the electric behavior, open-circuit condition as well as closed-circuit condition is considered. Through the numerous examples, the accuracy and robustness of present theory are demonstrated.

• Steel and Composite Structures
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• 제23권1호
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• pp.41-51
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• 2017

A $C^0$ FE model developed based on an efficient higher order zigzag theory is used for hygrothermal analysis of laminated composite plates. The $C^0$ FE model satisfies the inter-laminar shear stress continuity at the interfaces and zero transverse shear stress conditions at plate top and bottom. In this model the first derivatives of transverse displacement have been treated as independent variables to circumvent the problem of $C^1$ continuity associated with the above plate theory. In the present theory the above mentioned $C^0$ continuity of the present element is compensated in the stiffness matrix formulation by using penalty parameter approach. In order to avoid stress oscillations observed in the displacement based finite element, the stress field derived from temperature/moisture fields (initial strains) must be consistent with total strain field. Special steps are introduced by field consistent approach (e.g., sampling at gauss points) to compensate this problem. A nine noded $C^0$ continuous isoparametric element is used in the proposed FE model. Comparison of present numerical results with other existing solutions shows that the proposed FE model is efficient, accurate and free of locking.

• Smart Structures and Systems
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• 제5권5호
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• pp.531-546
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• 2009

In the present analysis, the spline finite strip with higher-order shear deformation is formulated for the static analysis of piezoelectric composite plates. The proposed method incorporates Reddy's third-order shear deformation theory, Touratier's "Sine" model, Afaq's exponential model, Cho's higher-order zigzag laminate theory, as well as the classic plate theory and the first-order plate theory. Thus, the analysis can be conducted based on any of the above-mentioned theories. The selection of a specific method is done by simply changing a few terms in a 2 by 2 square matrix and the results, obtained according to different plate theories, can be compared to each other. Numerical examples are presented for piezoelectric composite plates subjected to mechanical loading. The results based on different shear deformation theories are compared with the three-dimensional solutions. The behaviours of piezoelectric composite plates with different length-to-thickness ratios, fibre orientations, and boundary conditions are also investigated in these examples.

• Structural Engineering and Mechanics
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• 제42권4호
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• pp.471-488
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• 2012

An efficient one dimensional finite element model has been presented for the dynamic analysis of composite laminated beams, using the efficient layerwise zigzag theory. To meet the convergence requirements for the weak integral formulation, cubic Hermite interpolation is used for the transverse displacement ($w_0$), and linear interpolation is used for the axial displacement ($u_0$) and shear rotation (${\psi}_0$). Each node of an element has four degrees of freedom. The expressions of variationally consistent inertia, stiffness matrices and the load vector are derived in closed form using exact integration. The formulation is validated by comparing the results with the 2D-FE results for composite symmetric and sandwich beams with various end conditions. The employed finite element model is free of shear locking. The present zigzag finite element results for natural frequencies, mode shapes of cantilever and clamped-clamped beams are obtained with a one-dimensional finite element codes developed in MATLAB. These 1D-FE results for cantilever and clamped beams are compared with the 2D-FE results obtained using ABAQUS to show the accuracy of the developed MATLAB code, for zigzag theory for these boundary conditions. This comparison establishes the accuracy of zigzag finite element analysis for dynamic response under given boundary conditions.

• Advances in materials Research
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• 제12권1호
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• pp.43-65
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• 2023

Free vibration analysis of power law and sigmoidal sandwich plates made up of functionally graded materials (FGMs) has been carried out using finite element based higher-order zigzag theory. The present model satisfies all-important conditions such as transverse shear stress-free conditions at the plate's top and bottom surface along with continuity condition for transverse stresses at the interface. A Nine-noded C0 finite element having eleven degrees of freedom per node is used during the study. The present model is free from the requirement of any penalty function or post-processing technique and hence is computationally efficient. The present model's effectiveness is demonstrated by comparing the present results with available results in the literature. Several new results have been proposed in the present work, which will serve as a benchmark for future works. It has been observed that the material variation law, power-law exponent, skew angle, and boundary condition of the plate widely determines the free vibration behavior of sandwich functionally graded (FG) plate.

• Structural Engineering and Mechanics
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• 제27권1호
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• pp.1-16
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• 2007

In the present study, a spline finite strip with higher-order shear deformation is formulated for the stability and free vibration analysis of composite plates. The analysis is conducted based on Reddy's third-order shear deformation theory, Touratier's "Sine" model, Afaq's exponential model and Cho's higher-order zigzag laminate theory. Consequently, the shear correction coefficients are not required in the analysis, and an improved accuracy for thick laminates is achieved. The numerical results, based on different shear deformation theories, are presented in comparison with the three-dimensional elasticity solutions. The effects of length-to-thickness ratio, fibre orientation, and boundary conditions on the critical buckling loads and natural frequencies are investigated through numerical examples.

• Computers and Concrete
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• 제32권2호
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• pp.165-172
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• 2023

The vibration analysis of armchair, zigzag and chiral double-walled carbon nanotubes has been developed by inserting the nonlocal theory of elasticity into thin shell theory. First Donnell shell theory is employed while exercising wave propagation approach. Scale effects are realized by using different values of nonlocal parameters under certain boundary conditions. The natural frequencies have been investigated and displayed for various non-local parameters. It is noticed that on increasing nonlocal parameter, the frequency curve tends to decrease. The frequency estimates of clamped-free boundary condition are less than those of clamped-clamped and simply supported computations. The frequency comparisons are presented for armchair, zigzag and chiral nanotubes. The software MATLAB is used to extract the frequencies of double walled carbon nanotubes.

• Advances in nano research
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• 제15권3호
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• pp.263-275
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• 2023

The electron transport properties of Y-type zigzag branched carbon nanotubes (CNTs) are of great significance for micro and nano carbon-based electronic devices and their interconnection. Based on the semi-empirical method combining tight-binding density functional theory and non-equilibrium Green's function, the electron transport properties between the branches of Y-type zigzag branched CNT are studied. The results show that the drain-source current of semiconducting Y-type zigzag branched CNT (8, 0)-(4, 0)-(4, 0) is cut-off and not affected by the gate voltage in a bias voltage range [-0.5 V, 0.5 V]. The current presents a nonlinear change in a bias voltage range [-1.5 V, -0.5 V] and [0.5 V, 1.5 V]. The tangent slope of the current-voltage curve can be changed by the gate voltage to realize the regulation of the current. The regulation effect under negative bias voltage is more significant. For the larger diameter semiconducting Y-type zigzag branched CNT (10, 0)-(5, 0)-(5, 0), only the value of drain-source current increases due to the larger diameter. For metallic Y-type zigzag branched CNT (12, 0)-(6, 0)-(6, 0), the drain-source current presents a linear change in a bias voltage range [-1.5 V, 1.5 V] and is symmetrical about (0, 0). The slope of current-voltage line can be changed by the gate voltage to realize the regulation of the current. For three kinds of Y-type zigzag branched CNT with different diameters and different conductivity, the current-voltage curve trend changes from decline to rise when the branch of drain-source is exchanged. The current regulation effect of semiconducting Y-type zigzag branched CNT under negative bias voltage is also more significant.

• Structural Engineering and Mechanics
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• 제88권2호
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• pp.109-115
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• 2023

In this paper, frequencies of zigzag structure of carbon nanotubes isinvestigated based on Donnell shell theory. These tubes are wrapped with the ring supports in the axial direction. The fundamental frequency curves displayed in article show the dependence of vibrations attributes to zigzag single walled carbon nanotubes. Various zigzag indices are introduced against the variation of length to predict the vibration. Also, the influence of ring supports is sketched with proposed structure for frequency analysis. The frequencies of zigzag tube decreases as the length increases. It is observed that the frequencies decreases with ring support and have higher frequencies without ring. The problem is formulated using Partial Differential Equation. Three expressions of modal deformation displacement functions is used for the elimination of temporal variation to form the solution in the eigen from. For the stability of present study the results are compared with experimentally and numerically in the open text.