• Steel and Composite Structures
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• v.35 no.2
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• pp.249-260
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• 2020

The main purpose of this research work is to investigate the free vibration of conical shell structures reinforced by graphene platelets (GPLs) and the elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. To this end, a shell model is developed based on Donnell's theory. To solve the problem, the analytical Galerkin method is employed together with beam mode shapes as weighting functions. Due to importance of boundary conditions upon mechanical behavior of nanostructures, the analysis is carried out for different boundary conditions. The effects of boundary conditions, semi vertex angle, porosity distribution and graphene platelets on the response of conical shell structures are explored. The correctness of the obtained results is checked via comparing with existing data in the literature and good agreement is eventuated. The effectiveness and the accuracy of the present approach have been demonstrated and it is shown that the Donnell's shell theory is efficient, robust and accurate in terms of nanocomposite problems.

• Advances in nano research
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• v.9 no.2
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• pp.69-82
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• 2020

In this paper, a new explicit analytical formula is derived for the critical buckling load of Double Walled Carbon Nanotubes (DWCNTs) embedded in Winkler elastic medium without taking into account the effects of the nonlocal parameter, which indicates the effects of the surrounding elastic matrix combined with the intertube Van der Waals (VdW) forces. Furthermore, we present a model which predicts that the critical axial buckling load embedded in Winkler, Pasternak or Kerr elastic medium under axial compression using the nonlocal Donnell shell theory, this model takes into account the effects of internal small length scale and the VdW interactions between the inner and outer nanotubes. The present model predicts that the critical axial buckling load of embedded DWCNTs is greater than that without medium under identical conditions and parameters. We can conclude that the embedded DWCNTs are less susceptible to axial buckling than those without medium.

• Computers and Concrete
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• v.32 no.2
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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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• v.12 no.5
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• pp.483-488
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• 2022

The present work is an attempt to study the vibration analysis of the single-walled carbon nanotubes (SWCNTs) under the effect of the surface irregularity using Donnell's model. The surface irregularity represented by the parabolic form. According to Donnell's model and three-dimensional elasticity theory, a novel governing equations and its solution are derived and matched with the case of no irregularity effects. To understand the reaction of the nanotube to the irregularity effects in terms of natural frequency, the numerical calculations are done. The results obtained could provide a better representation of the vibration behavior of an irregular single-walled carbon nanotube, where the aspect ratio (L/d) and surface irregularity all have a significant impact on the natural frequency of vibrating SWCNTs. Furthermore, the findings of surface irregularity effects on vibration SWCNT can be utilized to forecast and prevent the phenomena of resonance of single-walled carbon nanotubes.

• Computers and Concrete
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• v.25 no.2
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• pp.133-144
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• 2020

This paper aims to study vibration characteristics of chiral and zigzag double-walled carbon nanotubes entrenched on Donnell shell model. The Eringen's nonlocal elastic equations are being combined with Donnell shell theory to observe small scale response. Wave propagation is proposed technique to establish field equations of model subjected to four distinct end supports. A nonlocal model has been formulated to explore the frequency spectrum of both chiral and zigzag double-walled CNTs along with diversity of indices and nonlocal parameter. The significance of scale effect in relevance of length-to-diameter and thickness- to- radius ratios are discussed and displayed in detail. The numerical solution based on this nonlocal Donnell shell model can be further used to predict other frequency phenomena of double-walled and multi-walled CNTs.

• Advances in aircraft and spacecraft science
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• v.7 no.4
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• pp.335-351
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• 2020

Thermal buckling of functionally graded sandwich cylindrical shells is presented in this study. Material properties and thermal expansion coefficient of FGM layers are assumed to vary continuously through the thickness according to a sigmoid function and simple power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FGM sandwich cylindrical shells with simply supported boundary conditions are derived according to the Donnell theory. The influences of cylindrical shell geometry and the gradient index on the critical buckling temperature of several kinds of FGM sandwich cylindrical shells are investigated. The thermal loads are assumed to be uniform, linear and nonlinear distribution across the thickness direction. An exact simple form of nonlinear temperature rise through its thickness taking into account the thermal conductivity and the inhomogeneity parameter is presented.

• Computers and Concrete
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• v.26 no.1
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• pp.53-62
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• 2020

Concrete is the most widely used substance in construction industry, so it's been required to improve its quality using new technologies. Nowadays, nanotechnology offers new frontiers for improving construction materials. In this paper, we study the stability analysis of the Single Walled Carbon Nanotubes (SWCNT) reinforced concrete cylindrical shell embedded in elastic foundation using the Donnell cylindrical shell theory. In this regard, we propose a new explicit analytical formula of the critical buckling load which takes into account the distribution of SWCNT reinforcement through the thickness of the concrete shell using the U, X, O and V forms and the elastic foundation using Winkler and Pasternak models. The rule of mixture is used to calculate the effective properties of the reinforced concrete cylindrical shell. The influence of diverse parameters on the stability behavior of the reinforced concrete shell is also discussed.

• Smart Structures and Systems
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• v.21 no.5
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• pp.583-590
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• 2018

Nowadays, many tunnels have been commissioned for several decades, which require effective inspection methods to assess their health conditions. The ambient vibration test has been widely adopted for the damage identification of concrete structures. In this study, the vibration characters of tunnel lining shells built with forepoling method was analyzed based on the analytical solutions of the Donnell-Mushtari shell theory. The broken rock, foreploing, rock-concrete contacts between rock mass and concrete lining, was represented by elastic boundaries with normal and shear stiffness. The stiffness of weak contacts has significant effects on the natural frequency of tunnel lining. Numerical simulations were also carried out to compare with the results of the analytical methods, showing that even though the low nature frequency is difficult to distinguish, the presented approach is convenient, effective and accurate to estimate the natural frequency of tunnel linings. Influences of the void, the lining thickness and the concrete type on natural frequencies were evaluated.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.1
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• pp.142-154
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• 1994

In this paper, stochastic imperfection sensitivity analyses of stiffened cylindrical shells under static load are presented. Multimode formulation is performed for the buckling load calculation based on the Donnell's theory and Galerkin approximation. Random imperfection field theory and response surface method are combined with deterministic bucking analysis scheme to perform stochastic imperfection sensitivity analyses of stiffened cylindrical shells considering random geometric imperfection. From the characteristics of probabilistic bucking load, the relation between reliability index and safety parameter can be obtained in addition to the relation between load and reliability index. Those results can be used to determine the range of required safety parameter and acceptable imperfection.

• Transactions of the Korean Society of Mechanical Engineers
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• v.3 no.4
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• pp.158-163
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• 1979

An approximate theory of circular chlindrical shells under arbitrary load is derived on the basis of Vlasov's semimembrane theory. With this approximate theory concrete cylindrical shells subjected to wind loading is analized and its accuracy is investigated with the results of Donnell's equation. In this study the foollowing results are abtained : (1) The expression of .kappa.$\_$2/=.part.$\^$2/.omega./.part. s$\^$2/ for the change of curvature gives much simplicated closed form colution. (2) This approximate theory is to be applicable with sufficient accuracy in the stress analysis of concrete cylindreical shells which the ratio L/D is equal or greater than three.