• Polymer(Korea)
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• v.24 no.6
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• pp.810-819
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• 2000

Poly(p-hydroxybenzoate) (PHB)/poly(ethylene terephthalate) (PET) 8/2 thermotropic liquid crystalline copolyester, poly(ethylene 2,6-naphthalate) (PEN), and PET ternary blend was spun to fiber by melt spinninB process, and tensile properties of the fibers were measured. The matrix of the fibers, PET and PEN, were dissolved in ο-chlorophenol at 55$^{\circ}C$ for 2 hours, and the liquid crystalline polymer fibrils were observed using a scanning electron microscope. Halpin-Tsai equation for modulus calculation of short fiber reinforced composite and the rule of mixture for continuous reinforcement composite were modified, and the tensile modulus were calculated and compared with experimental modulus. To minimize difference between the theoretical and the experimental moduli, dimensionless viscosity constant (K) was given and used to modify two equations. The theoretical tensile modulus using the newly modified equations presentel a similar to the experimental tensile modulus of composite, and the modified equations presented a unique way to determine the tensile modulus of the liquid crystalline polymer reinforced thermoplastic composites.

• Steel and Composite Structures
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• v.25 no.3
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• pp.347-360
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• 2017

The goal of this study is to fill this apparent gap in the area about vibration analysis of multiwalled carbon nanotubes (MWCNTs) curved panels by providing 3-D vibration analysis results for functionally graded multiwalled carbon nanotubes (FG-MWCNTs) sandwich structure with power-law distribution of nanotube. The effective material properties of the FG-MWCNT structures are estimated using a modified Halpin-Tsai equation. Modified Halpin-Tsai equation was used to evaluate the Young's modulus of MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. Also, the mass density and Poisson's ratio of the MWCNT/phenolic composite are considered based on the rule of mixtures. Parametric studies are carried out to highlight the influence of MWCNT volume fraction in the thickness, different types of CNT distribution, boundary conditions and geometrical parameters on vibrational behavior of FG-MWCNT thick curved panels. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Free, Simply supported and Clamped at the curved edges. For an overall comprehension on 3-D vibration analysis of sandwich panel, some mode shape contour plots are reported in this research work.

• Steel and Composite Structures
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• v.32 no.6
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• pp.821-832
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• 2019

An analysis on thermal buckling and postbuckling of composite laminated plates reinforced with a low amount of graphene platelets is performed in the current investigation. It is assumed that graphaene platelets are randomly oriented and uniformly dispersed in each layer of the composite media. Elastic properties of the nanocomposite media are obtained by means of the modified Halpin-Tsai approach which takes into account the size effects of the graphene reinforcements. By means of the von $K{\acute{a}}rm{\acute{a}}n$ type of geometrical nonlinearity, third order shear deformation theory and nonuniform rational B-spline (NURBS) based isogeometric finite element method, the governing equations for the thermal postbuckling of nanocomposite plates in rectangular shape are established. These equations are solved by means of a direct displacement control strategy. Numerical examples are given to study the effects of boundary conditions, weight fraction of graphene platelets and distribution pattern of graphene platelets. It is shown that, with introduction of a small amount of graphene platelets into the matrix of the composite media, the critical buckling temperature of the plate may be enhanced and thermal postbuckling deflection may be alleviated.

• Advances in nano research
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• v.14 no.5
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• pp.443-450
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• 2023

Carbon nanotubes (CNTs) have received increased interest in reinforcing research for polymer matrix composites due to their exceptional mechanical characteristics. Its high surface area/volume ratio and aspect ratio enable polymer-based composites to make the most of its features. This study focuses on the experimental tensile testing and fabrication of carbon nanotube reinforced composite (CNTRC) beams, exploring various micromechanical models. By examining the performance of these models alongside experimental results, the research aims to better understand and optimize the mechanical properties of CNTRC materials. Tensile properties of neat epoxy and 0.3%; 0.4% and 0.5% by CNT reinforced laminated single layer (0°/90°) carbon fiber composite beams were investigated. The composite plates were produced in accordance with ASTM D7264 standard. The tensile test was performed in order to see the mechanical properties of the composite beams. The results showed that the optimum amount of CNT was 0.3% based on the tensile capacity. The capacity was significantly reduced when 0.4% CNT was utilized. Moreover, the experimental results are compared with Finite Element Models using ABAQUS. Hashin Failure Criteria was utilized to predict the tensile capacity. Good conformance was observed between experimental and numerical models. More importantly is that Young' Moduli of the specimens is compared with the prediction Halpin-Tsai and Mixture-Rule. Although Halpin-Tsai can accurately predict the Young's Moduli of the specimens, the accuracy of Mixture-Rule was significantly low.

• Composites Research
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• v.34 no.2
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• pp.123-128
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• 2021

This paper dealt with multi-scale natural frequency characteristics of wavy CNT (carbon nanotube) reinforced composites by applying the Mori-Tanaka method, rule of mixture, and Halpin-Tsai equation. By compelling benefit of an ad-hoc Eshelby tensor, the load-transfer characteristics of CNT with a waviness implanted in the polymer matrix was determined. The numerical results obtained are in good agreement with those reported by other investigators. Furthermore, the new results reported in this paper show the interactions between CNT weight, waviness ratios and layup sequences of laminated composites. Key observation points are discussed and significant considerations are given in practical designing of CNT reinforced composites.

• Computers and Concrete
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• v.27 no.4
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• pp.369-383
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• 2021

This article deals with the frequency analysis of viscoelastic sandwich disk with graphene nano-platelets (GPLs) reinforced viscoelastic concrete (GPLRVC) face sheets and honeycomb core. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin-Tsai model are engaged to provide the effective material constant of the concrete. By employing Hamilton's principle, the governing equations of the structure are derived and solved with the aid of the Generalize Differential Quadrature Method (GDQM). In this paper, viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. Afterward, a parametric study is carried out to investigate the effects of the outer to inner radius ratio, hexagonal core angle, thickness to length ratio of the concrete, the weight fraction of GPLs into concrete, and the thickness of honeycomb core to inner radius ratio on the frequency of the viscoelastic sandwich disk with honeycomb core and FG-GPLRVC face sheet.

• Advances in nano research
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• v.13 no.3
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• pp.233-245
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• 2022

Resently, the use of smart structures has been heightened up rapidly. For this issue, vibration analysis related to a graphene nanoplatelet composite (GPLRC) nanodisk which is attached to a piezoelectric layer and is subjected to thermal loads is explored in the current paper. The formulation of this study is obtained through the energy method and nonlocal strain gradient theory, and then it is solved employing generalized differential quadrature method (GDQM). Halpin-Tsai model in addition to the mixture's rule are utilized to capture the material properties related to the reinforced composite layer. The compatibility conditions are presented for exhibiting the perfect bounding between two layers. The results of this study are validated by employing the other published articles. The impact of such parameters as external voltage, the radius ratio, temperature difference, and nonlocality on the vibrational frequency of the system is investigated in detail.

• Steel and Composite Structures
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• v.48 no.3
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• pp.263-273
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• 2023

This paper investigates dynamic characteristics of a graphene nanoplatelets reinforced composite (GNPRC) sandwich doubly curved shell based on the first-order shear deformation theory (FSDT) and Hamilton's principle. The sandwich doubly curved shell is fabricated from a core made of honeycomb materials sandwiched by composite GNPs reinforced face-sheets. Effective materials properties of composite face-sheets are assumed to vary based on Halpin-Tsai micromechanical models and rule of mixture. Furthermore, the material properties of honeycomb core are estimated using Gibson's formula. The fundamental frequencies of the shell are computed with changes of main geometrical and material properties such as amount and distribution type of graphene nanoplatelets, side length ratio, thickness to length ratio of and side length ratio of honeycomb. The Navier's technique is presented to obtain responses. Accuracy and trueness of the present model and analytical solution is confirmed through comparison of the results with available results in literature. It is concluded that an increase in thickness to length ratio yields a softer core with lower natural frequencies. Furthermore, increase in height to length ratio leads to significant decrease in natural frequencies.

• Steel and Composite Structures
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• v.36 no.6
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• pp.689-702
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• 2020

The current study deals with the size-dependent free vibration analysis of graphene nanoplatelets (GNPs) reinforced polymer nanocomposite plates resting on Pasternak elastic foundation containing different boundary conditions. Based on a four variable refined shear deformation plate theory, which considers shear deformation effect, in conjunction with the Eringen nonlocal elasticity theory, which contains size-dependency inside nanostructures, the equations of motion are established through Hamilton's principle. Moreover, the effective material properties are estimated via the Halpin-Tsai model as well as the rule of mixture. Galerkin's mathematical formulation is utilized to solve the equations of motion for the vibrational problem with different boundary conditions. Parametrical examples demonstrate the influences of nonlocal parameter, total number of layers, weight fraction and geometry of GNPs, elastic foundation parameter, and boundary conditions on the frequency characteristic of the GNPs reinforced nanoplates in detail.

• Structural Engineering and Mechanics
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• v.73 no.6
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• pp.685-698
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• 2020

The dynamic stability of a functionally graded polymer microbeam reinforced by graphene oxides subjected to a periodic axial force is investigated. The microbeam is assumed to rest on an elastic substrate and is subjected to various immovable boundary restraints. The weight fraction of graphene oxides nanofillers is graded across the beam thickness. The effective Young's modulus of the functionally graded graphene oxides reinforced composite (FG-GORC) was determined using modified Halpin-Tsai model, with the mixture rule used to evaluate the effective Poisson's ratio and the mass density. An improved third order shear deformation theory (TSDT) is used in conjunction with the Chebyshev polynomial-based Ritz method to derive the Mathieu-Hill equations for dynamic stability of the FG-GORC microbeam, in which the scale effect is taken into account based on modified couple stress theory. Then, the Mathieu-Hill equation was solved using Bolotin's method to predict the principle unstable regions of the FG-GORC microbeams. The numerical results show the effects of the small scale, the graphene oxides nanofillers as well as the elastic substrate on the dynamic stability behaviors of the FG-GORC microbeams.