• Steel and Composite Structures
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• 제51권1호
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• pp.1-8
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• 2024

Transient dynamic behavior of a sandwich beam under thermal and impulsive loads has been researched in the context of higher-order beam theory. The impulse load of blast type has been enforced on the top exponent of the sandwich beam while it is in a thermal environment. The core of the sandwich beam is cellular with auxetic rectangular pattern, whereas the layers have been built with the incorporation of graphene oxide powder (GOP) and are micromechanically introduced through Halpin-Tsai formulization. Governing equations for the sandwich beam have been solved through inverse Laplace transform style for obtaining the dynamical deflections. The connection of beam deflections on temperature variability, GOP quantity, pulse load situation and core relative density has been surveyed in detail.

• Advances in nano research
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• 제16권3호
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• pp.303-311
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• 2024

This paper conducts a thorough economic evaluation of integrating nanoparticles into concrete structures within the construction industry, aiming to elevate the material properties of concrete. Employing the Halpin-Tsai micromechanics theory for deriving the effective material properties of the nanocomposite concrete structure, the research investigates the nuanced impact of nanoparticles on various mechanical properties, including the modulus of elasticity, compressive strength, and their indirect effects on the percentage of reinforcement. Implementing the Euler theory to formulate the governing equation based on Hamilton's principle, the study delves into the pricing dynamics of nanoparticles and their influence on the overall cost structure of concrete structures. Notably, the findings reveal that a measured increase in the volume percentage of nanoparticles, up to 1%, results in a remarkable 78% improvement in elastic modulus and a substantial 142% reduction in armature percentage. Remarkably, from an economic perspective, the incremental cost associated with the integration of nanoparticles is relatively modest (around $1 per ton of concrete), considering the substantial enhancements in mechanical properties achieved.

• Macromolecular Research
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• 제17권10호
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• pp.797-806
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• 2009

The mechanical and thermal behaviors of polyamide-6/clay nanocomposites were studied using the continuum-based, micromechanical models such as Mori-Tanaka, Halpin-Tsai and shear lag. Mechanic-based model prediction provides a better understanding regarding the dependence of the nanocomposites' reinforcement efficiency on conventional filler structural parameters such as filler aspect ratio ($\alpha$), filler orientation (S), filler weight fraction (${\Psi}_f$), and filler/matrix stiffness ratio ($E_f/E_m$). For an intercalated and exfoliated nanocomposite, an effective, filler-based, micromechanical model that includes effective filler structural parameters, the number of platelets per stack (n) and the silicate inter-layer spacing ($d_{001}$), is proposed to describe the mesoscopic intercalated filler and the nanoscopic exfoliated filler. The proposed model nicely captures the experimental modulus behaviors for both intercalated and exfoliated nanocomposites. In addition, the model prediction of the heat distortion temperature is examined for nanocomposites with different filler aspect ratio. The predicted heat distortion temperature appears to be reasonable compared to the heat distortion temperature obtained by experimental tests. Based on both the experimental results and model prediction, the reinforcement efficiency and heat resistance of the polyamide-6/clay nanocomposites definitely depend on both conventional (${\alpha},\;S,\;{\Psi}_f,\;E_f/E_m$) and effective (n, $d_{001}$) filler structural parameters.

• Steel and Composite Structures
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• 재36권6호
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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.

• Steel and Composite Structures
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• 재36권6호
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• pp.711-727
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• 2020

In the present research, the free vibration analysis of functionally graded (FG) nanocomposite deep spherical shells reinforced by graphene platelets (GPLs) on elastic foundation is performed. The elastic foundation is assumed to be Winkler-Past ernak-type. It is also assumed that graphaene platelets are randomly oriented and uniformly dispersed in each layer of the nanocomposite shell. Volume fraction of the graphene platelets as nanofillers may be different in the layers. The modified HalpinTsai model is used to approximate the effective mechanical properties of the multilayer nanocomposite. With the aid of the first order shear deformation shell theory and implementing Hamilton's principle, motion equations are derived. Afterwards, the generalized differential quadrature method (GDQM) is utilized to study the free vibration characteristics of FG-GPLRC spherical shell. To assess the validity and accuracy of the presented method, the results are compared with the available researches. Finally, the natural frequencies and corresponding mode shapes are provided for different boundary conditions, GPLs volume fraction, types of functionally graded, elastic foundation coefficients, opening angles of shell, and thickness-to-radius ratio.

• Structural Engineering and Mechanics
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• 제73권6호
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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.

• Structural Engineering and Mechanics
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• 제74권6호
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• pp.809-819
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• 2020

For the first time, the influence of in-plane magnetic field on wave propagation of Graphene Nano-Platelets (GNPs) polymer composite nanoplates is investigated here. The impact of three- parameter Kerr foundation is also considered. There are two different reinforcement distribution patterns (i.e. uniformly and non-uniformly) while the material properties of the nanoplate are estimated through the Halpin-Tsai model and a rule of mixture. To consider the size-dependent behavior of the structure, Eringen Nonlocal Differential Model (ENDM) is utilized. The equations of wave motion derived based on a higher-order shear deformation refined theory through Hamilton's principle and an analytical technique depending on Taylor series utilized to find the wave frequency as well as phase velocity of the GNPs reinforced nanoplates. A parametric investigation is performed to determine the influence of essential phenomena, such as the nonlocality, GNPs conditions, Kerr foundation parameters, and wave number on the both longitudinal and flexural wave characteristics of GNPs reinforced nanoplates.

• Structural Engineering and Mechanics
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• 제67권4호
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• pp.403-415
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• 2018

In the present study, nonlinear dynamic response of polymer-CNT-fiber multiscale nanocomposite plate resting on elastic foundations in thermal environments using the finite element method is performed. In this regard, the governing equations are derived based on Inverse Hyperbolic Shear Deformation Theory and von $K{\acute{a}}rm{\acute{a}}n$ geometrical nonlinearity. Three type of distribution of temperature through the thickness of the plate namely, uniform linear and nonlinear are considered. The considered element is C1-continuous with 15 DOF at each node. The effective material properties of the multiscale composite are calculated using Halpin-Tsai equations and fiber micromechanics in hierarchy. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. Five types of impulsive loads are considered, namely the step, sudden, triangular, half-sine and exponential pulses. After examining the validity of the present work, the effects of the weight percentage of SWCNTs and MWCNTs, nanotube aspect ratio, volume fraction of fibers, plate aspect, temperature, elastic foundation parameters, distribution of temperature and shape of impulsive load on nonlinear dynamic response of CNT reinforced multi-phase laminated composite plate are studied in details.

• Steel and Composite Structures
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• 제27권3호
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• pp.255-271
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• 2018

This paper deals with the transient dynamic analysis and elastic wave propagation in a functionally graded graphene platelets (FGGPLs)-reinforced composite thick hollow cylinder, which is subjected to shock loading. A micromechanical model based on the Halpin-Tsai model and rule of mixture is modified for nonlinear functionally graded distributions of graphene platelets (GPLs) in polymer matrix of composites. The governing equations are derived for an axisymmetric FGGPLs-reinforced composite cylinder with a finite length and then solved using a hybrid meshless method based on the generalized finite difference (GFD) and Newmark finite difference methods. A numerical time discretization is performed for the dynamic problem using the Newmark method. The dynamic behaviors of the displacements and stresses are obtained and discussed in detail using the modified micromechanical model and meshless GFD method. The effects of the reinforcement of the composite cylinder by GPLs on the elastic wave propagations in both displacement and stress fields are obtained for various parameters. It is concluded that the proposed micromechanical model and also the meshless GFD method have a high capability to simulate the composite structures under shock loadings, which are reinforced by FGGPLs. It is shown that the modified micromechanical model and solution technique based on the meshless GFD method are accurate. Also, the time histories of the field variables are shown for various parameters.

• Advances in nano research
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• 제9권4호
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• pp.295-307
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• 2020

The vibrational characteristics of Multi-Phase Nanocomposite (MPC) reinforced annular/circular plate under initially stresses are presented using the state-space formulation based on three-dimensional elasticity theory (3D-elasticity theory) and Differential Quadrature Method (DQM). The MPC reinforced annular/circular plate is under initial lateral stress and composed of multilayers with Carbon Nanotubes (CNTs) uniformly dispersed in each layer, but its properties change layer-by-layer along the thickness direction. The State-Space based Differential Quadrature Method (SS-DQM) is presented to examine the frequency behavior of the current structure. Halpin-Tsai equations and fiber micromechanics are used in the hierarchy to predict the bulk material properties of the multi-scale composite. A singular point is investigated for modeling the circular plate. The CNTs are supposed to be randomly oriented and uniformly distributed through the matrix of epoxy resin. Afterward, a parametric study is done to present the effects of various types of sandwich circular/annular plates on frequency characteristics of the MPC reinforced annular/circular plate using 3D-elasticity theory.