• 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.

• 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.

• Structural Engineering and Mechanics
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• 제75권1호
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• pp.1-18
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• 2020

Present research is aimed to investigate the free vibration behavior of functionally graded (FG) nanocomposite conical panel reinforced by graphene platelets (GPLs) on the elastic foundation. Winkler-Pasternak elastic foundation surrounds the mentioned shell. For each ply, graphaene platelets are randomly oriented and uniformly dispersed in an isotropic matrix. It is assumed that the Volume fraction of GPLs reainforcement could be different from layer to layer according to a functionally graded pattern. The effective elastic modulus of the conical panel is estimated according to the modified Halpin-Tsai rule in this manuscript. Cone is modeled based on the first order shear deformation theory (FSDT). Hamilton's principle and generalized differential quadrature (GDQ) approach are also used to derive and discrete the equations of motion. Some evaluations are provided to compare the natural frequencies between current study and some experimental and theoretical investigations. After validation of the accuracy of the present formulation and method, natural frequencies and the corresponding mode shapes of FG-GPLRC conical panel are developed for different parameters such as boundary conditions, GPLs volume fraction, types of functionally graded and elastic foundation coefficients.

• Computers and Concrete
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• 제25권5호
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• pp.427-432
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• 2020

In this research, the buckling analysis of sandwich beam with composite reinforced by graphene platelets (GPLs) in two face sheets is investigated. Three type various porosity patterns including uniform, symmetric and asymmetric are considered through the thickness direction of the core. Also, the top and bottom face sheets layers are considered composite reinforced by GPLs/CNTs based on Halpin-Tsai micromechanics model and extended mixture rule, respectively. Based on various shear deformation theories such as Euler-Bernoulli, Timoshenko and Reddy beam theories, the governing equations of equilibrium using minimum total potential energy are obtained. It is seen that the critical buckling load decreases with an increase in the porous coefficient, because the stiffness of sandwich beam reduces. Also, it is shown that the critical buckling load for asymmetric distribution is lower than the other cases. It can see that the effect of graphene platelets on the critical buckling load is higher than carbon nanotubes. Moreover, it is seen that the difference between carbon nanotubes and graphene platelets for Reddy and Euler-Bernoulli beam theories is most and least, respectively.

• Smart Structures and Systems
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• 제26권4호
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• pp.469-480
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• 2020

This is the first research on the smart control and vibration analysis of a Graphene nanoplatelets (GPLs) Reinforced Composite (GPLRC) porous cylindrical shell covered with piezoelectric layers as sensor and actuator (PLSA) in the framework of numerical based Generalized Differential Quadrature Method (GDQM). The stresses and strains are obtained using the First-order Shear Deformable Theory (FSDT). Rule of the mixture is employed to obtain varying mass density and Poisson's ratio, while the module of elasticity is computed by modified Halpin-Tsai model. The external voltage is applied to sensor layer and a Proportional-Derivative (PD) controller is used for sensor output control. Governing equations and boundary conditions of the GPLRC cylindrical shell are obtained by implementing Hamilton's principle. The results show that PD controller, length to radius ratio (L/R), applied voltage, porosity and weight fraction of GPL have significant influence on the frequency characteristics of a porous GPLRC cylindrical shell. Another important consequence is that at the lower value of the applied voltage, the influence of the smart controller on the frequency of the micro composite shell is much more significant in comparison with the higher ones.

• Steel and Composite Structures
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• 제29권5호
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• pp.569-578
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• 2018

This paper aims to investigate the transient vibration behavior of functionally graded carbon nanotube (FG-CNT) reinforced nanocomposite plate resting on Pasternak foundation under pulse excitation. The plate is considered to be composed of matrix material and multi-walled carbon nanotubes (MWCNTs) with distribution as per the functional grading concept. The functionally graded distribution patterns in nanocomposite plate are explained more appropriately with the layer-wise variation of carbon nanotubes weight fraction in the thickness coordinate. The layers are stacked up in such a way that it yields uniform and three other types of distribution patterns. The effective material properties of each layer in nanocomposite plate are obtained by modified Halpin-Tsai model and rule of mixtures. The governing equations of an illustrative case of simply-supported nanocomposite plate resting on the Pasternak foundation are derived from third order shear deformation theory and Navier's solution technique. A converge transient response of nanocompiste plate under uniformly distributed load with triangular pulse is obtained by varying number of layer in thickness direction. The validity and accuracy of the present model is also checked by comparing the results with those available in literature for isotropic case. Then, numerical examples are presented to highlight the effects of distribution patterns, foundation stiffness, carbon nanotube parameters and plate aspect ratio on the central deflection response. The results are extended with the consideration of proportional damping in the system and found that nanocomposite plate with distribution III have minimum settling time as compared to the other distributions.

• Advances in nano research
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• 제7권2호
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• pp.109-123
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• 2019

In this article, the free vibration analysis of annular sandwich plates with various functionally graded (FG) porous cores and carbon nanotubes reinforced composite (CNTRC) facesheets is investigated based on modified couple stress theory (MCST) and first order shear deformation theories (FSDT). The annular sandwich plate is composed of two face layers and a functionally graded porous core layer which contains different porosity distributions. Various approaches such as extended mixture rule (EMR), Eshelby-Mori-Tanaka (E-M-T), and Halpin-Tsai (H-T) are used to determine the effective material properties of microcomposite circular sandwich plate. The governing equations of motion are extracted by using Hamilton's principle and FSDT. A Ritz method has been utilized to calculate the natural frequency of an annular sandwich plate. The effects of material length scale parameters, boundary conditions, aspect and inner-outer radius ratios, FG porous distributions, pore compressibility and volume fractions of CNTs are considered. The results are obtained by Ritz solutions that can be served as benchmark data to validate their numerical and analytical methods in the future work and also in solid-state physics, materials science, and micro-electro-mechanical devices.

• Geomechanics and Engineering
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• 제24권3호
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• pp.267-280
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• 2021

The research presented in this paper deals with dynamic stability analysis of the graphene nanoplatelets (GPLs) reinforced composite spinning disk. The presented small-scaled structure is simulated as a disk covered by viscoelastic substrate which is two-parametric. The centrifugal and Coriolis impacts due to the spinning are taken into account. The stresses and strains would be obtained using the first-order-shear-deformable-theory (FSDT). For Poisson ratio, as well as various amounts of mass densities, the mixture rule is employed, while a modified Halpin-Tsai model is inserted for achieving the elasticity module. The structure's boundary conditions (BCs) are obtained employing GPLs reinforced composite (GPLRC) spinning disk's governing equations applying principle of Hamilton which is based on minimum energy and ultimately have been solved employing numerical approach called generalized-differential quadrature-method (GDQM). Spinning disk's dynamic properties with different boundary conditions (BCs) are explained due to the curves drawn by Matlab software. Also, the simply-supported boundary conditions is applied to edges 𝜃=𝜋/2, and 𝜃=3𝜋/2, while, cantilever, respectively, is analyzed in R=R_i, and R₀. The final results reveal that the GPLs' weight fraction, viscoelastic substrate, various GPLs' pattern, and rotational velocity have a dramatic influence on the amplitude, and vibration behavior of a GPLRC rotating cantilevered disk. As an applicable result in related industries, the spinning velocity impact on the frequency is more effective in the higher radius ratio's amounts.

• Steel and Composite Structures
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• 제43권5호
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• pp.639-660
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• 2022

The bending and buckling behaviours of FG-GRNC laminated sandwich plates are investigated by using novel five-variables quasi 3D higher order shear deformation plate theory by considering the modified continuum nonlocal strain gradient theory. To calculate the effective Young's modulus of the GRNC sandwich plate along the thickness direction, and Poisson's ratio and mass density, the modified Halpin-Tsai model and the rule of the mixture are employed. Based on a new field of displacement, governing equilibrium equations of the GRNC sandwich plate are solved using a developed approach of Galerkin method. A detailed parametric analysis is carried out to highlight the influences of length scale and material scale parameters, GPLs distribution pattern, the weight fraction of GPLs, geometry and size of GPLs, the geometry of the sandwich plate and the total number of layers on the stresses, deformation and critical buckling loads. Some details are studied exclusively for the first time, such as stresses and the nonlocality effect.

• Structural Engineering and Mechanics
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• 제85권2호
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• pp.147-161
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• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.