• Structural Engineering and Mechanics
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• 제85권4호
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• pp.445-459
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• 2023

The current investigation is the first endeavor to apply the full layerwise finite element method (FEM) in free vibration analysis of functionally graded (FG) composite plates reinforced with graphene nanoplatelets (GPLs) in thermal environment. Unlike the equivalent single-layer (ESL) theories, the layerwise FEM focuses on all three-dimensional (3D) effects. The GPLs weight fraction is presumed invariable in each layer but varies through the plate thickness in a layerwise model. The modified Halpin-Tsai model is employed to acquire the effective Young's modulus. The rule of mixtures is applied to specify the effective Poisson's ratio and mass density. First, the current method is validated by comparing the numerical results with those stated in the available works. Next, a thorough numerical study is performed to examine the influence of various factors involving the pattern of distribution, weight fraction, geometry, and size of GPLs, together with the thickness-to-span ratio, thermal environment, and boundary conditions of the plate, on its free vibration behaviors. Numerical results demonstrate that employing a small percentage of GPL as reinforcement considerably grows the natural frequencies of the pure epoxy. Also, distributing more square-shaped GPLs, involving a smaller amount of graphene layers, and vicinity to the upper and lower surfaces make it the most efficient method to enhance the free vibration behaviors of the plate.

• Steel and Composite Structures
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• 제48권1호
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• pp.1-17
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• 2023

The main goal of this paper is to study vibration of damaged core laminated sectorial plates with Functionally graded (FG) face sheets based on three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. Three complicated equations of motion for the sectorial plates under consideration are semi-analytically solved by using 2-D differential quadrature method. Using the 2-D differential quadrature method in the r- and z-directions, allows one to deal with sandwich annular sector plate with arbitrary thickness distribution of material properties and also to implement the effects of different boundary conditions of the structure efficiently and in an exact manner. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The sandwich annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution and boundary conditions.

• Structural Engineering and Mechanics
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• 제66권3호
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• pp.317-328
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• 2018

In this paper, a new refined quasi-three-dimensional (3D) shear deformation theory for the bending analysis of functionally graded plate is presented. The number of unknown functions involved in this theory is only four against five or more in the case of the other shear and normal deformation theories. Due to its quasi-3D nature, the stretching effect is taken into account in the formulation of governing equations. In addition, the effect of different micromechanical models on the bending response of these plates is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG plates whose properties vary continuously across the thickness according to a simple power law. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of displacements across the thickness, and the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The problem is solved for a plate simply supported on its edges and the Navier solution is used. The results of the present method are compared with others from the literature where a good agreement has been found. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG plates.

• Steel and Composite Structures
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• 제49권3호
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• pp.307-323
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• 2023

In this research, the study of the thermoelastic flexural analysis of silicon carbide/Aluminum graded (FG) sandwich 2D uniform structure (plate) under harmonic sinusoidal temperature load over time is presented. The plate is modeled using a simple two dimensional integral shear deformation plate theory. The current formulation contains an integral terms whose aim is to reduce a number of variables compared to others similar solutions and therefore minimize the computation time. The transverse shear stresses vary according to parabolic distribution and vanish at the free surfaces of the structure without any use of correction factors. The external load is applied on the upper face and varying in the thickness of the plates. The structure is supposed to be composed of "three layers" and resting on nonlinear visco-Pasternak's-foundations. The governing equations of the system are deduced and solved via Hamilton's principle and general solution. The computed results are compared with those existing in the literature to validate the current formulation. The impacts of the parameters (material index, temperature exponent, geometry ratio, time, top/bottom temperature ratio, elastic foundation type, and damping coefficient) on the dynamic flexural response are studied.

• Steel and Composite Structures
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• 제37권6호
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• pp.711-731
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• 2020

This paper deals with free vibration of FG sandwich annular sector plates on Pasternak elastic foundation with different boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. The influence of carbon nanotubes (CNTs) waviness, aspect ratio, internal pores and graphene platelets (GPLs) on the vibrational behavior of functionally graded nanocomposite sandwich plates is investigated in this research work. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness of upper and bottom layers of the sandwich sectorial plates and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The core of structure is porous and the internal pores and graphene platelets (GPLs) are distributed in the matrix of core either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. A semi-analytic approach composed of 2D-Generalized Differential Quadrature Method (2D-GDQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The new results can be used as benchmark solutions for future researches.

• Journal of Information Processing Systems
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• 제12권3호
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• pp.392-409
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• 2016

The aim of this paper is to examine the effectiveness of combining three popular tools used in pattern recognition, which are the Active Appearance Model (AAM), the two-dimensional discrete cosine transform (2D-DCT), and Kernel Fisher Analysis (KFA), for face recognition across age variations. For this purpose, we first used AAM to generate an AAM-based face representation; then, we applied 2D-DCT to get the descriptor of the image; and finally, we used a multiclass KFA for dimension reduction. Classification was made through a K-nearest neighbor classifier, based on Euclidean distance. Our experimental results on face images, which were obtained from the publicly available FG-NET face database, showed that the proposed descriptor worked satisfactorily for both face identification and verification across age progression.

• Advances in aircraft and spacecraft science
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• 제7권2호
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• pp.115-134
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• 2020

This paper proposes a bending analysis for a functionally graded piezoelectric (FGP) plate through utilizing a two-variable shear deformation plate theory under simply-supported edge conditions. The number of unknown functions used in this theory is only four. The electric potential distribution is assumed to be a combination of a cosine function along the cartesian coordinate. Applying the analytical solutions of FGP plate by using Navier's approach and the principle of virtual work, the equilibrium equations are derived. The paper also discusses thoroughly the impact of applied electric voltage, plate's aspect ratio, thickness ratio and inhomogeneity parameter. Results are compared with the analytical solution obtained by classical plate theory, first-order-shear deformation theory, higher-order shear deformation plate theories and quasi-three-dimensional sinusoidal shear deformation plate theory.

• Wind and Structures
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• 제27권6호
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• pp.369-380
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• 2018

In this research work, nonlinear thermal buckling behavior of functionally graded (FG) plates is explored based a new higher-order shear deformation theory (HSDT). The present model has just four unknowns, by using a new supposition of the displacement field which enforces undetermined integral variables. A shear correction factor is, thus, not necessary. A power law distribution is employed to express the disparity of volume fraction of material distributions. Three kinds of thermal loading, namely, uniform, linear, and nonlinear and temperature rises over z-axis direction are examined. The non-linear governing equations are resolved for plates subjected to simply supported boundary conditions at the edges. The results are approved with those existing in the literature. Impacts of various parameters such as aspect and thickness ratios, gradient index, type of thermal load rising, on the non-dimensional thermal buckling load are all examined.

• Bulletin of the Korean Chemical Society
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• 제35권5호
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• pp.1349-1355
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• 2014

A three-dimensional (3D) $Co_3O_4$/mildly oxidized multiwalled carbon nanotubes (moCNTs)/reduced mildly oxidized graphene oxide (rmGO) ternary composite was prepared via a simple and green hydrolysishydrothermal approach by mixing $Co(Ac)_2{\cdot}4H_2O$ with moCNTs and mGO suspension in mixed ethanol/$H_2O$. As characterized by scanning electron microscopy and transmission electron microscopy, $Co_3O_4$ nanoparticles with size of 20-100 nm and moCNTs are effectively anchored in mGO. Cyclic voltammetry and galvanostatic charge-discharge measurements were adopted to investigate the electrochemical properties of $Co_3O_4$/moCNTs/rmGO ternary composite in 6 M KOH solution. In a potential window of 0-0.6 V vs. Hg/HgO, the composite delivers an initial specific capacitance of 492 $Fg^{-1}$ at 0.5 $Ag^{-1}$ and the capacitance remains 592 $Fg^{-1}$ after 2000 cycles, while the pure $Co_3O_4$ shows obviously capacitance fading, indicating that rmGO and moCNTs greatly enhance the electrochemical performance of $Co_3O_4$.

• Steel and Composite Structures
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• 제30권6호
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• pp.603-615
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• 2019

In the present work, free vibration of beams made of imperfect functionally graded materials (FGMs) including porosities is investigated. Because of faults during process of manufacture, micro voids or porosities may arise in the FGMs, and this situation causes imperfection in the structure. Therefore, material properties of the beams are assumed to vary continuously through the thickness direction according to the volume fraction of constituents described with the modified rule of mixture including porosity volume fraction which covers two types of porosity distribution over the cross section, i.e., even and uneven distributions. The governing equations of power law FGM (P-FGM) and sigmoid law FGM (S-FGM) beams are derived within the frame works of classical beam theory (CBT) and first order shear deformation beam theory (FSDBT). The resulting equations are solved using separation of variables technique and assuming FG beams are simply supported at both ends. To validate the results numerous comparisons are carried out with available results of open literature. The effects of types of volume fraction function, beam theory and porosity volume fraction, as well as the variations of volume fraction index, span to depth ratio and porosity volume fraction, on the first three non-dimensional frequencies are examined in detail.