• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.9
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• pp.1441-1451
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• 1997

This paper addresses method which can be used for analyzing thermal stresses of a functionally graded material(FGM) using semi-analytical approach. FGM is a nonhomogeneous material whose composition changes continuously from a metal surface to a ceramic surface. An infinite one dimensional FGM plate is considered. The temperature distribution in the FGM is obtained by approximate Green's function solution. To expedite the convergence of the solutions, alternative Green's function solution is derived and shows good agreement with results from finite difference method. Thermal stresses are calculated using temperature distribution of the plate.

• Steel and Composite Structures
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• v.22 no.3
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• pp.473-495
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• 2016

This work presents a bending, buckling, and vibration analysis of functionally graded plates by employing a novel higher-order shear deformation theory (HSDT). This theory has only four unknowns, which is even less than the first shear deformation theory (FSDT). A shear correction coefficient is, thus, not needed. Unlike the conventional HSDT, the present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton's principles and solved via Navier's procedure. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

• Structural Engineering and Mechanics
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• v.78 no.5
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• pp.529-543
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• 2021

Inevitable source-uncertainties in geometry configuration, boundary condition, and material properties may deviate the structural dynamics from its expected responses. This paper aims to examine the influence of these uncertainties on the vibration of functionally graded beams. Finite element procedures are presented for Timoshenko beams and utilized to generate reliable datasets. A prerequisite to the uncertainty quantification of the beam vibration using Monte Carlo simulation is generating large datasets, that require executing the numerical procedure many times leading to high computational cost. Utilizing artificial neural networks to model beam vibration can be a good approach. Initially, the optimal network for each beam configuration can be determined based on numerical performance and probabilistic criteria. Instead of executing thousands of times of the finite element procedure in stochastic analysis, these optimal networks serve as good alternatives to which the convergence of the Monte Carlo simulation, and the sensitivity and probabilistic vibration characteristics of each beam exposed to randomness are investigated. The simple procedure presented here is efficient to quantify the uncertainty of different stochastic behaviors of composite structures.

• Steel and Composite Structures
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• v.27 no.1
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• pp.109-122
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• 2018

In This work an analysis of the propagation of waves of functionally graduated plates is presented by using a high order hyperbolic (HSDT) shear deformation theory. This theory has only four variables, which is less than the theory of first order shear deformation (FSDT). Therefore, a shear correction coefficient is not required. Unlike other conventional shear deformation theories, the present work includes a new field of displacement which introduces indeterminate integral variables. The properties of materials are supposed classified in the direction of the thickness according to two simple distributions of a power law in terms of volume fractions of constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

• Steel and Composite Structures
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• v.33 no.6
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• pp.865-875
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• 2019

The current article proposed to develop a geometrical model for the analysis and modelling of the uniaxial functionally graded structure using the higher-order displacement kinematics with and without the presence of porosity including the distribution. Additionally, the formulation is capable of modelling three different kinds of grading patterns i.e., Power-law, sigmoid and exponential distribution of the individual constituents through the thickness direction. Also, the model includes the distribution of porosity (even and uneven kind) through the panel thickness. The structural governing equation of the porous graded structure is obtained (Hamilton's principle) and solved mathematically by means of the isoparametric finite element technique. Initially, the linear frequency parameters are obtained for different geometrical configuration via own computer code. The comparison and the corresponding convergence studies are performed for the unidirectional FG structure for the validation purpose. Finally, the impact of different influencing parameters like aspect ratio (O), thickness ratio (S), curvature ratio (R/h), porosity index (λ), type of porosity (even or uneven), power-law exponent (n), boundary condition on the free vibration characteristics are obtained for the FG panel and discussed in details.

• Steel and Composite Structures
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• v.45 no.6
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• pp.839-850
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• 2022

This paper presents an analytical solution to study the combined effect of non-local and stretching effect on the vibration of advanced functionally graded (FG) nanoplates. A new quasi-3D plate theory is presented; there are only five unknowns and any shear correction factor is used. A new displacement field with a new shear warping function is proposed. The equilibrium equations of the FG nanoplates are obtained using the Hamilton principle and solved numerically using the Navier technique. The material properties of functionally graded nanoplates are presumed to change according to the power-law distribution of ceramic and metal constituents. The numerical results of this work are compared with those of other published results to indicate the accuracy and convergence of this theory. Hence, a profound parameterstudy is also performed to show the influence of many parameters of the functionally graded nanoplates on the free vibration responses is investigated.

• Steel and Composite Structures
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• v.44 no.5
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• pp.651-676
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• 2022

Most of the experimental, theoretical, and numerical studies on the stability of functionally graded composites are deterministic, while there are full of complex interactions of variables with an inherently probabilistic nature, this paper presents a non-intrusive framework to investigate the stochastic nonlinear buckling behaviors of porous functionally graded cylindrical shells exposed to inevitable source-uncertainties. Euler-Lagrange equations are theoretically derived based on the three variable refined shear deformation theory. Closed-form solutions for the shell buckling loads are achieved by solving the deterministic eigenvalue problems. The analytical results are verified with numerical results obtained from finite element analyses that are conducted in the commercial software ABAQUS. The non-intrusive framework is completed by integrating the Monte Carlo simulation with the verified closed-form solutions. The convergence studies are performed to determine the effective pseudorandom draws of the simulation. The accuracy and efficiency of the framework are verified with statistical results that are obtained from the first and second-order perturbation techniques. Eleven cases of individual and compound uncertainties are investigated. Sensitivity analyses are conducted to figure out the five cases that have profound perturbative effects on the shell buckling loads. Complete probability distributions of the first three critical buckling loads are completely presented for each profound uncertainty case. The effects of the shell thickness, volume fraction index, and stochasticity degree on the shell buckling load under compound uncertainties are studied. There is a high probability that the shell has non-unique buckling modes in stochastic environments, which should be known for reliable analysis and design of engineering structures.

• Journal of the Korean Vacuum Society
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• v.22 no.6
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• pp.313-320
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• 2013

The $AlAs_xSb_{1-x}$ step-graded buffer (SGB) layer was grown on the Silicon (Si) substrate to overcome lattice mismatch between Si substrate and $Al_{0.3}Ga_{0.7}As$/GaAs multiple quantum wells (MQWs). The value of root-mean-square (RMS) surface roughness for 5 nm-thick GaAs grown on $AlAs_xSb_{1-x}$ step-graded buffer layer was ~1.7 nm. $Al_{0.3}Ga_{0.7}As$/GaAs MQWs with AlAs/GaAs short period superlattice (SPS) were formed on the $AlAs_xSb_{1-x}$/Si substrate. Photoluminescence (PL) peak at 10 K for the $Al_{0.3}Ga_{0.7}As$/GaAs MQW structure showed relatively low intensity at ~813 nm. The RMS surface roughness of the $Al_{0.3}Ga_{0.7}As$/GaAs MQW structure was ~42.9 nm. The crystal defects were observed on the cross-sectional transmission electron microscope (TEM) images of the $Al_{0.3}Ga_{0.7}As$/GaAs MQW structure. The decrease of PL intensity and increase of RMS surface roughness would be due to the formation of the crystal defects.

• Advances in nano research
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• v.12 no.5
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• pp.467-482
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• 2022

In the current work, static and free torsional vibration of functionally graded (FG) nanorods are investigated using Fourier sine series. The boundary conditions are described by the two elastic torsional springs at the ends. The distribution of functionally graded material is considered using a power-law rule. The systems of equations of the mechanical response of nanorods subjected to deformable boundary conditions are achieved by using the modified couple stress theory (MCST) and taking the effects of torsional springs into account. The idea of the study is to construct an eigen value problem involving the torsional spring parameters with small scale parameter and functionally graded index. This article investigates the size dependent free torsional vibration based on the MCST of functionally graded nano/micro rods with deformable boundary conditions using a Fourier sine series solution for the first time. The eigen value problem is constructed using the Stokes' transform to deformable boundary conditions and also the convergence and accuracy of the present methodology are discussed in various numerical examples. The small size coefficient influence on the free torsional vibration characteristics is studied from the point of different parameters for both deformable and rigid boundary conditions. It shows that the torsional vibrational response of functionally graded nanorods are effected by geometry, small size effects, boundary conditions and material composition. Furthermore, for all deformable boundary conditions in the event of nano-sized FG nanorods, the incrementing of the small size parameters leads to increas the torsional frequencies.

• Steel and Composite Structures
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• v.20 no.3
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• pp.623-649
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• 2016

Most of the early studies on plates vibration are focused on two-dimensional theories, these theories reduce the dimensions of problems from three to two by introducing some assumptions in mathematical modeling leading to simpler expressions and derivation of solutions. However, these simplifications inherently bring errors and therefore may lead to unreliable results for relatively thick plates. The main objective of this research paper is to present 3-D elasticity solution for free vibration analysis of continuously graded carbon nanotube-reinforced (CGCNTR) rectangular plates resting on two-parameter elastic foundations. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. In this study, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The formulations are based on the three-dimensional elasticity theory. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and results reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. The novelty of the present work is to exploit Eshelby-Mori-Tanaka approach in order to reveal the impacts of the volume fractions of oriented CNTs, different CNTs distributions, various coefficients of foundation and different combinations of free, simply supported and clamped boundary conditions on the vibrational characteristics of CGCNTR rectangular plates. The new results can be used as benchmark solutions for future researches.