• Proceedings of the Materials Research Society of Korea Conference
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• 2003.11a
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• pp.37-37
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• 2003

탄소-탄소 복합체는 가벼우면서 고온에서도 강도의 저하가 적은 특성을 가지고 있어 터빈 블레이드 소재, 우주왕복선의 내열타일 등 광범위 한 고온재료로 응용이 이루어지고 있거나 기대되는 소재이다. 그러나 고온 산화분위기에서 쉽게 산화되는 단점이 있어 이러 한 산화특성을 향상시키는 방법으로 SiC, Si$_3$N$_4$ 등 내산화 저항성이 우수한 재료를 탄소-탄소 복합체 위에 코팅하는 연구가 행해지고 있다. 하지만 이들 코팅층과 탄소-탄소 복합체간의 열팽창계수 차이에 의한 열응력 발생으로 코팅층에 균열이 발생한다. 따라서 탄소-탄소 복합체와 코팅층간의 열응력을 최소화하여 균열 발생을 억제하기 위해 기능경사재료 (Functionally Graded Material, FGM)를 중간층으로 도입하는 방법이 최근 활발히 연구되고 있다. FGM 중간충의 형성방법 중 화학기상증착법 (CVD)은 증착물의 조성이나 미세구조 조절이 용이한 방법으로 알려져 있어 최근 CVD법에 의한 FGM층의 형성에 많은 연구가 진행되고 있지만, 지금까지 CVD법을 이용한C/SiC FGM 중간충의 형성 연구결과에서는 모든 조성비의 C/SiC층의 증착과 치밀한 구조를 지닌 증착층을 얻기가 어려워 체계적인 연구의 진행이 어려웠다.

• Advances in nano research
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• v.14 no.5
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• pp.475-493
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• 2023

In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.

• Smart Structures and Systems
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• v.6 no.8
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• pp.975-989
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• 2010

Based on the theory of piezo-elasticity, the paper obtains the exact solutions of functionally graded piezoelectric hollow cylinders with different piezoelectric parameter $g_{31}$. Two kinds of piezoelectric hollow cylinders are considered herein. One is a multi-layered cylinder with different parameter $g_{31}$ in different layers; the other is a continuously graded cylinder with arbitrarily variable $g_{31}$. By using the Airy stress function method with plane strain assumptions, the exact solutions of the mechanic and electrical components of both cylinders are obtained when they are subjected to external voltage (actuator) and pressure (sensor), simultaneously. Furthermore, good agreement is achieved between the theoretical and numerical results, and useful conclusions are given.

• Computers and Concrete
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• v.26 no.3
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• pp.285-292
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• 2020

In engineering structures, to having the projected structure to serve all the engineering purposes, the theory to be used during the modeling stage is also of great importance. In the present work, an analytical solution of the free vibration of the beam composed of functionally graded materials (FGMs) is presented utilizing different beam theories. The comparison of supposed beam theory for free vibration of functionally graded (FG) beam is examined. For this aim, Euler-Bernoulli, Rayleigh, Shear, and Timoshenko beam theories are employed. The functionally graded material properties are assumed to vary continuously through the thickness direction of the beam with respect to the volume fraction of constituents. The governing equations of free vibration of FG beams are derived in the frameworks of four beam theories. Resulting equations are solved versus simply supported boundary conditions, analytically. To verify the results, comparisons are carried out with the available results. Parametrical studies are performed for discussing the effects of supposed beam theory, the variation of beam characteristics, and FGM properties on the free vibration of beams. In conclusion, it is found that the interaction between FGM properties and the supposed beam theory is of significance in terms of free vibration of the beams and that different beam theories need to be used depending on the characteristics of the beam in question.

• Advances in materials Research
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• v.5 no.2
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• pp.107-120
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• 2016

The static analysis of the simply supported functionally graded plate under transverse load by using a new sinusoidal shear deformation theory based on the neutral surface concept is investigated analytically in the present paper. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. The mechanical properties of the FGM plate are assumed to vary continuously through the thickness according to a power law formulation except Poisson's ratio, which is kept constant. The equilibrium and stability equations are derived by employing the principle of virtual work. Results are provided for thick to thin plates and for different values of the gradient index k, which subjected to sinusoidal or uniformly distributed lateral loads. The accuracy of the present results is verified by comparing it with finite element solution. From the obtained results, it can be concluded that the proposed theory is accurate and efficient in predicting the displacements and stresses of functionally graded plates.

• Geomechanics and Engineering
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• v.29 no.6
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• pp.667-681
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• 2022

This paper presents a thermoelastic analysis of variable thickness plates made of functionally graded materials (FGM) subjected to mechanical and thermal loads. The thermal load is applied to the plate as a temperature difference between the top and bottom surfaces. Temperature distribution in the plate is obtained using the steady-state heat equation. Except for Poisson's ratio, all mechanical properties of the plate are assumed to vary linearly along the thickness direction based on the volume fractions of ceramic and metal. The plate is resting on an elastic foundation modeled based on the Winkler foundation model. The governing equations are derived based on the third-order shear deformation theory (TSDT) and are solved numerically for various boundary conditions using the differential quadrature method (DQM). The effects of various parameters on the stress distribution and deflection of the plate are investigated such as the value of thermal and mechanical loads, volume fractions of ceramic and metal, and the stiffness coefficients of the foundation.

• Structural Engineering and Mechanics
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• v.55 no.6
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• pp.1087-1097
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• 2015

In this paper, the effect of functionally graded material (FGM) coatings on the fracture behavior of semi-elliptical cracks in cylinders is assessed. The objective is to calculate the stress intensity factor (SIF) of a longitudinal semi-elliptical crack on the wall of an aluminum cylinder with FGM coating. A three-dimensional finite element method (FEM) is used for constructing the mechanical models and analyzing the SIFs of cracks. The effect of many geometrical parameters such as relative depth, crack aspect ratio, FG coating thickness to liner thickness as well as the mechanical properties of the FG coating on the SIF of the cracks is discussed. For a special case, the validity of the FE model is examined. The results indicated that there is a particular crack aspect ratio in which the maximum value of SIFs changes from the deepest point to the surface point of the crack. Moreover, it was found that the SIFs decrease by increasing the thickness ratio of the cylinder. But, the cylinder length has no effect on the crack SIFs.

• Coupled systems mechanics
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• v.9 no.3
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• pp.237-264
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• 2020

This article investigates the static behaviour of functionally graded (FG) plates sometimes declared as advanced composite plates by using a simple and accurate quasi-3D and 2D hyperbolic higher-order shear deformation theories. The properties of functionally graded materials (FGMs) are assumed to vary continuously through the thickness direction according to exponential law distribution (E-FGM). The kinematics of the present theories is modeled with an undetermined integral component and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate; therefore, it does not require the shear correction factor. The fundamental governing differential equations and boundary conditions of exponentially graded plates are derived by employing the static version of principle of virtual work. Analytical solutions for bending of EG plates subjected to sinusoidal distributed load are obtained for simply supported boundary conditions using Navier'is solution procedure developed in the double Fourier trigonometric series. The results for the displacements and stresses of geometrically different EG plates are presented and compared with 3D exact solution and with other quasi-3D and 2D higher-order shear deformation theories to verify the accuracy of the present theory.

• Smart Structures and Systems
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• v.30 no.2
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• pp.121-133
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• 2022

An analytical approach for the free vibration behavior of a sandwich cylindrical shell with a functionally graded (FG) core is presented. It is considered that the FG distribution is in the direction of thickness. The material properties are temperature-dependent. The sandwich cylindrical shell with a FG core is considered with two cases. In the first model, i.e., Ceramic-FGM-Metal (CFM), the interior layer of the cylindrical shell is rich metal while the exterior layer is rich ceramic and the FG material is located between two layers and for the second model i.e., Metal-FGM-Ceramic (MFC), the material distribution is in reverse order. This study develops Carrera's Unified Formulation (CUF) to analyze sandwich cylindrical shell with an FG core for the first time. Considering the Principle of Virtual Displacements (PVDs) according to the CUF, the dependent boundary conditions and governing equations are obtained. The coupled governing equations are derived using Galerkin's method. In order to validate the present results, comparisons are made with the available solutions in the previous researches. The effects of different geometrical and material parameters on the free vibration behavior of a sandwich cylindrical shell with an FG core are examined.

• Steel and Composite Structures
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• v.25 no.2
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• pp.127-139
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• 2017

In this paper, an exact analytical solution for simply supported sandwich plate which considers the permeation effect of adhesives is presented. The permeation layer is described as functionally graded material (FGM), the elastic modulus of which is assumed to be graded along the thickness following the exponential law. Based on the exact three-dimensional (3-D) elasticity theory, the solution of stresses and displacements for each layer is derived. By means of the recursive matrix method, the solution can be efficiently obtained for plates with many layers. The present solution obtained can be used as a benchmark to access other simplified solutions. The comparison study indicates that the finite element (FE) solution is close to the present one when the FGM layer in the FE model is divided into a series of homogeneous layers. However, the present method is more efficient than the FE method, with which the mesh division and computation are time-consuming. Moreover, the solution based on Kirchhoff-Love plate theory is greatly different from the present solution for thick plates. The influence of the thickness of the permeation layer on the stress and displacement fields of the sandwich plate is discussed in detail. It is indicated that the permeation layer can effectively relieve the discontinuity stress at the interface.