• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.239-263
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• 2016

The paper studies the natural oscillation of the three-layered solid sphere with a middle layer made of Functionally Graded Material (FGM). It is assumed that the materials of the core and outer layer of the sphere are homogeneous and isotropic elastic. The three-dimensional exact equations and relations of linear elastodynamics are employed for the investigations. The discrete-analytical method proposed by the first author in his earlier works is applied for solution of the corresponding eigenvalue problem. It is assumed that the modulus of elasticity, Poisson's ratio and density of the middle-layer material vary continuously through the inward radial direction according to power law distribution. Numerical results on the natural frequencies related to the torsional and spheroidal oscillation modes are presented and discussed. In particular, it is established that the increase of the modulus of elasticity (mass density) in the inward radial direction causes an increase (a decrease) in the values of the natural frequencies.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.713-722
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• 2020

This article aims to illustrate the damped dynamic responses of layered functionally graded (FG) thick 2D beam under dynamic pulse sinusoidal load by using finite element method, for the first time. To investigate the response of thick beam accurately, two-dimensional plane stress problem is assumed to describe the constitutive behavior of thick beam structure. The material is distributed gradually through the thickness of each layer by generalized power law function. The Kelvin-Voigt viscoelastic constitutive model is exploited to include the material internal damping effect. The governing equations are obtained by using Lagrange's equations and solved by using finite element method with twelve -node 2D plane element. The dynamic equation of motion is solved numerically by Newmark implicit time integration procedure. Numerical studies are presented to illustrate stacking sequence and material gradation index on the displacement-time response of cantilever beam structure. It is found that, the number of waves increases by increasing the graduation distribution parameter. The presented mathematical model is useful in analysis and design of nuclear, marine, vehicle and aerospace structures those manufactured from functionally graded materials (FGM).

• Korean Journal of Metals and Materials
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• v.46 no.8
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• pp.538-544
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• 2008

MMCs were manufactured in two different forms. One was two-layered non FGM composite and the other was four-layered FGM composite. The matrix used in this study was AZ31 magnesium alloy and the reinforcement was $Al_{18}B_4O_{33}$. The composite materials contained reinforcement fibers with a volume fraction of 0, 15, 25 and 40%. Squeeze infiltration method was used for the fabrication of each block. The thermal properties of the FGM alloy and composite joints were studied by conducting thermal cycling tests. The numerical calculation (the finite elements method-FEM) results exhibited a good agreement with the experimental results. Thermal stresses induced by thermal cycling test were clearly reduced in the functionally graded materials.

• Journal of the Korean Ceramic Society
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• v.37 no.7
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• pp.693-699
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• 2000

Casting behavior of Zr(Y,Ce)O2 TZP/Mullite suspension during pressure filtration was investigated to prepare multi-layered Functionally Gradient Materials(FGM). The dispersion stabilities of each layer suspension were investigated by examination of zeta potential and viscosity. The each suspensions with 20 vol.% solid loading and 100 첸 of viscosity was prepared after fix of the dispersing agent (Sodium hexa-meta phosphate) and the binder (Hydroxyethyl cellulose), and then the cakes were formed at the 2.5 MPa~10.0MPa pressure range. The cake thickness of all suspensions was increased with the square root of time at the constant pressure, and the relations between filtration pressure(P)a nd dehydration rate (Q=dh/dt) showed that the flows of filtrates in the consolidated layers were laminar. The permeabilities were nearly constant during filtration, and kozeny constants(Kc) of the suspensions were 4.8~6.7. These valumes were seen as close to 5, which might be homogeneous particle packing during filtration. On the basis of those data, the multi layered compaction with 9 mm thickness and 52.5% green density was prepared by continuous pressure filtration.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.12 no.3
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• pp.144-148
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• 2002

Hydroxyapatite/titanium composites were prepared as 4-layered functionally graded materials (FGM) using a spark plasma sintering (SPS) apparatus. The maximum density and the biaxial strength of hydroxyapatite/titanium composites were achieved by SPS with a holding time 8 minutes at $1200^{\circ}C$. However, the hydroxyapatite was decomposed tetracalcium phosphate (TetCP) at $1100^{\circ}C$, and calcium titanate compounds ($CaTiO_3$) were formed. When titanium was added to hydroxyapatite, decomposition of hydroxyapatite was occurred easily at the low temperature.

• 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.29 no.2
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• pp.117-126
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• 2022

The vibrational characteristic of three-layered cylindrical shell (CS) submerged in fluid with the ring support has been studied. The inner and outer layer is supposed to construct by isotropic layer. The composition of central layer is of functionally graded material type. Acoustic Wave condition has been utilized to present the impact of fluid. The central layer of cylindrical shell (CS) varies by volume fraction law that has been expressed in terms of polynomial. The main shell frequency equation has been obtained by theory of Love's shell and Rayleigh-Ritz technique. The oscillation of natural frequency has been examined under a variety of end conditions. The dependence of axial model has been executed with the help of characteristic beam function. The natural frequencies (NFs) of functionally graded material (FGM) shell have been observed of cylindrical shell along the shell axial direction. Different physical parameters has been used to examine the vibration characteristics due to the effect of volume fraction law. MATLAB software has been used to get result.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.12
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• pp.1647-1653
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• 2011

The cycle time in injection moulding greatly depends on the cooling time of the plastic part that is controlled by cooling channels. Cooling channels are required to facilitate the heat transfer rate from the die to the coolant without reducing the strength of the die. Employing layered manufacturing techniques (LMT), a die embedding conformal cooling channels can be fabricated directly while conventional cooling channels are usually made of straight drilled hole. Meanwhile, H13 tool steel is widely used as the die material because of its high thermal resistance and dimensional stability. However, H13 with a low thermal conductivity is not efficient for certain part geometries. In this context, the use of functionally graded materials (FGMs) between H13 and copper may circumvent a tradeoff between the strength and the heat transfer rate. This paper presents a method for modeling of conformal cooling channels made of FGMs.

• Structural Engineering and Mechanics
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• v.11 no.1
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• pp.49-70
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• 2001

This paper is concerned with a study on thermo-elastoplastic characteristics of functionally graded composite. Compared to the classical layered composites, it shows a wide range of thermo-elastoplastic characteristics according to the choice of two major parameters, the thickness-wise volume fraction of constituents and the relative thickness ratio of the graded layer. Therefore, by selecting an appropriate combination of the two parameters, one is expected to design the most suitable heat-resisting composite for a given thermal circumstance. Here, we address the parametric investigation on its characteristics together with theoretical study on thermo-elastoplasticity and numerical techniques for its finite element approximations. Through the numerical experiments, we examine the influence of two parameters on the thermo-elastoplastic characteristics.

• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.365-391
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• 2007

The vibration and stability analysis is investigated for composite cylindrical shells that composed of ceramic, FGM, and metal layers subjected to various loads. Material properties of FG layer are varied continuously in thickness direction according to a simple power distribution in terms of the ceramic and metal volume fractions. The modified Donnell type stability and compatibility equations are obtained. Applying Galerkin's method analytic solutions are obtained for the critical parameters. The detailed parametric studies are carried out to study the influences of thickness variations of the FG layer, radius-to-thickness ratio, lengths-to-radius ratio, material composition and material profile index on the critical parameters of three-layered cylindrical shells. Comparing results with those in the literature validates the present analysis.