• Structural Engineering and Mechanics
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• 제68권3호
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• pp.299-312
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• 2018

In this paper, an extended finite element method is proposed to analyze both geometric and material non-linear behavior of general Functionally Graded Material (FGM) plate-shell type structures. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the elastoplastic behavior of the ceramic particle-reinforced metal-matrix FGM plates-shells. The standard quadrilateral 4-nodes shell element with three rotational and three translational degrees of freedom per node, S4, is extended in the present study, to deal with elasto-plastic analysis of geometrically non-linear FGM plate-shell structures. The elastoplastic material properties are assumed to vary smoothly through the thickness of the plate-shell type structures. The nonlinear approach is based on Mori-Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the ceramic/metal FGM is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. In order to to highlight the effectiveness and the accuracy of the present finite element procedure, numerical examples of geometrically non-linear elastoplastic functionally graded plates and shells are presented. The effects of the geometrical parameters and the volume fraction index on nonlinear responses are performed.

• 소성∙가공
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• 제6권3호
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• pp.239-249
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• 1997

The behaviour of alloys in the semi-solid state strongly depends on the imposed stress state and on the morphology of the phase which can vary from dendritic to globular. To optimal net shape forging of semi-solid materials, it is important to investigate for filling phenomena in forging process of arbitrarily shaped dies. To produce a automotive part which has good mechanical property, the filling pattern according to die velocity and solid fraction distribution has to be estimated for arbitrarily shaped dies. Therefore, the estimation of filling characteristic in the forging simulation with arbitrarily shaped dies of semi-solid materials are calculated by finite element method with proposed algorithm. The proposed theoretical model and a various boundary conditions for arbitrarily shaped dies is investigated with the coupling calculation between the liquid phase flow and the solid phase deformation. The simulation process with arbitrarily shaped dies is performed to the isothermal conditions of two dimensional problems. To analysis of forging process by using semi-solid materials, a new stress-strain relationship is described, and forging analysis is performed by viscoelastic model for the solid phase and the Darcy's law for the liquid flow. The calculated results for forging force and filling limitations will be compared to experimental data. The filling simulation of simple products performed with the uniform billet temperature(584$^{\circ}C$) from the induction heating by the commercial package MAGMAsoft. The initial step of computation is the touching of semi-solid material with the end of die gate and the initial concept of proposed system just fit with the capability of MAGMAsoft.

• Earthquakes and Structures
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• 제13권3호
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• pp.255-265
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• 2017

In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam.

• Earthquakes and Structures
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• 제15권4호
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• pp.369-382
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• 2018

A free vibration analysis and wave propagation of functionally graded porous beams has been presented in this work using a high order hyperbolic shear deformation theory. Unlike other conventional shear deformation theories, a new displacement field that introduces indeterminate integral variables has been used to minimize the number of unknowns. The constituent materials of the beam are assumed gradually variable along the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The variation of the pores in the direction of the thickness influences the mechanical properties. It is therefore necessary to predict the effect of porosity on vibratory behavior and wave velocity of FG beams in this study. A new function of the porosity factor has been developed. Hamilton's principle is used for the development of wave propagation equations in the functionally graded beam. The analytical dispersion relationship of the FG beam is obtained by solving an eigenvalue problem. Illustrative numerical examples are given to show the effects of volume fraction distributions, beam height, wave number, and porosity on free vibration and wave propagation in a functionally graded beam.

• Wind and Structures
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• 제29권6호
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• pp.457-469
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• 2019

In this paper, a numerical solution is presented for supersonic flutter analysis of cantilever non-symmetric functionally graded (FG) sandwich plates. The plate is considered to be composed of two different functionally graded face sheets and an isotropic homogeneous core made of ceramic. Based on the first order shear deformation theory (FSDT) and linear piston theory, the set of governing equations and boundary conditions are derived. Dimensionless form of the governing equations and boundary conditions are derived and solved numerically using generalized differential quadrature method (GDQM) and critical velocity and flutter frequencies are calculated. For various values of the yaw angle, effect of different parameters like aspect ratio, thickness of the plate, power law indices and thickness of the core on the flutter boundaries are investigated. Numerical examples show that wings and tail fins with larger length and shorter width are more stable in supersonic flights. It is concluded for FG sandwich plates made of Al-Al₂O₃ that increase in volume fraction of ceramic (Al₂O₃) increases aeroelastic stability of the plate. Presented study confirms that improvement of aeroelastic behavior and weight of wings and tail fins of aircrafts are not consistent items. It is shown that value of the critical yaw angle depends on aspect ratio of the plate and other parameters including thickness and variation of properties have no considerable effect on it. Results of this paper can be used in design and analysis of wing and tail fin of supersonic airplanes.

• Structural Engineering and Mechanics
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• 제75권2호
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• pp.193-209
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• 2020

This paper presents a new hyperbolic shear deformation plate theory including the stretching effect for free vibration of the simply supported functionally graded plates in thermal environments. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The present one has a new displacement field which introduces undetermined integral variables. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equation of motion of the vibrated plate obtained via the classical Hamilton's principle and solved using Navier's steps. The accuracy of the proposed solution is checked by comparing the present results with those available in existing literature. The effects of the temperature field, volume fraction index of functionally graded material, side-to-thickness ratio on free vibration responses of the functionally graded plates are investigated. It can be concluded that the present theory is not only accurate but also simple in predicting the natural frequencies of functionally graded plates with stretching effect in thermal environments.

• 대한기계학회논문집B
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• 제35권12호
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• pp.1325-1333
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• 2011

해석적, 수치해석적, 실험적인 방법을 통하여 반원형상의 채널로 구성된 냉각판의 열수력학적인 특성을 고찰하였다. 본 연구에서는 레이놀즈 수 30-2000, 그에 따른 냉각판의 압력손실 30-105 Pa 의 구간에서 수행되었으며, 냉각채널 부피비 0.04, 시스템 크기 $10{\times}10$, $20{\times}20$ 및 $50{\times}50$ 각각에 대하여 최적화 및 최적화되지 않은 1, 2, 3 차 형상 6 개가 포함되었다. 해석적 방법으로 설계된 혈관구조 설계를 검증하기 위하여 3 차원 수치해석이 수행되었으며, 실험을 통하여 수치해석모델에 대한 타당성이 검증되었고, 전 범위에 걸쳐서 수치해석 및 실험결과가 비교적 잘 일치된 경향을 나타내었다. 또한, 최적화된 냉각판의 유동저항 및 열저항 모두 최적화되지 않은 냉각판에 비하여 뚜렷하게 작게 나타났으며, 제시된 수치해석 모델 역시 모두 냉각판의 성능예측에 유용한 도구임이 확인되었다.

• International Journal of Aeronautical and Space Sciences
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• 제16권3호
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• pp.418-424
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• 2015

The chemical response of energetic materials is analyzed in terms of 1) the thermal decomposition under the thermal stimulus and 2) the reactive flow upon the mechanical impact, both of which give rise to an exothermic thermal runaway or an explosion. The present study aims at building a set of chemical kinetics that can precisely model both thermal and impact initiation of a heavily aluminized cyclotrimethylene-trinitramine (RDX) which contains 35% of aluminum. For a thermal decomposition model, the differential scanning calorimetry (DSC) measurement is used together with the Friedman isoconversional method for defining the frequency factor and activation energy in the form of Arrhenius rate law that are extracted from the evolution of product mass fraction. As for modelling the impact response, a series of unconfined rate stick data are used to construct the size effect curve which represents the relationship between detonation velocity and inverse radius of the sample. For validation of the modeled results, a cook-off test and a pressure chamber test are used to compare the predicted chemical response of the aluminized RDX that is either thermally or mechanically loaded.

• Steel and Composite Structures
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• 제34권4호
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• pp.511-524
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• 2020

In this research, a simple four-variable trigonometric integral shear deformation model is proposed for the static behavior of advanced functionally graded (AFG) ceramic-metal plates supported by a two-parameter elastic foundation and subjected to a nonlinear hygro-thermo-mechanical load. The elastic properties, including both the thermal expansion and moisture coefficients of the plate, are also supposed to be varied within thickness direction by following a power law distribution in terms of volume fractions of the components of the material. The interest of the current theory is seen in its kinematics that use only four independent unknowns, while first-order plate theory and other higher-order plate theories require at least five unknowns. The "in-plane displacement field" of the proposed theory utilizes cosine functions in terms of thickness coordinates to calculate out-of-plane shear deformations. The vertical displacement includes flexural and shear components. The elastic foundation is introduced in mathematical modeling as a two-parameter Winkler-Pasternak foundation. The virtual displacement principle is applied to obtain the basic equations and a Navier solution technique is used to determine an analytical solution. The numerical results predicted by the proposed formulation are compared with results already published in the literature to demonstrate the accuracy and efficiency of the proposed theory. The influences of "moisture concentration", temperature, stiffness of foundation, shear deformation, geometric ratios and volume fraction variation on the mechanical behavior of AFG plates are examined and discussed in detail.

• 천문학회보
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• 제41권1호
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• pp.70.3-70.3
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• 2016

Active galactic nuclei (AGNs) typically show a non-thermal continuum locally represented by a power-law and many prominent emission lines in the UV and optical regions. AGNs are classified by two types, where Type I AGNs exhibit both broad and narrow lines and only narrow lines are observed in Type 2 AGNs. The unification models of AGNs invoke the existence of a molecular torus just outside of the broad line region. In the presence of a high column HI region associated with the molecular torus, we propose that significant fraction of broad line photons near Lyman series can be scattered by atomic hydrogen in the torus. In particular, $Ly{\alpha}$ being the strongest emission line, strong linear polarization may develop around $Ly{\alpha}$ through Rayleigh scattering. We adopt a Monte Carlo technique to investigate the polarized transfer of $Ly{\alpha}$ in a thick HI region with the shape of a torus. We consider the range of HI column density N_HI = 1020-23 with fixed geometric parameters of the torus such as the inner and outer radii and the height. We present the polarized spectra and angular distribution of Rayleigh scattered radiation around $Ly{\alpha}$. We find that the $Ly{\alpha}$ core part is polarized in the direction perpendicular to the symmetry axis whereas in the far wing part it is polarized in the parallel direction. It is concluded that the unification of AGNs implies that $Ly{\alpha}$ can be uniquely polarized through Rayleigh scattering.