• Nuclear Engineering and Technology
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• 제44권1호
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• pp.43-52
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• 2012

To compute a permeability coefficient along a rough fracture that takes into account the fracture geometry, this study performed detailed measurements of fracture roughness using a confocal laser scanning microscope, a quantitative analysis of roughness using a spectral analysis, and a homogenization analysis to calculate the permeability coefficient on the microand macro-scale. The homogenization analysis is a type of perturbation theory that characterizes the behavior of microscopically inhomogeneous material with a periodic boundary condition in the microstructure. Therefore, it is possible to analyze accurate permeability characteristics that are represented by the local effect of the facture geometry. The Cpermeability coefficients that are calculated using the homogenization analysis for each rough fracture model exhibit an irregular distribution and do not follow the relationship of the cubic law. This distribution suggests that the permeability characteristics strongly depend on the geometric conditions of the fractures, such as the roughness and the aperture variation. The homogenization analysis may allow us to produce more accurate results than are possible with the preexisting equations for calculating permeability.

• 대한기계학회논문집A
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• 제31권3호
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• pp.388-394
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• 2007

Many engineering problems require the calculation of effective material properties of a structure which is composed of repeated micro-structures. The homogenization method has been used to calculate the effective (homogenized) properties of composites and several homogenization procedures for different physical fields have been introduced. This research describes the modified homogenization technique for magnetostatic problems. Assuming that the material is periodically repeated, its effective permeability can be prescribed by calculating the homogenized magnetic reluctivity using the finite element analysis of the micro unit cell. Validity of the suggested method is confirmed by comparing the results by the energy based method as well as the widely known homogenization method.

• Food Science and Biotechnology
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• 제17권2호
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• pp.324-329
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• 2008

The effect of ultra-high pressure homogenization on the emulsifying properties of whey protein was investigated in a model emulsion made with whey protein isolate and soya oil under various pH. The emulsifying properties, the average diameter of the oil droplets ($d_{vs}$), and the protein load, were measured for each emulsion produced at different homogenization pressures (50 to 200 MPa) and pH values (4.6 to 8.0). According to the results of variance analysis and response surface, the pH had more influence on oil droplet size and protein load than homogenization pressure. The model equations, which were obtained by response surface analysis, show that pH and homogenization pressure had the major effect on oil droplet size and protein load. Higher homogenization pressure decreased the average droplet size and the protein load. Homogenization at high pressure, as opposed to low pressure, causes no overprocessing, but the effect was pH-dependent. The average diameter of the oil droplets increased slightly by decreasing the pH from 8.0 to 6.5 and then increased dramatically toward the isoelectric point of whey protein (i.e., at pH 4.6). Moreover associated droplets were found at acidic pH and their size was increased at high temperature.

• Structural Engineering and Mechanics
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• 제38권4호
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• pp.503-516
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• 2011

Uncertainty in concrete properties, including concrete modulus of elasticity and modulus of rupture, are predicted by developing a microstructural homogenization model. The homogenization model is developed by analyzing a concrete representative volume element (RVE) using the finite element (FE) method. The concrete RVE considers concrete as a three phase composite material including: cement paste, aggregate and interfacial transition zone (ITZ). The homogenization model allows for considering two sources of variability in concrete, randomly dispersed aggregates in the concrete matrix and uncertain mechanical properties of composite phases of concrete. Using the proposed homogenization technique, the uncertainty in concrete modulus of elasticity and modulus of rupture (described by numerical cumulative probability density function) are determined. Deflection uncertainty of reinforced concrete (RC) beams, propagated from uncertainties in concrete properties, is quantified using Monte Carlo (MC) simulation. Cracked plane frame analysis is used to account for tension stiffening in concrete. Concrete homogenization enables a unique opportunity to bridge the gap between concrete materials and structural modeling, which is necessary for realistic serviceability prediction.

• Composites Research
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• 제36권3호
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• pp.205-210
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• 2023

본 연구에서는 폼 구조의 효율적인 유효 기계적 물성 및 열전도율 예측을 위한 균질화 데이터 기반 전이학습 프레임워크를 개발하였다. Eshelby 텐서 기반의 평균장 균질화(Mean-field homogenization, MFH)는 타원체 형태의 공동을 포함하는 다공성 구조의 물성을 효율적으로 예측할 수 있지만, 셀룰러(cellular) 폼 구조의 물성은 정확하게 예측하기 어렵다. 한편, 유한요소 균질화(Finite element homogenization, FEH)는 정확성은 높지만 상대적으로 높은 해석 시간을 동반한다. 본 논문에서는 평균장 균질화와 유한요소 균질화의 장점을 결합한 데이터 기반 전이학습 프레임워크(Framework)를 제안하였다. 구체적으로, 대량의 평균장 균질화 데이터를 도출하여 사전학습 모델(Pre-trained model)을 구축하고, 상대적으로 소량의 유한요소 균질화 데이터를 이용하여 미세 조정(Fine-tuning) 하였다. 제안된 프레임워크를 검증하기 위한 수치 예제를 수행하였으며, 해석 정확도를 확인하였다. 본 연구의 결과는 다양한 폼 구조를 가진 재료의 해석에 적용할 수 있을 것으로 기대한다.

• 대한수학회지
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• 제46권5호
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• pp.1041-1069
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• 2009

We study the periodic homogenization of the non-stationary Stokes equations. The fundamental homogenization theorem and corrector theorem are proved under a very general assumption on the viscosity coefficients and data. The proofs are based on a weak formulation suitable for an application of classical Tartar's method of oscillating test functions. Such a weak formulation is derived by adapting an argument in Teman's book [Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam, 1984].

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.684-689
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• 2008

In this study, homogenization method combined with the effective interface model for the characterization of properties of the nanoparticulate composites is developed. In order to characterize particle size effect of nanocomposites, effective interface model has been developed. The application range of analytical micromechanics approach is limited because a simple analytical approach is valid only for simple and uniform geometry of fiber particles. Therefore this study focuses on the analysis of mechanical properties of the effect interface through the continuum homogenization method instead of using analytical micromechanics approach. Using the homogenization method, elastic stiffness properties of the effective interface are numerically evaluated and compared with the analytically obtained micromechanics solutions. The suggested homogenization method is expected to be applied to optimization problems for nanocomposite design.

• Structural Engineering and Mechanics
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• 제67권5호
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• pp.527-544
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• 2018

In this paper, the effect of homogenization models on stress analysis is presented for functionally graded plates (FGMs). The derivation of the effective elastic proprieties of the FGMs, which are a combination of both ceramic and metallic phase materials, is of most of importance. The majority of studies in the last decade, the Voigt homogenization model explored to derive the effective elastic proprieties of FGMs at macroscopic-scale in order to study their mechanical responses. In this work, various homogenization models were used to derive the effective elastic proprieties of FGMs. The effect of these models on the stress analysis have also been presented and discussed through a comparative study. So as to show this effect, a refined plate theory is formulated and evaluated, the number of unknowns and governing equations were reduced by dividing the transverse displacement into both bending and shear parts. Based on sinusoidal variation of displacement field trough the thickness, the shear stresses on top and bottom surfaces of plate were vanished and the shear correction factor was avoided. Governing equations of equilibrium were derived from the principle of virtual displacements. Analytical solutions of the stress analysis were obtained for simply supported FGM plates. The obtained results of the displacements and stresses were compared with those predicted by other plate theories available in the literature. This study demonstrates the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Finally, this study offers benchmark results for the multi-scale analysis of functionally graded plates.

• 전산구조공학
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• 제8권3호
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• pp.51-57
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• 1995

다공평판에서의 응력해석에 균질화기법이 사용되었다. 표준적인 유한요소법에 미소좌표계확장을 도입한 균질화 기법은 다공평판을 microscale 모델과 macroscale 모델로 나누어 해석한다. 같은 패턴이 반복되는 최소의 기하학적단위를 microscale에서의 단위구조로 취하여 등가물성치를 산출한다. Macroscale 모델에서는 다공평판을 구멍이 없는 일반평판으로 가정하여 앞에서 산출한 등가물성치와 주어진 경계조건을 이용하여 변위를 산출하고, microscale 모델에서 다공평판의 응력을 계산한다. 균질화기법은 다공평판외에도 기본단위의 반복도가 심한 복합구조의 응력해석에서 유용한 전처리 및 후처리 개념을 제공하며, 계산에 필요한 자유도를 현저히 줄이면서 적절한 등가물성치와 응력분포의 계산을 가능케 하여준다.

• 한국지하수토양환경학회:학술대회논문집
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• 한국지하수토양환경학회 2005년도 INTERNATIONAL SYMPOSIUM ON SOIL & GROUNDWATER ENVIRONMENT
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• pp.191-192
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• 2005