• Structural Engineering and Mechanics
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• 제11권4호
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• pp.373-392
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• 2001

The main idea behind the paper is to present two alternative methods of homogenization of the heat conduction problem in composite materials, where the heat conductivity coefficients are assumed to be random variables. These two methods are the Monte-Carlo simulation (MCS) technique and the second order perturbation second probabilistic moment method, with its computational implementation known as the Stochastic Finite Element Method (SFEM). From the mathematical point of view, the deterministic homogenization method, being extended to probabilistic spaces, is based on the effective modules approach. Numerical results obtained in the paper allow to compare MCS against the SFEM and, on the other hand, to verify the sensitivity of effective heat conductivity probabilistic moments to the reinforcement ratio. These computational studies are provided in the range of up to fourth order probabilistic moments of effective conductivity coefficient and compared with probabilistic characteristics of the Voigt-Reuss bounds.

• 대한기계학회논문집A
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• 제33권2호
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• pp.153-161
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• 2009

Three-dimensional finite-element methods(FEM) have been used to analyze the thermal stress of an exhaust gas recirculation(EGR) cooler due to thermal and pressure load. Since efficiency and capability of the heat exchanger are mainly dependent on net heat transferring area of the EGR cooler system, the tube inside the system has a numerous dimples on the surface. Thus for finite element analysis, firstly the dimple-typed tube is modeled as a plain element without the dimple, and then the equivalent thermal conductivities and elastic modulus are calculated. This work describes the numerical homogenization procedure of the dimple-typed tube and verifies the equivalent material properties by comparison of a single unit and the actual full model. Finally, the homogenization scheme presented in this study can be efficiently applied to finite element analyses for the thermal stress and deformation behavior of the EGR cooler system with the dimple-typed tube.

• 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.

• 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.

• 한국기계가공학회지
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• 제18권12호
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• pp.28-37
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• 2019

Due to their flexible tailoring qualities, composites have become fascinating materials for structural engineers. While the research area of fiber-reinforced composite materials was previously limited to synthetic materials, natural fibers have recently become the primary research focus as the best alternative to artificial fibers. The natural fibers are eco-friendly and relatively cheaper than synthetic fibers. The main concern of current research into natural fiber-reinforced composites is the prediction and enhancement of the effective material properties. In the present work, finite element analysis is used with a numerical homogenization approach to determine the effective material properties of jute fiber-reinforced epoxy composites with various volume fractions of fiber. The finite element analysis results for the jute fiber-reinforced epoxy composite are then compared with several well-known analytical models.

• Smart Structures and Systems
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• 제12권5호
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• pp.579-594
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• 2013

A new enthalpy - based procedure for the homogenization of the electromechanical material parameters of composite piezoelectric modules with integrated electrodes is presented. It is based on a finite element (FE) modeling of the latter's representative volume element (RVE). In contrast to most previously published homogenization approaches that are based on averaged quantities, the presented method uses a direct evaluation of the electromechanical enthalpy. Hence, for the linear orthotropic piezoelectric composite behavior full set of elastic, piezoelectric, and dielectric material parameters, 17 load cases (LC) are used where each load case leads directly to one material parameter. This gives the possibility to elaborate a very strict and easy to program processing. In conjunction with the 17 LC, the enthalpy - based homogenization is particularly suitable for laminated composite piezoelectric modules with integrated electrodes. In this case, the electric load has to be given at the electrodes rather than at the RVE FE model boundaries. The proposed procedure is validated through its comparison to literature available results on a classical 1-3 piezoelectric micro fiber (longitudinally polarized) reinforced composite and a $d_{15}$ shear piezoelectric macro-fiber (transversely polarized) composite module.

• 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.

• Structural Engineering and Mechanics
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• 제4권6호
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• pp.613-630
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• 1996

The homogenization method is used to develop a beam element in space for thermo-mechanical analysis of unidirectional composites. Local stress and temperature field in the microscale are described using the function of homogenization. The global (macroscopic) behaviour of the structure is supposed to be that of a beam. Beam-type kinematical hypotheses (including independent shear rotations) are hence applied and superposed on the microdescription. A macroscopic stiffness matrix for such a beam element is then developed which contains the microscale properties of the single cell of periodicity. The presented model enables us to analyse without too much computational effort complicated composite structures such as e.g. toroidal coils of a fusion reactor. We need only a FE mesh sufficiently fine for a correct description of the local geometry of a single cell and a few of the newly developed elements for the description of the global behaviour. An unsmearing procedure gives the stress and temperature field in the different materials of a single cell.

• 대한기계학회논문집
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• 제18권5호
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• pp.1245-1252
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• 1994

A solution of heat transfer problems of composite materials has been tried using homogenization technique. Homogenization technique, which was derived by applying asymptotic expansion to the standard finite element method, helped compute the equivalent thermal conductivity matrices of base cells which constituted the composite material with repeated patterns. The homogenization technique made it possible to compute the solution of the heat transfer problem of composite materials with lower degrees of freedom compared to those of other numerical methods. The equivalent thermal conductivities computed by computed by homogenization technique are also applicable to other numerical methods such as finite difference method.

• 한국전산구조공학회논문집
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• 제13권1호
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• pp.51-61
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• 2000

본 논문은 구조물의 미시적 측면에서 유효평균탄성계수를 결정하기 위한 균질화기법인 점근적 방법을 적용하였고, 탄성값을 조사하기 위하여 유한요소법으로 정식화하였다. 수치 예로서 물성치가 각기 다른 등방성 재료를 적층한 부재의 임의 단면에서 단위요소를 해석영역으로 설정하고 산출된 탄성계수를 기존의 해석방법으로부터 산출된 값과 비교하였다. 균질화기법으로 산출된 탄성계수는 과소평가되어 나타나며, 이는 해석영역을 유한요소 정식화하는 과정에서 수정항만큼 차이가 난다는 것을 증명하였다. 기존 해석방법으로는 복합재료의 탄성계수가 단순히 재료의 산술적 평균값으로 계산되는 것과는 달리, 미시적으로 복합재 단위요소의 반복성을 고려함으로써 제안된 해석방법이 보다 유용하다는 것을 보여 주었다.