• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.369-387
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• 2016

In this work, random homogenization analysis for the effective thermal properties of a three-dimensional composite material with unidirectional fibers is presented by combining the equivalent inclusion method with Random Factor Method (RFM). The randomness of the micro-structural morphology and constituent material properties as well as the correlation among these random parameters are completely accounted for, and stochastic effective thermal properties as thermal expansion coefficients as well as their correlation are then sought. Results from the RFM and the Monte-Carlo Method (MCM) are compared. The impact of randomness and correlation of the micro-structural parameters on the random homogenized results is revealed by two methods simultaneously, and some important conclusions are obtained.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.559-568
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• 2003

We introduce the notion of two-scale convergence for partial differential equations with random coefficients that gives a very efficient way of finding homogenized differential equations with random coefficients. For an application, we find the homogenized matrices for linear second order elliptic equations with random coefficients. We suggest a natural way of finding the two-scale limit of second order equations by considering the flux term.

• Structural Engineering and Mechanics
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• v.11 no.4
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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.

• Composites Research
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• v.15 no.5
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• pp.44-52
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• 2002

To study numerically the mechanical behaviors of advanced composite materials considering the microscopic phenomena as well as the macroscopic properties and behaviors, a multi-scale modeling and analysis by the mathematical homogenization method with the help of the finite element method(FEM) are reviewed. The hierarchical modeling strategy and the formulation are briefly described first to give some idea of the multi-scale framework. The latter half of this article focuses on the verification of the multi-scale analysis by the homogenization method in its applications to real advanced materials. The first example is the verification of the predicted macroscopic(homogenized) properties based on the microstructure of porous ceramics. In spite of the complexity of the random microstructure, the error between the predicted and the measured values was only 1%. Next, two applications to the process simulation of fiber reinforced polymer matrix composites are presented. The permeability characteristics are evaluated for sheared weave fabrics for resin transfer molding(RTM) simulation, and the thermoforming of FRTP sheet is analyzed considering the large deformation of the knit structure during the deep-draw forming was verified by comparison with the experimental results.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.15 no.1
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• pp.21-26
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• 2005

In order to simulate the powder compaction process and to assess the effects of packing randomness and particle arrangement 2-dimensional model of rod array compaction using quasi-random multiparticle array is introduced. The elastic modulus of porous ceramics is computed by the homogenization method. With 3 Al₂O₃ and 3 Al particles the compaction processes associated with the porosities are simulated by the explicit finite element method, based on the elastic modulus found by the homogenization method. The simulation results are compared with both previous analytical ones and experimental measurements. Finally, in order to find the relationship between the friction coefficient of powder particles and the relative density, the sensitivity analysis is performed.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2007.10a
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• pp.344-347
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• 2007

For modeling the non-periodic and randomly scattered powder particles, the quasi-random multi-particle array is introduced. The multi-scale process simulation, which enables to formulate a regression model with a response surface method, is performed by employing a homogenization method. The size of ${Al_2}{O_3}$ particle, amplitude of cyclic compaction pressure, and friction coefficient are considered as optimal process parameters. The optimal conditions of process parameters providing the highest relative density are finally found by using the grid search method.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.417-447
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• 2010

The uncertainty often observed in experimental strengths of masonry constituents makes critical the selection of the appropriate inputs in finite element analysis of complex masonry buildings, as well as requires modelling the building ultimate load as a random variable. On the other hand, the utilization of expensive Monte Carlo simulations to estimate collapse load probability distributions may become computationally impractical when a single analysis of a complex building requires hours of computer calculations. To reduce the computational cost of Monte Carlo simulations, direct computer calculations can be replaced with inexpensive Response Surface (RS) models. This work investigates the use of RS models in Monte Carlo analysis of complex masonry buildings with random input parameters. The accuracy of the estimated RS models, as well as the good estimations of the collapse load cumulative distributions obtained via polynomial RS models, show how the proposed approach could be a useful tool in problems of technical interest.

• Journal of the Korean Society for Heat Treatment
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• v.34 no.3
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• pp.122-129
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• 2021

This study focuses on the microstructural development of 99% magnesium alloy sheet manufactured using twin roll casting (TRC) process. Herein, a plate with a thickness of 5 mm was manufactured using the TRC process, homogenization heat treatment was performed at 400℃ for 2-32 h, and finally, the change in microstructure was evaluated via optical microscopy and textural analysis. The results suggest that the plate manufactured using the TRC process was not destroyed and was successfully rolled into a plate. Microscopic observation suggested that the dendritic cast structure was arranged along the rolling direction. And the central layer of the rolled plate, where was present in a liquid state at the beginning of rolling, solidified later during the TRC process to form central segregation. The initial cast structure and inhomogeneous structure of the plate were recrystallized by homogenization heat treatment for only 2 h, and it was confirmed that the segregated part of the central layer became homogeneous and recrystallization occurred. Grain growth occurred as the heat treatment time increased, and secondary recrystallization occurred, wherein only some grains were grown. The textural analysis, which was conducted via X-ray diffraction, confirmed that the relatively weak basal plane texture developed using the TRC process was formed into a random texture after heat treatment.

• Journal of the Korea Institute of Military Science and Technology
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• v.5 no.1
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• pp.83-95
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• 2002

Thermal conductivity of ceramic fibrous insulator was analysed and predicted by using the modeling/simulation technique. Ceramic fibrous insulators are widely used as high temperature insulator on account of their lightweight mass and heat resisting properties. Especially it is suitable to protect the high speed aircraft and missiles from severe aero-thermodynamic heating. Thermal conductivity of ceramic fibrous insulator could be determined from the conductive heat transfer and the radiative heat transfer through the insulator. In order to estimate conductive thermal conductivity, homogenization technique was applied, while radiative thermal conductivity was computed by means of random number and radiation probability. Particularly radiation probability can make it possible to estimate the conductivity of fibrous insulator without any experimental constant. The calculated conductivity predicted in the present study have a reasonable accuracy with an average error of 7 percent to experimental data.

• Journal of the Korean Geotechnical Society
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• v.16 no.4
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• pp.63-70
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• 2000

The quantitative analyses and the mechanical interpretation of discontinuity planes are the most important factor for the study of strength and deformation properties of rock masses containing discontinuity planes. However, the relationship between the factors investigated in the field and the actual mechanical properties of discontinuity planes is not fully understood. The main purpose of this study is to investigate the effects of density, length, and spacing of joints on elastic modulus of rock masses as these values vary. A new parameter which has a direct relation with the elastic modulus of discontinuity planes is also preposed in this study. The combination of finite element methods and homogenization methods has been used for the numerical analyses of a uintcell with discontinuity planes, which is generated using random-number generation methods. The elastic modulus of the discontinuity plane is found from the numerical analyses. The final results propose not only the relation between the investigation parameters of discontinuity planes and the elastic modulus of rock masses but also a new parameter, an effect area ratio having a linear relation with the elastic modulus of rock masses.