• Interaction and multiscale mechanics
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• 제5권1호
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• pp.27-40
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• 2012

The two-dimensional incompressible flow of a linear viscoelastic fluid we considered in this research has rapidly oscillating initial conditions which contain both the large scale and small scale information. In order to grasp this double-scale phenomenon of the complex flow, a multiscale analysis method is developed based on the mathematical homogenization theory. For the incompressible flow of a linear viscoelastic Maxwell fluid, a well-posed multiscale system, including averaged equations and cell problems, is derived by employing the appropriate multiple scale asymptotic expansions to approximate the velocity, pressure and stress fields. And then, this multiscale system is solved numerically using the pseudospectral algorithm based on a time-splitting semi-implicit influence matrix method. The comparisons between the multiscale solutions and the direct numerical simulations demonstrate that the multiscale model not only captures large scale features accurately, but also reflects kinetic interactions between the large and small scale of the incompressible flow of a linear viscoelastic fluid.

• Interaction and multiscale mechanics
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• 제3권3호
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• pp.213-234
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• 2010

A multiscale method is presented for analysis of thin slab structures in which the microstructures can not be reduced to two-dimensional plane stress models and thus three dimensional treatment of microstructures is necessary. This method is based on the classical asymptotic expansion multiscale approach but with consideration of the special geometric characteristics of the slab structures. This is achieved via a special form of multiscale asymptotic expansion of displacement field. The expanded three dimensional displacement field only exhibits in-plane periodicity and the thickness dimension is in the global scale. Consequently by employing the multiscale asymptotic expansion approach the global macroscopic structural problem and the local microscopic unit cell problem are rationally set up. It is noted that the unit cell is subjected to the in-plane periodic boundary conditions as well as the traction free conditions on the out of plane surfaces of the unit cell. The variational formulation and finite element implementation of the unit cell problem are discussed in details. Thereafter the in-plane material response is systematically characterized via homogenization analysis of the proposed special unit cell problem for different microstructures and the reasoning of the present method is justified. Moreover the present multiscale analysis procedure is illustrated through a plane stress beam example.

• Journal of Mechanical Science and Technology
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• 제20권1호
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• pp.110-124
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• 2006

The multi scale wavelet-Galerkin method implemented in an adaptive manner has an advantage of obtaining accurate solutions with a substantially reduced number of interpolation points. The method is becoming popular, but its numerical efficiency still needs improvement. The objectives of this investigation are to present a new numerical scheme to improve the performance of the multi scale adaptive wavelet-Galerkin method and to give detailed implementation procedure. Specifically, the subdomain technique suitable for multiscale methods is developed and implemented. When the standard wavelet-Galerkin method is implemented without domain subdivision, the interaction between very long scale wavelets and very short scale wavelets leads to a poorly-sparse system matrix, which considerably worsens numerical efficiency for large-sized problems. The performance of the developed strategy is checked in terms of numerical costs such as the CPU time and memory size. Since the detailed implementation procedure including preprocessing and stiffness matrix construction is given, researchers having experiences in standard finite element implementation may be able to extend the multi scale method further or utilize some features of the multiscale method in their own applications.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권2호
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• pp.215-227
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• 2020

A new multiscale finite element method for elliptic problems with highly oscillating coefficients are introduced. A hybridization yields a locally flux-conserving numerical scheme for multiscale problems. Our approach naturally induces a homogenized equation which facilitates error analysis. Complete convergence analysis is given and numerical examples are presented to validate our analysis.

• Journal of information and communication convergence engineering
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• 제7권4호
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• pp.545-550
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• 2009

A method fully utilizing multiscale line filter responses is presented to estimate the point spread function(PSF) of a CT scanner and diameters of small tubular structures based on the PSF. The estimation problem is formulated as a least square fitting of a sequence of multiscale responses obtained at each medical axis point to the precomputed multiscale response curve for the ideal line model. The method was validated through phantom experiments and demonstrated through phantom experiments and demonstrated to accurately measure small-diameter structures which are significantly overestimated by conventional methods based on the full width half maximum(FWHM) and zero-crossing edge detection.

• 대한기계학회논문집A
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• 제28권3호
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• pp.251-258
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• 2004

Since the multiscale wavelet-based numerical methods allow effective adaptive analysis, they have become new analysis tools. However, the main applications of these methods have been mainly on elliptic problems, they are rarely used for eigenvalue analysis. The objective of this paper is to develop a new multiscale wavelet-based adaptive Galerkin method for eigenvalue analysis. To this end, we employ the hat interpolation wavelets as the basis functions of the finite-dimensional trial function space and formulate a multiresolution analysis approach using the multiscale wavelet-Galerkin method. It is then shown that this multiresolution formulation makes iterative eigensolvers very efficient. The intrinsic difference-checking nature of wavelets is shown to play a critical role in the adaptive analysis. The effectiveness of the present approach will be examined in terms of the total numbers of required nodes and CPU times.

• Composites Research
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• 제36권5호
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• pp.329-334
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• 2023

기존의 멀티스케일 유한요소법(Multiscale finite element, FE² )은 거시 스케일의 모든 적분점에서 대표 체적요소(representative volume element, RVE)의 미시 경계치 문제를 반복적으로 계산하기 때문에 긴 해석 시간과 많은 데이터 저장 공간을 필요로 한다. 이를 해결하기 위해 본 연구에서 평균장 균질화 데이터 기반 멀티스케일 해석 기법을 개발하였다. 데이터 기반 전산역학(data-driven computational mechanics, DDCM) 해석은 변형률-응력 데이터 셋을 직접적으로 사용하는 모델-프리(model-free)접근 방식이다. 멀티스케일 해석을 수행하기 위해, 평균장 균질화(mean-field homogenization)를 활용하여 복합재의 미세구조에 대한 변형률-응력 데이터베이스(database)를 효율적으로 구축하고, 이를 기반으로 데이터 기반 전산역학 시뮬레이션을 수행하였다. 본 논문에서는 개발한 멀티 스케일 해석 프레임워크(framework)를 예제에 적용하여, 초탄성(hyperelasticity) 복합재의 미세 구조를 고려한 데이터 기반 전산역학 시뮬레이션 결과를 확인하였다. 따라서, 데이터 기반 전산역학 접근 방식을 활용한 멀티스케일 해석기법은 다양한 재료 및 구조에 적용될 수 있으며, 멀티스케일 해석 연구 및 응용 가능성을 열어줄 것으로 기대된다.

• Interaction and multiscale mechanics
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• 제1권1호
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• pp.1-31
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• 2008

The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical or cylindrical particles has been briefly reviewed. Basic equations of the finite element method using the explicit time integration have been given. The micr-macro transition for the discrete element method has been discussed. Theoretical formulations for macroscopic stress and strain tensors have been given. Determination of macroscopic constitutive properties using dimensionless micro-macro relationships has been proposed. The formulation of the multiscale DEM/FEM model employing the DEM and FEM in different subdomains of the same body has been presented. The coupling allows the use of partially overlapping DEM and FEM subdomains. The overlap zone in the two coupling algorithms is introduced in order to provide a smooth transition from one discretization method to the other. Coupling between the DEM and FEM subdomains is provided by additional kinematic constraints imposed by means of either the Lagrange multipliers or penalty function method. The coupled DEM/FEM formulation has been implemented in the authors' own numerical program. Good performance of the numerical algorithms has been demonstrated in a number of examples.

• Interaction and multiscale mechanics
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• 제4권3호
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• pp.173-185
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• 2011

A multiscale modeling scheme that addresses the influence of the nanoparticle size in nanocomposites consisting of nano-sized spherical particles embedded in a polymer matrix is presented. A micromechanics-based constitutive model for nanoparticle-reinforced polymer composites is derived by incorporating the Eshelby tensor considering the interface effects (Duan et al. 2005a) into the ensemble-volume average method (Ju and Chen 1994). A numerical investigation is carried out to validate the proposed micromechanics-based constitutive model, and a parametric study on the interface moduli is conducted to investigate the effect of interface moduli on the overall behavior of the composites. In addition, molecular dynamics (MD) simulations are performed to determine the mechanical properties of the nanoparticles and polymer. Finally, the overall elastic moduli of the nanoparticle-reinforced polymer composites are estimated using the proposed multiscale approach combining the ensemble-volume average method and the MD simulation. The predictive capability of the proposed multiscale approach has been demonstrated through the multiscale numerical simulations.

• Interaction and multiscale mechanics
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• 제3권1호
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• pp.1-22
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• 2010

In this paper one introduces a method of multiscale modelling called collection of dynamical systems with dimensional reduction. The method is suggested to be an appropriate approach to theoretical modelling of phenomena in mechanics of materials having in mind especially dynamics of processes. Within this method one formalizes scale of averaging of processes during modelling. To this end a collection of dynamical systems is distinguished within an elementary dynamical system. One introduces a dimensional reduction procedure which is designed to be a method of transition between various scales. In order to consider continuum models as obtained by means of the dimensional reduction one introduces continuum with finite-dimensional fields. Owing to geometrical elements associated with the elementary dynamical system we can formalize scale of averaging within continuum mechanics approach. In general presented here approach is viewed as a continuation of the rational mechanics.