• Interaction and multiscale mechanics
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• 제6권2호
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• pp.211-235
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• 2013

An incompressible smoothed particle hydrodynamics (ISPH) method based on the incremental pressure projection method is developed in this study. The Rayleigh-B$\acute{e}$nard convection in a square enclosure is used as a validation case and the results obtained by the proposed ISPH model are compared to the benchmark solutions. The comparison shows that the established ISPH method has a good performance in terms of accuracy. Subsequently, the proposed ISPH method is employed to simulate natural convection from a heated cylinder in a square enclosure. It shows that the predictions obtained by the ISPH method are in good agreements with the results obtained by previous studies using alternative numerical methods. A rotating and heated cylinder is also considered to study the effect of the rotation on the heat transfer process in the enclosure space. The numerical results show that for a square enclosure at, the addition of kinetic energy in the form of rotation does not enhance the heat transfer process. The method is also applied to simulate forced convection from a circular cylinder in an unbounded uniform flow. In terms of results, it turns out that the proposed ISPH model is capable to simulate heat transfer problems with the complex and moving boundaries.

• Interaction and multiscale mechanics
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• 제2권2호
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• pp.129-151
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• 2009

This paper presents a meshfree procedure using a convex generalized meshfree (GMF) approximation for the large deformation analysis of particle-reinforced rubber compounds on microscopic level. The convex GMF approximation possesses the weak-Kronecker-delta property that guarantees the continuity of displacement across the material interface in the rubber compounds. The convex approximation also ensures the positive mass in the discrete system and is less sensitive to the meshfree nodal support size and integration order effects. In this study, the convex approximation is generated in the GMF method by choosing the positive and monotonic increasing basis function. In order to impose the periodic boundary condition in the unit cell method for the microscopic analysis, a singular kernel is introduced on the periodic boundary nodes in the construction of GMF approximation. The periodic boundary condition is solved by the transformation method in both explicit and implicit analyses. To simulate the interface de-bonding phenomena in the rubber compound, the cohesive interface element method is employed in corporation with meshfree method in this study. Several numerical examples are presented to demonstrate the effectiveness of the proposed numerical procedure in the large deformation analysis.

• 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.

• 한국식품과학회지
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• 제36권5호
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• pp.728-732
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• 2004

본 연구에서는 난백의 거품형성능력 및 안정성을 간편하게 평가하기 위한 표준방법을 제시하고자 시료의 양, whipping 속도 및 시간이 거품형성에 미치는 영향을 조사하고 적합한 거품형성조건을 선정하였다. 선정된 조건(시료량 70g, 1,200rpm, 2분)으로 난백의 거품형성능력 및 안정성을 20회 반복 측정하여 평가한 결과 높은 재현성을 나타내었으며 시료의 변화(신선한 난백, 동결건조 난백분말, 상업용 난백분말) 및 계란의 저장기간에 따른 거품형성능력 및 안정성의 유의적 차이를 효과적으로 구별할 수 있었다.

• Interaction and multiscale mechanics
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• 제7권1호
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• pp.543-561
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• 2014

We present a full energy and force formulation of the quasicontinuum method with non-local and local transition elements. Non-local transition elements are developed to transmit inhomogeneity from the atomistic to the continuum regions. Local transition elements are developed to resolve the mathematical mismatch between non-local atoms and the local continuum. The rationale behind these transition elements is provided by analyzing the energy and force transitions between atoms and continuum under the Cauchy-Born rule. We show that breakdown of the Cauchy-Born rule occurs for slaved atoms of local elements within the cutoff of non-local atoms. The inadequacy of the Cauchy-Born rule at the transition region naturally leads to the need of atomistic treatment of transition slaved and transition representative atoms. Such an atomistic treatment together with a full or cutoff sampling allows non-local transition elements containing these transition entities to transmit inhomogeneity. Different force formulations for transition representative atoms and pure local representative atoms allow the local transition elements to resolve non-local and local mismatches. The method presented herein is validated by force calculations in an unstressed perfect crystal as well as an unrelaxed grain boundary model. A nanoindentation simulation in 3D is conducted to demonstrate the accuracy and efficiency of the proposed method.

• Interaction and multiscale mechanics
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• 제6권4호
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• pp.357-375
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• 2013

In this paper, the forced vibration problem of an Euler-Bernoulli beam that is joined with a semi-infinite field of a compressible fluid is considered as a boundary value problem (BVP). This BVP includes two partial differential equations (PDE) and some boundary conditions (BC), which are introduced comprehensively. After that, the closed-form solution of this fluid-structure interaction problem is obtained in the frequency domain. Some mathematical techniques are utilized, and two unknown functions of the BVP, including the beam displacement at each section and the fluid dynamic pressure at all points, are attained. These functions are expressed as an infinite series and evaluated quantitatively for a real example in the results section. In addition, finite element analysis is carried out for comparison.

• Interaction and multiscale mechanics
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• 제1권2호
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• pp.303-315
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• 2008

In this paper, thermodynamical properties of crystalline silicon under strain are calculated using classical molecular dynamics (MD) simulations based on the Tersoff interatomic potential. The Helmholtz free energy of the silicon crystal under strain is calculated by using the ensemble method developed by Frenkel and Ladd (1984). To account for quantum corrections under strain in the classical MD simulations, we propose an approach where the quantum corrections to the internal energy and the Helmholtz free energy are obtained by using the corresponding energy deviation between the classical and quantum harmonic oscillators. We calculate the variation of thermodynamic properties with temperature and strain and compare them with results obtained by using the quasi-harmonic model in the reciprocal space.

• Interaction and multiscale mechanics
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• 제1권2호
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• pp.177-190
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• 2008

In this paper, both experimental measurement and theoretical analysis are used to investigate the out-of-plane resonant characteristics of a cantilevered piezoceramic plate in air and three different kinds of fluid. The experimental method, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), is the major technique used in this study to measure the resonant characteristics of the cantilivered piezoceramic plate. Both resonant frequencies and full-field mode shapes are obtained from this experimental technique. Numerical computations based on the finite element analysis are presented for comparison with the experimental results. Good quality of mode shapes for the cantilevered piezoceramic plate in air is obtained from the AF-ESPI technique. However, the quality decreases as the viscosity of fluids increases. From the results provided from experimental measurements and numerical computations, it is indicated that the resonant frequencies of the cantilevered piezoceramic plate in fluid decrease with the increase of the viscosity of fluids. Good agreements between the experimental measured data and the numerical calculated results are found for both resonant frequencies and mode shapes of the cantilevered piezoceramic plate in fluid.

• Interaction and multiscale mechanics
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• 제1권1호
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• pp.103-121
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• 2008

This paper presents an optimization-based method for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain braced frame. Based on a non-stochastic modeling of uncertainty, we assume that the parameters both of brace stiffnesses and external forces are uncertain but bounded. A brace member represents the sum of the stiffness of the actual brace and the contributions of some non-structural elements, and hence we assume that the axial stiffness of each brace is uncertain. By using the $\mathcal{S}$-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. The minimum bounding ellipsoids are computed for a braced frame under several uncertain circumstances.

• Interaction and multiscale mechanics
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• 제4권2호
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• pp.155-164
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• 2011

The lattice strain evolution within polycrystalline solids is influenced by the crystal orientation and grain interaction. For multi-phase polycrystals, due to potential large differences in properties of each phase, lattice strains are even more strongly influenced by grain interaction compared with single phase polycrystals. In this research, the effects of the grain interaction and crystal orientation on the lattice strain evolution in a two-phase polycrystals are investigated. Duplex steel of austenite and ferrite phases with equal volume fraction is selected for the analysis, of which grain arrangement sensitivity is confirmed in the literature through both experiment and simulation (Hedstr$\ddot{o}$m et al. 2010). Analysis on the grain interaction is performed using the results obtained from the finite element calculation based on the model of restricted slip within crystallographic planes. The dependence of lattice strain on grain interactions as well as crystal orientation is confirmed and motivated the need for more in-depth analysis.