• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.9
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• pp.1051-1061
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• 2011

The influences of density variation on stress and displacement fields at a propagating Mode-III crack tip in orthotropic functionally graded materials (OFGMs) are studied. The crack propagates dynamically at a right angle to the gradient of physical properties. Three kinds of elasticity and density gradients are analyzed in this study. They are as follows: (1) the density varies without elasticity variation, (2) the directions of the density and elasticity gradients are opposite to each other, and (3) same. For these cases, the stress and displacement fields at the crack tip are developed and the dynamic stress intensity factors for propagating cracks are also studied. When the crack speed is low, the influence of density variation on the stresses and displacement is low. However, when the crack speed is high, this influence is very high.

• Journal of the Korean Society of Industry Convergence
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• v.9 no.1
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• pp.37-44
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• 2006

Stress and displacement fields of a Mode III crack propagating along the normal to gradient in an orthotropic functionally gradient materials (OFGM), which has (1) an exponential variation of shear modulus and density, and (2) linear variation of shear modulus with a constant density, are derived. The equations of motion in OFGM are developed and solution to the displacement and stress fields for a propagating crack at constant speed though an asymptotic analysis. The first three terms in expansion of stress and displacement are derived to explicitly bring out the influence of nonhomogeneity. When the FGM constant ${\zeta}$ is zero or $r{\rightarrow}0$, the fields for OFGM are almost same as the those for homogeneous orthotropic material. Using the stress components, the effects of nonhomogeneity on stress components are discussed.

• The Korean Journal of Rheology
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• v.10 no.4
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• pp.202-216
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• 1998

Improved version of previous 'Orthotropic' closure approximation, termed 'ORW' has been numerically developed using new homogeneous flow data. Previous 'Orthotropic' closure approximation, i.e., ORF or ORL showed non-physical oscillation for interaction coefficient $C_1$<0.001 at simple shear flow. It also shows non-physcial oscillation and under-prediction compared with 'Distribution Function Calculation' at non-homogeneous flow of center-gated disk. These phenomena are mainly due to the flow data of 'Distribution Function Calculation' which were used for least-square optimization. ORW obtained by fitting flow data of low interaction coefficient does not show non-physical oscillation and results in reasonably good behaviors at non-homogeneous flows as well as homogeneous flows. Fitting function forms have not been found to improve overall behaviors. It has been found that considering all the eigenvalues of orientation tensor (including the third eigenvalues) might end up with a better closure approximation than just considering the first and second eigenvalues. It is, however, very important and yet difficult to select appropriate function forms of eigenvalues. Numerical simulation including coupling and in-plane velocity gradient effects were performed for injection mold filing process with a film-gated strip and a center-gated disk using ORW and various other closure approximations for comparisons. Although ORW is in excellent agreement with 'Distribution Function Calculation', the predicted results seem to have consistent error in comparison with experimental data. The diffusivity term with constant interaction coefficient might have to be further investigated in order to accurately describe orientation states.

• Composites Research
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• v.26 no.6
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• pp.363-372
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• 2013

Numerical simulation for Resin Transfer Molding manufacturing process is attempted by using the eXtended Finite Element Method (XFEM) combined with the level set method. XFEM allows to obtaining a good numerical precision of the pressure near the resin flow front, where its gradient is discontinuous. The enriched shape functions of XFEM are derived by using the level set values so as to correctly describe the interpolation with the resin flow front. In addition, the level set method is used to transport the resin flow front at each time step during the mold filling. The level set values are calculated by an implicit characteristic Galerkin FEM. The multi-frontal solver of IPSAP is adopted to solve the system. This work is validated by comparing the obtained results with analytic solutions. Moreover, a localization method of XFEM and level set method is proposed to increase the computing efficiency. The computation domain is reduced to the small region near the resin flow front. Therefore, the total computing time is strongly reduced by it. The efficiency test is made with a simple channel flow model. Several application examples are analyzed to demonstrate ability of this method.

• Nuclear Engineering and Technology
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• v.18 no.1
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• pp.1-8
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• 1986

A magnetic quadrupole doublet was fabricated for use at the pre-target position of SNU 1.5MV Van de Graaff accelerator and then its optical characteristics were measured and analysed. The physical dimensions are: pole length 180mm, aperture radius 25mm, pole tip radius 28.75mm. Material for poles and return yokes is carbon steel KS-SM40C. Coils have 480 turns per one pole and air-cooling is adopted. Applying the d.c. current 2.99$\pm$0.03A to the lens, and using the Hall probe, magnetic field elements $B_{\theta}$ , $B_{\gamma}$, were measured at the selected Points along each coordinate direction r,$\theta$, z. From the area integration and orthogonal polynomial fitting for the measured data, the magnetic Field gradient G=566.3$\pm$2.1 gauss/cm at lens center, the effective length L=208.3$\pm$1.44mm along the lens axis have been obtained. The harmonic contents were determined up to 20-pole from the generalized least squares fitting. The results indicate that sextupole/quadrupole is below 1.4$\pm$0.9% and all the other multipoles are below 0.5% in the region within 18mm radius at the center of lens.