• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.3
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• pp.181-192
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• 2012

Here in this paper, the steady paint film flow on a vertical wall of a non-Newtonian pseudo plastic fluid for drainage problem has been investigated. The exact solution of the nonlinear problem is obtained for the velocity profile. Also the average velocity, volume flux, shear stress on the wall, force to hold the wall in position and normal stress difference have been derived. We retrieve Newtonian case, when material constant ${\mu}_1$ and relaxation time ${\lambda}_1$ equal zero. The results for co-rotational Maxwell fluid is also obtained by taking material constant ${\mu}_1$ = 0. The effect of the zero shear viscosity ${\eta}_0$, the material constant ${\mu}_1$, the relaxation time ${\lambda}_1$ and gravitational force on the velocity profile for drainage problem are discussed and plotted.

• Advances in Computational Design
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• v.2 no.3
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• pp.123-141
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• 2017

Solving a system of linear or non-linear equations is required to analyze any kind of structures. There are many ways to solve a system of equations, and they can be classified as implicit and explicit techniques. The explicit methods eliminate round-off errors and use less memory. The dynamic relaxation method (DR) is one of the powerful and simple explicit processes. The important point is that the DR does not require to store the global stiffness matrix, for which it just uses the residual loads vector. In this paper, a new approach to the DR method is expressed. In this approach, the damping, mass and time steps are similar to those of the traditional method of dynamic relaxation. The difference of this proposed method is focused on the method of calculating the damping. The proposed method is expressed such that the time step is constant, damping is equal to zero except in steps with maximum energy and the concentrated damping can be applied to minimize the energy of system in this step. In this condition, the calculation of damping in all steps is not required. Then the volume of computation is reduced. The DR method for form-finding of membrane structures is employed in this paper. The form-finding of the three plans related to the membrane structures with different loading is considered to investigate the efficiency of the proposed method. The numerical results show that the convergence rate based on the proposed method increases in all cases than other methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.4
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• pp.459-479
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• 2015

Two-dimensional steady laminar natural convection around a heat conducting and generating solid body inside a square enclosure with different thermal boundaries is performed. The mathematical model is governed by the coupled equation of mass, momentum and energy. These equations are discretized by finite volume method with power-law scheme and solved numerically by SIMPLE algorithm with under-relaxation technique. Effect of Rayleigh number, temperature difference ratio of solid-fluid, aspect ratio of solid-enclosure and the thermal conductivity ratio of solid-fluid are investigated numerically for Pr = 0.7. The flow and heat transfer aspects are demonstrated in the form of streamlines and isotherms respectively.

• Proceedings of the Korean Magnestics Society Conference
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• 2000.09a
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• pp.279-286
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• 2000

Magnetic field dependence of magnetization reversal in Co/Pt multilayers has been quantitatively investigated. Serial samples of Co/Pt multilayers have been prepared by dc-magnetron sputtering under various Ar pressure. Magnetization reversal was monitored by magnetization viscosity measurement and direct domain observation using a magneto-optical microscope system, and the wall-motion speed and the nucleation rate R were determined using a domain reversal model based on time-resolved domain reversal patterns. Both and R were found to be exponentially dependent on the reversing applied field. From the exponential dependencies, the activation volumes of the wall motion and nucleation could be determined based on a thermally activated relaxation model, and the wall-motion activation volume was revealed to be slightly larger than the nucleation activation volume.

• Journal of Magnetics
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• v.5 no.4
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• pp.116-119
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• 2000

Magnetic field dependence of magnetization reversal in Co/Pt multilayers was quantitatively investigated. Serial samples of Co/Pt multilayers were prepared by dc-magnetron sputtering under various Ar pressures. Magnetization reversal was monitored by magnetization viscosity measurement and direct domain observation using a magneto-optical microscope system, and the wall-motion speed V and the nucleation rate R were determined using a domain reversal model based on time-resolved domain reversal patterns. Both V and R were found to be exponentially dependent on the applied reversing field. From the exponential dependencies, the activation volumes for wall motion and nucleation could be determined, based on a thermally activated relaxation model, and the wall-motion activation volume was found to be slightly larger than the nucleation activation volume.

• Korean Journal of Metals and Materials
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• v.46 no.9
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• pp.572-576
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• 2008

Elastostatic compression tests were carried out on amorphous alloys to evaluate their energy absorption capability during homogeneous deformation at room temperature. Experiments demonstrated that a compressive stress below the global yield imposed on amorphous alloys for extended periods causes homogeneous plastic strain associated with the irreversible structural disordering. During the disordering process, free volume was created, dissipating the externally applied strain energy and the rate of creation was found to converge to a saturated value. We evaluated the capability of energy absorption of amorphous alloys during homogeneous deformation using recent theories on the evolution of the structural state.

• Polymer(Korea)
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• v.31 no.4
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• pp.335-342
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• 2007

The goal of this study is to investigate the effect of molecular structure modifications on the kinetics of physical aging of thin films formed from 6FDA-based polyimides with time. The permeability for 6FDA-based polyimide thin films containing carboxyl acid groups commonly decreased 20-50% after the isothermal aging and the selectivity gained anywhere from 10% to 30% while the rate of permeability loss on the change of polymer structure showed different reciprocal relationship between 6FDA-6FpDA based polyimides and 6FDA-DAM based polyimides. The Lorenz-Lorentz equation was used to relate changes in refractive index to densification and volume relaxation with aging time. The permeability as a function of aging time fits the expected form $P=Ae^{(-B/f)}$. The results matched well with the data for different polymer membranes.

• Ocean Systems Engineering
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• v.8 no.4
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• pp.381-407
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• 2018

This paper presents a hybrid numerical approach, which combines a two-phase Navier-Stokes model (NS) and the fully nonlinear potential theory (FNPT), for modelling wave-structure interaction. The former governs the computational domain near the structure, where the viscous and turbulent effects are significant, and is solved by OpenFOAM/InterDyMFoam which utilising the finite volume method (FVM) with a Volume of Fluid (VOF) for the phase identification. The latter covers the rest of the domain, where the fluid may be considered as incompressible, inviscid and irrotational, and solved by using the Quasi Arbitrary Lagrangian-Eulerian finite element method (QALE-FEM). These two models are weakly coupled using a zonal (spatially hierarchical) approach. Considering the inconsistence of the solutions at the boundaries between two different sub-domains governed by two fundamentally different models, a relaxation (transitional) zone is introduced, where the velocity, pressure and surface elevations are taken as the weighted summation of the solutions by two models. In order to tackle the challenges associated and maximise the computational efficiency, further developments of the QALE-FEM have been made. These include the derivation of an arbitrary Lagrangian-Eulerian FNPT and application of a robust gradient calculation scheme for estimating the velocity. The present hybrid model is applied to the numerical simulation of a fixed horizontal cylinder subjected to a unidirectional wave with or without following current. The convergence property, the optimisation of the relaxation zone, the accuracy and the computational efficiency are discussed. Although the idea of the weakly coupling using the zonal approach is not new, the present hybrid model is the first one to couple the QALE-FEM with OpenFOAM solver and/or to be applied to numerical simulate the wave-structure interaction with presence of current.

• Advances in nano research
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• v.16 no.4
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• pp.413-426
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• 2024

This paper investigates the dynamic behavior of a simply supported viscoelastic plate made of functionally graded carbon nanotube reinforced composite under dynamic loading. Carbon nanotubes are distributed in 5 different shapes: U, V, A, O and X, depending on the shape they form through the thickness of the plate. The displacement fields are derived in the Laplace domain using a higher-order shear deformation theory. Equations of motion are obtained through the application of the energy method and Hamilton's principle. The resulting equations of motion are solved using Navier's method. Transforming the Laplace domain displacements into the time domain involves Durbin's modified inverse Laplace transform. To validate the accuracy of the developed algorithm, a free vibration analysis is conducted for simply supported plate made of functionally graded carbon nanotube reinforced composite and compared against existing literature. Subsequently, a parametric forced vibration analysis considers the influence of various parameters: volume fractions of carbon nanotubes, their distributions, and ratios of instantaneous value to retardation time in the relaxation function, using a linear standard viscoelastic model. In the forced vibration analysis, the dynamic distributed load applied to functionally graded carbon nanotube reinforced composite viscoelastic plate is obtained in terms of double trigonometric series. The study culminates in an examination of maximum displacement, exploring the effects of different carbon nanotube distributions, volume fractions, and ratios of instantaneous value to retardation times in the relaxation function on the amplitudes of maximum displacements.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1923-1930
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• 2002

In this paper, we present modeling and simulation of microlens formation by means of a deep X-ray lithography followed by a thermal treatment of a PMMA (Polymethylmethacrylate) sheet. According to this modeling, X-ray irradiation causes the decrease of molecular weight of PMMA, which in turn decreases the glass transition temperature and consequently causes a net volume increase during the thermal cycle resulting in a swollen microlens. In this modeling, the free volume theory including the relaxation process during the cooling process was considered. The simulation results indicate that the modeling in this study is able to predict the fabricated microlens shapes and the variation pattern of the maximum heights of microlens which depends on the conditions of the thermal treatment. The prediction model could be applied to optimization of microlens fabrication process and to designing a micro mold insert for micromolding processes.