• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.335-350
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• 2016

Based on the notion of $q_k$-derivative introduced by the authors in [17], we prove in this paper existence and uniqueness results for nonlinear second-order impulsive $q_k$-difference equations with anti-periodic boundary conditions. Two results are obtained by applying Banach's contraction mapping principle and Krasnoselskii's fixed point theorem. Some examples are presented to illustrate the results.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2003.10a
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• pp.243-249
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• 2003

The head-on collision of two solitary waves are examined using a boundary element method. Attachment, detachment times and alplitudes and maximum run-up times and amplitudes are computed. Consolidation times show local minimum value if two waves are of equal amplitudes are colliding. Attachment times show local maximum value if the amplitudes of two waves are the same. The detachment time show local maximum if two wves are the same. The detachment amplitude show local minimum values if the amplitude e(=a/h) is greater than 0.3.

• Journal of Energy Engineering
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• v.11 no.2
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• pp.99-105
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• 2002

A finite volume numerical approach is developed and used to simulate convection-dominated melting and solidification problems. The present approach is based on the enthalpy-porosity method that is traditionally used to track the motion of the liquid-solid front and to obtain the temperature and velocity profiles in the liquid-phase. The enthalpy-porosity model treats the solid-phase as the porosity in all computational cells that are located on the solid-liquid interfacial boundary. Concerning the computational cells that are fully located in the solid side of the interfacial boundary, the zero value of the porosity severely suppresses the velocity vector to practically a non-existent value that could be set equal to zero. A comparative analysis with the previous numerical approaches is performed to demonstrate the improved features of the presented model. Results of a melting and solidification experiments are also used to assess and evaluate the performance of the model.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1252-1253
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• 2011

The railway signaling system is being converted to the computer system from the existing mechanical device, and the dependency on software is being increased rapidly. Though the size and degree of complexity of software for railway signaling system are slower than the development speed of hardware, it is expected that the size will be grown bigger gradually and the degree of complexity will be increased also. Accordingly, the validation of reliability and safety of embedded software for train control system was started to become influential as the important issue. In this paper, we presented boundary value analysis tool for railway signaling system software, and presented its result of implementation.

• Journal of Mechanical Science and Technology
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• v.16 no.5
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• pp.655-665
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• 2002

Two-dimensional elastic analysis of doubly periodic circular holes in an infinite plane is given in this paper. Two cases of loading, remote tension and remote shear, are considered. A rectangular cell is cut from the infinite plane. In both cases, the boundary value problem can be reduced to a complex mixed one. It is found that the eigenfunction expansion variational method is efficient to solve the problem. Based on the deformation response under certain loading, the notched medium could be modeled by an orthotropic medium without holes. Elastic properties for the equivalent orthotropic medium are investigated, and the stress concentration along the hole contour is studied. Finally, numerical examples and results are given.

• Korean Institute of Interior Design Journal
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• v.19 no.1
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• pp.137-147
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• 2010

The purpose of this study is to research a method of creating a new type of boundary by repeated disposition of single unit of modularized membrane successively. In the contemporary architectural indoor space, more highly dimensional analysis of boundary is required and the necessity of establishing boundary of a new concept that may satisfy cultural value, social value and artistic value as a whole as well as aesthetic and functional merit has been increased. In order to create a membrane that may fulfil the requirements of the diversified programs of space like this, an approach of complicated mechanism and high-dimensional calculation are required. At this time, digital GA modelling, parametric modelling technique may expand its range of possibility. One thing to be noted at this juncture is that indefinite expandability involved in digital modelling technique, modelling by grid of absolute and relative coordinates and convenience of systematization may surpass limitation of analogue or simple numerical calculation being progressed in the past. And in order to create solid process including unit modelling or pattern formation, Precise calculation process of computer is necessitated inevitably.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.11 no.12
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• pp.1099-1107
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• 1998

In this study, the microstructure and electric conductivity of 5mol% $Gd_2O_3$-5mol% $Y_2O_3-ZrO_2$ system(5G5YZ) with a variation of sintering time at $1600^{\circ}C$ were investigated. By the result of TEM analysis of 5G5YZ sintered for 12h, a microcrack was observed near grain boundary. The change of the sintering time did not affect the lattice conductivity, but the grain boundary contribution was varied with the sintering time. The grain boundary conductivity of the sample sintered for 1h showed the highest value. Furthermore, the activation energy of the total conductivity was independent upon the sintering time and showed approximately 1.01eV. The highest conductivity measured at $1000^{\circ}C$ was 0.0197S/cm with the sample sintered for 1h. Comparing to 0h’s, the thickness ration of grain boundary as a function of sintering time were 0.88, 1.11 and 1.29 for 1h, 5h and 12h, respectively. In case of the sample sintered for 1h, the thickness of the grain boundary showed the lowest value. The increase of the sintering time over 1h made the decrease of the electric conductivity as well as the increase of the grain growth and the thickness of the grain boundary. As a result, it seemed that the proper sintering time for 5G5YZ composition was 1h.

• Advances in nano research
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• v.12 no.5
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• pp.467-482
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• 2022

In the current work, static and free torsional vibration of functionally graded (FG) nanorods are investigated using Fourier sine series. The boundary conditions are described by the two elastic torsional springs at the ends. The distribution of functionally graded material is considered using a power-law rule. The systems of equations of the mechanical response of nanorods subjected to deformable boundary conditions are achieved by using the modified couple stress theory (MCST) and taking the effects of torsional springs into account. The idea of the study is to construct an eigen value problem involving the torsional spring parameters with small scale parameter and functionally graded index. This article investigates the size dependent free torsional vibration based on the MCST of functionally graded nano/micro rods with deformable boundary conditions using a Fourier sine series solution for the first time. The eigen value problem is constructed using the Stokes' transform to deformable boundary conditions and also the convergence and accuracy of the present methodology are discussed in various numerical examples. The small size coefficient influence on the free torsional vibration characteristics is studied from the point of different parameters for both deformable and rigid boundary conditions. It shows that the torsional vibrational response of functionally graded nanorods are effected by geometry, small size effects, boundary conditions and material composition. Furthermore, for all deformable boundary conditions in the event of nano-sized FG nanorods, the incrementing of the small size parameters leads to increas the torsional frequencies.

• Journal of Mechanical Science and Technology
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• v.14 no.2
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• pp.197-206
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• 2000

A boundary integral equation method in the shape design sensitivity analysis is developed for the elasticity problems with axisymmetric non-homogeneous bodies. Functionals involving displacements and tractions at the zonal interface are considered. Sensitivity formula in terms of the interface shape variation is then derived by taking derivative of the boundary integral identity. Adjoint problem is defined such that displacement and traction discontinuity is imposed at the interface. Analytic example for a compound cylinder is taken to show the validity of the derived sensitivity formula. In the numerical implementation, solutions at the interface for the primal and adjoint system are used for the sensitivity. While the BEM is a natural tool for the solution, more generalization should be made since it should handle the jump conditions at the interface. Accuracy of the sensitivity is evaluated numerically by the same compound cylinder problem. The endosseous implant-bone interface problem is considered next as a practical application, in which the stress value is of great importance for successful osseointegration at the interface. As a preliminary step, a simple model with tapered cylinder is considered in this paper. Numerical accuracy is shown to be excellent which promises that the method can be used as an efficient and reliable tool in the optimization procedure for the implant design. Though only the axisymmetric problem is considered here, the method can be applied to general elasticity problems having interface.

• Journal of Korean Society of Steel Construction
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• v.8 no.3 s.28
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• pp.55-65
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• 1996

For stability analysis of stifened rectangular thin plates with various boundary conditions, Ritz method is presented. An energy method is especially useful in those cases where a rigorous solution of the diferential eqution is unknown or where we have a plate reinforced by stiffeners and it is required to find only an approximate value of the critical load. The strain energy due to the plate bending and the work done by the in-plane forces are taken into account in order to apply the principle of the minimum potential energy. The buckling mode shapes of flexural beams with various boundary conditions are derived, and shape functions consistent with the given boundary conditions in the two orthogonal directions are chosen from those displacement functions of beams. The matrix equations for stability of stiffened rectangular thin plates are determined from the stationary condition of the total potential energy. Numerical example for stability behaviors of horizontally and vertically stiffened plates subjected to uniform compression, bending and shear loadings are presented and the obtained results are compared with other researchers' results.