• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1169-1181
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• 2006

We introduce a new biharmonic kernel for the upper half plane, and then study the properties of its relevant potentials, such as the convergence in the mean and the boundary behavior. Among other things, we shall see that Fatou's theorem is valid for these potentials, so that the biharmonic Poisson kernel resembles the usual Poisson kernel for the upper half plane.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1361-1370
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• 2009

In this paper, we consider singular fourth-order two point boundary value problems $u^{(4)}$ (t) = f(t, u), 0 < t < 1, u(0) = u(l) = u'(0) = u'(l) = 0, where $f:(0,1){\times}(0,+{\infty}){\rightarrow}[0,+{\infty})$ may be singular at t = 0, 1 and u = 0. By using the upper and lower solution method, we obtained the existence of positive solutions to the above boundary value problems. An example is also given to illustrate the obtained theorems.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.439-460
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• 2002

We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.355-367
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• 1999

We prove the existence of 2N-1 distinct ordered positive solutions of a class of semilinear elliptic Dirichlet boundary value problems on Rn when the forcing term has N distinct positive stable zeros and the coefficient function decaying to the zero at infinity.

• Journal of Ocean Engineering and Technology
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• v.13 no.2 s.32
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• pp.11-17
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• 1999

The objective of this paper is to introduce very fast but still stable solution using finite element procedures, and it has been used in an iterative mode for product design applications. A lot of numerical techniques have been developed to deal with the material, geometric and boundary condition non-linearities occurred in the stamping process. One of them, the One-Step FEM is very efficient and useful tool for a design and trouble-shooting in various stamping processes. In this method, the mathod, the material is assumed to deform directly from the initial flat blank to the final configuration without any intermediate steps. The formulation is based on the deformation theory of plasticity and the upper bound theorem. As a result of the calculations, the initial blank shape is obtained, together with the material flow, strains and thickness distribution in the part.

• Proceedings of the Korean Geotechical Society Conference
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• 2008.03a
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• pp.1144-1154
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• 2008

In this paper, the behaviour of shell foundation was studied. In order to perform this study, three studies such as theoretical, numerical and experimental programs were performed. In the theoretical program, the general shallow foundation theories and failure mechanism developed by Terzaghi, Mayerhof and others were reviewed and compared. Based on the previous shallow foundation behaviour, the shell foundation theory was developed using the upper boundary theorem. In the numerical study, the 2 and 3 dimensional FEM simulations were carried out using an uncoupled-analysis approach. From the analysis results, the adequate depth of shell foundation was evaluated. It was also evaluated the bearing capacity according to the shell angle ($120^{\circ}$, $90^{\circ}$, $60^{\circ}$). In the experimental study, the laboratory model tests were carried out for five cases of different foundation shapes including the rectangular and circular foundation in order to verify the theoretical and nemerical study. According to the results of this study, the bearing capacity of shell foundation was theoretically about 15% larger than that of general foundation. However, in the model test, the bearing capacity of shell foundation was about 25 to 30% larger than that of general foundation. In the case of shell angle, the maximum bearing capacity of shell foundation shows when the shell angle of foundation was $60^{\circ}$. In addition, Even if the shell foundation has the various advantages compared with the general foundations as described above, the practical verifications in full scale size will be necessary to use in the field and will be helpful in the technical development of other special foundations.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.7
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• pp.1314-1321
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• 1992

In analyzing the plastic flow of axisymmetric tube extrusion a new method of formulation using the stream function approach and upper-bound theorem is proposed which permits the prediction of plastically deformed zone in analytic expression as well as metal flow. It is shown that the formulation proposed in this work covers the solid extrusion and tube extrusion in axisymmetric case. The effect of some process parameters such as area reduction, the ratio of radii(inner radius to outer radius) and friction factor on extrusion pressure, deformation zone and plastic flow through stream-lined dies has been studied. The presented theoretical analysis can be effectively used for the prediction of deformation zone and plastic flow.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.549-558
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• 2012

A topology optimization method for phononic crystals is developed for the design of sound barriers, using the level set approach. Given a frequency and an incident wave to the phononic crystals, an optimal shape of periodic inclusions is found by minimizing the norm of transmittance. In a sound field including scattering bodies, an acoustic wave can be refracted on the obstacle boundaries, which enables to control acoustic performance by taking the shape of inclusions as the design variables. In this research, we consider a layered structure which is composed of inclusions arranged periodically in horizontal direction while finite inclusions are distributed in vertical direction. Due to the periodicity of inclusions, a unit cell can be considered to analyze the wave propagation together with proper boundary conditions which are imposed on the left and right edges of the unit cell using the Bloch theorem. The boundary conditions for the lower and the upper boundaries of unit cell are described by impedance matrices, which represent the transmission of waves between the layered structure and the semi-infinite external media. A level set method is employed to describe the topology and the shape of inclusions. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. Through several numerical examples, the applicability of the proposed method is demonstrated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.33-40
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• 1998

Although a structural analysis based on e linear elastic theory yields good results for deformations and stresses produced by working loads, it fails to assess the teal load-carrying of the plates on the verge of yielding. In case of a limit analysis of plates, the yield line theory is widely used on the basis of the upper bound theorem and theoretically it overestimates the strength of the plate. There is, therefore, a general need for analytical methods of predicting the inelastic behavior and load-carrying capacities of plate subjected to arbitrary loadings and boundary conditions. The $\rho$-version of finite element method has been presented for determining the accurate limit load of plates. The numerical results by $\rho$-version model compares with the results obtained by the h-version software ADINA as well as with the available analytical solutions in literatures.

• Journal of the Korean Geotechnical Society
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• v.24 no.7
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• pp.51-60
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• 2008

In this paper, the behaviour of shell foundation was studied. In the theoretical program, the general shallow foundation theories and failure mechanism developed by Terzaghi, Mayerhof and others were reviewed and compared. In the numerical study, the 2 and 3 dimensional FEM simulations were carried out using an uncoupled-analysis approach. The results obtained from the model test show that the bearing capacity of shell foundation was about 25% to 30% larger than that of general foundation. Due to the cases of shell angle, the maximum bearing capacity of shell foundation shows when the shell angle of foundation was $60^{\circ}$. In addition, even if the shell foundation has various advantages compared with the general foundations as described above, the practical verifications in full scale size will be necessary to use in the field and will be helpful in the technical development of other special foundations.