• Journal of the Korean Society for Precision Engineering
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• v.21 no.12
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• pp.133-139
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• 2004

In general, the contact pressure to the die cannot be easily determined by using upper bound solution. Recently, the authors have proposed the method determining the contact pressure with the upper bound solution for the forming with the plane stain plastic deformation. In this paper, the method is applied to an axisymmetric forward extrusion process. The contact pressure to the die of the axisymmetric extrusion has been determined with the upper bound solution and compared with the result of rigid plastic FEM. The optimal semi-angles of die have been obtained minimizing the relative contact pressure to die fur the extrusion ratio.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1996.03b
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• pp.40-47
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• 1996

An upper bound solution of tube drawing process using a fixed tapered plug has been obtained , which reduces to an solution for tube sinking by setting friction factor between tube and plug at zero. Effects of various process paraments have been discussed based on the solution.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1123-1139
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• 2014

In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with order 1 < ${\alpha}$ < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.288-294
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• 2008

Motivated by the fact that upper solution bounds for the continuous Lyapunov equation are valid under some very restrictive conditions, an attempt is made to extend the set of Hurwitz matrices for which such bounds are applicable. It is shown that the matrix set for which solution bounds are available is only a subset of another stable matrices set. This helps to loosen the validity restriction. The new bounds are illustrated by examples.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.598-603
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• 2001

For metal forming analysis, upper-bound solution is practical method because the solution is overestimated. It is limited to determine stresses on tools by using upper-bound solution. In this study, new scheme to calculate stresses on tools based on upper bound solution is proposed. To verify the proposed scheme, plane strain drawing has been considered. The stresses on tools obtained by the proposed scheme are compared with results of rigid plastic FEM. And the stresses on tools have been determined by the proposed scheme in the forging within plane strain deformation.

• Transactions of Materials Processing
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• v.12 no.1
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• pp.11-17
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• 2003

For metal forming analysis, upper-bound solution is a practical method because the solution is overestimated. However it is not easy to determine the stresses on dies by using upper-bound solution. In this study, new scheme to calculate the stresses on dies based on upper bound solution is proposed. In the velocity fields, imaginary velocity is adapted to analyze the normal pressure on die surfaces. To verify the proposed scheme. plane strain drawing has been considered. The stresses on dies obtained by the proposed scheme are compared with the results of rigid plastic FEM and the experimental results. In the experiments, pressure film is used to measure the normal pressure on dies.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.751-758
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• 1995

We prove the existence of solution for a Dirichlet singular boundary value problem. The proofs are based on the method of upper and lower solutions.

• 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 Korean Society of Industrial and Systems Engineering
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• v.19 no.39
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• pp.9-18
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• 1996

Many algorithms have been developed for optimizing the asymmectric traveling salesman problem known as a representative NP-Complete problem. The most efficient ones of them are branch and bound algorithms based on the subtour elimination approach. To increase efficiency of the branch and bound algorithm. number of decision nodes should be decreased. For this the minimum bound that is more close at the optimal solution should be found or an effective bounding strategy should be used. If the optimal solution has been known, we may apply it usefully to branching. Because a good feasible solution should be found as soon as possible and have similar features of the optimal solution. By the way, the upper bound solution in branch and bound algorithm is most close at the optimal solution. Therefore, the upper bound solution can be used instead of the optimal solution and information of which can be applied to new branching criteria. As mentioned above, this paper will propose an effective branching rule using the information of the upper bound solution in the branch and bound algorithm. And superiority of the new branching rule will be shown by comparing with Bellmore-Malone's one and carpaneto-Toth's one that were already proposed.

• Proceedings of the Korean Geotechical Society Conference
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• 1999.10a
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• pp.193-200
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• 1999

Since Broms and Bennermark(1967) suggested the face stability criterion based on laboratory extrusion tests and field observations, the face stability of a tunnel driven in cohesive material has been studied by several authors. And recently, more general solution for the tunnel front is given by Leca and Panet(1988). They adopted a limit state design concept to evaluate the face stability of a shallow tunnel driven into cohesionless material and showed that the calculated upper bound solution represented the actual behavior reasonably well. In this study, two factors are simultaneously considered for assessing tunnel face stability: One is the effective stress acting on the tunnel front calculated by upper bound solution; and the other is the seepage force calculated by numerical analysis under the condition of steady state ground water flow. The model tests were performed to evaluate the seepage force acting on the tunnel front and these results were compared with results of numerical analysis. Consequently, the methodology to evaluate the stability of a tunnel face including limit analysis and seepage analysis is suggested under the condition of steady state ground water flow.