• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.9-16
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• 2014

Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. 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. The "Hamilton-Jacobi(H-J)" equation and computationally robust numerical technique of "up-wind scheme" lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H-J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes are not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.37 no.2
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• pp.11-20
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• 2000

Topological relationships play an important role in query optimization in spatial databases. If topological relationships are known a priori, then expensive query processing can be avoided. In this paper we address the problems of： ⅰ) identifying topological relationships among spatial objects, ⅱ) checking consistency of specified topological relationships, and ⅲ) exhaustively deriving new topological relationships from the ones specified. These activities lead to an efficient query processing when queries associated with topological relationships are invoked. Specifically, eight types of topological relationships (｛equal, disjoint, overlap, meets, contains, contained-in, properly-contains, and properly-contained-in｝) are considered. We present an algorithm to check the consistency of specified topological relationships and to derive all possible relationships from the given set of known relationships.

• Proceedings of the KIEE Conference
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• 2008.10c
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• pp.23-25
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• 2008

This paper presents a topological shape optimization for electromagnetic system using a Level Set method. The optimization is progressed by updating the implicit Level Set function from the Hamilton-Jacobi equation. The up-wind scheme is used for numerical implementation of the Hamilton-Jacobi equation. In order to validate the proposed optimization, the core part of a C-core actuator is optimized by three cases using different materials; (single steel), (two steels), and (steel and magnet).

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.8
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• pp.1-7
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• 2005

This paper proposes a local improvement method that combines extended topological clean up and optimization-based smoothing for homogenizing triangular grid system. First extended topological clean up procedures are applied to improve the connectivities of grid elements. Then, local optimization-based smoothing is performed for maximizing the distortion metric that measures grid quality. Using the local improvement strategy, we implement the grid homogenizations for two triangular grid examples. It is shown that the suggested algorithm improves the quality of the triangular grids to a great degree in an efficient manner and also can be easily applied to the remeshing algorithm in adaptive mesh refinement technique.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.77-81
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• 2003

SDM (Structural Dynamics Modification) is a tool to improve dynamic characteristics of a structure, more specifically of a base structure, by adding or deleting auxiliary (modifying) structures. In this paper, the goal of the optimal SDM is set to maximize the natural frequency of a base plate structure by attaching serially-connected beam stiffeners. The design variables are chosen as positions of the attaching beam stiffeners, where the number of stiffeners is considered as a design space. The problem of non-matching interface nodes between the base plate and beam stiffeners is solved by using localized Lagrange multipliers, which act to glue the two structures with non-matching interface nodes. As fer the cases of non-matching interface nodes problem, the governing equation of motion of a structure can be considered from the viewpoint of a topological modification, which involves the change of the number of structural members and DOFs. Consequently, the eigenpairs of the beam-stiffened plate structure are obtained by using an eigen reanalysis technique of topological modifications. Evolution Strategies (ES), which is a probabilistic population-based optimization technique that mimics the principles from biological evolution in nature, is utilized as a mean for the optimization.

• East Asian mathematical journal
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• v.33 no.1
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.408-409
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• 2008

This paper presents a new development for topology optimization of heat-dissipating structure with forced convection. To cool down electric devices or machines, two types of convection models have been widely used: Natural convection model with a large Archimedes number and Forced convection with a small Archimedes number. Nowadays, many engineering application areas such as electrochemical conversion device or fuel cell devices adopt the forced convection to transfer generated heat. Therefore, to our knowledge, it becomes an important issue to design flow channels inside which generated heat transfer. Thus, this paper studies optimal topological designs considering fluid-heat interaction. To consider the effect of the advection in the heat transfer problem, the incompressible Navier-stokes equation is solved. This paper numerically studies the coupling phenomena and presents optimal channel design considering forced convection.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.30 no.1
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• pp.82-88
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• 2007

This paper considers a topological optimization of a computer network design with a cost constraint. The objective is to find the topological layout of links, at maximal reliability, under the constraint that the network cost is less or equal than a given level of budget. This problem is known to be NP-hard. To efficiently solve the problem, a genetic approach is proposed. Two illustrative examples are used to explain and test the proposed approach. Experimental results show evidence that the proposed approach performs more efficiently for finding a good solution or near optimal solution in comparison with a simulated annealing method.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1310-1315
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• 2003

In many practical engineering design problems, there are some design and manufacturing considerations that are difficult or infeasible to express in terms of an objective function or a constraint. In this situation, a set of optimal candidate designs having different topological complexities, not just a single optimal design, is preferred. To generate systematically such design candidates, we propose a hierarchical multiscale design resolution control scheme. In order to adjust its topological complexity by choosing a different starting resolution level in the hierarchical design space, we propose to employ a general M-band wavelet transform in transforming the original design space into the multiscale design space.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.643-645
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• 2008

To obtain weight reduction and high performance, level set based topology optimization in magnetic fields is promising for the design of magnetic devices where the precise boundary shape and topological chanages are required. Level set function is introduced to represent ferromagnetic material boundaries and material properties of the magnetic reluctivity are determined. The optimization problem is formulated for maximizing the actuating force in a prescribed direction under limited usage of ferromagnetic material.