• Honam Mathematical Journal
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• v.33 no.2
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• pp.279-300
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• 2011

For a subset system M on any poset, M-Scott notions, such as M-way below relation,M-continuity,M-Scott convergence (of nets and filters respectively) and M-Scott topology are proposed Any approximating auxiliary relation on a poset can be represented by an M-way below relation such that this poset is M-continuous. It is shown that a poset is M-continuous iff the M-Scott topology is completely distributive. The topology induced by the M-Scott convergence coincides with the M-Scott topology. If the M-way below relation satisfies the property of interpolation then a poset is M-continuous if and only if the M-Scott convergence coincides with the M-Scott topological convergence. Also, M-continuity is characterized by a certain Galois connection.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.4
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• pp.50-56
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• 2003

Most engineering products contain more than one component. Failure occurs either at the connection itself or in the component at the point of attachment of the connection in many engineering structures. The allocation and design of connections such as bolts, spot-welds, adhesive etc. usually play an important role in the structure of multi-components. Topology optimization of connection component provides more practical solution in design of multi-component connection system. In this study, a topology optimization based on density distribution approach has been applied to optimal location of fasteners such as T-shape, L-shape and multi-component connection system. From the results, it was verified that the number of iteration was reduced, and the optimal topology was obtained very similarly comparing with ESO method. Therefore, it can be concluded that the density distribution method is very suitable for topology optimization of multi-component structures.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.16 no.1
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• pp.69-74
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• 2007

Topology optimization of the inner reinforcement for a vehicle's hood has been performed by evolutionary structural optimization(ESO) using a smoothing scheme. The purpose of this study is to obtain optimal topology of the inner reinforcement for a vehicle's hood considering the static stiffness of bending and torsion simultaneously. To do this, the multiobjective optimization technique was implemented. Optimal topologies were obtained by the ESO method. From several combinations of weighting factors, a Pareto-optimal solution was obtained. Also, a smoothing scheme was implemented to suppress the checkerboard pattern in the procedure of topology optimization. It is concluded that ESO method with a smoothing scheme is effectively applied to topology optimization of the inner reinforcement of a vehicle's hood considering the static stiffness of bending and torsion.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2003.04a
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• pp.15-20
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• 2003

Most engineering products contain more than one component. Failure occurs either at the connection itself or in the component at the point of attachment of the connection in many engineering structures. The allocation and design of connections such as bolts, spot-welds, adhesive etc. usually play an important role in the structure of multi-components. Topology optimization of connection component provides more practical solution in design of multi-component connection system. In this study, a topology optimization based on density distribution approach has been applied to optimal location of fasteners such as T-shape, L-shape and multi-component connection system. From the results, it was verified that the number of iteration was reduced, and the optimal topology was obtained very similarly comparing with ESO method. Therefore, it can be concluded that the density distribution method is very suitable for topology optimization of multi-component structures.

• Computational Structural Engineering : An International Journal
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• v.1 no.1
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• pp.21-29
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• 2001

The general topology optimization can be considered as optimal material distribution. Such an approach can be unstable, unless composite materials are introduced. In this research, a nodal volume fraction method is used to obtain the optimum topology of continuum structures. This method is conducted from a composite material model composed of isotropic matter and spherical void. Because the appearance of the chessboard patterns makes the interpretation of the optimal material layout very difficult, this method contains a chessboard prevention strategy. In this research, several topology optimization problems are presented to demonstrate the validity of the present method and the recursive quadratic programming algorithm is used to solve the topology optimization problems.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.11
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• pp.1925-1932
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• 2003

Topology optimization is widely accepted as a conceptual design tool for the product design. Since the resulted layout of the topology optimization is a kind of digital images represented by the density distribution, the seamless process is required to transform digital images to the CAD model for the practical use. In this paper, the general process to construct a CAD model is developed to apply for topology images based on elements. The node density and the morphology technique are adopted to extract boundary contour of the shape and remove the noise of images through erosion and dilation operation. The proposed method automatically generates point data sets of the geometric model. The process is integrated with Pro/Engineer, so that the engineer in practice can directly handle with curves or surfaces form digital images.

• Proceedings of the Korea Contents Association Conference
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• 2005.11a
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• pp.601-607
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• 2005

In this paper, we aggregate multi-links information between boundary nodes using the line segment scheme that aggregates topology information within PG referring bandwidth and delay parameter. To do this, we propose a modified line segment algorithm using two line segment method that represents two points which consist of delay-bandwidth pair to reduce topology information and provide a flexibility to the multiple-links aggregation. And we apply it to current star topology aggregation. Through the simulation result analysis, the proposed star topology aggregation scheme presents the better performance than existing scheme.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.915-932
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• 2010

The goal of this paper is to study extension problems of several continuities in computer topology. To be specific, for a set $X\;{\subset}\;Z^n$ take a subspace (X, $T_n^X$) induced from the Khalimsky nD space ($Z^n$, $T^n$). Considering (X, $T_n^X$) with one of the k-adjacency relations of $Z^n$, we call it a computer topological space (or a space if not confused) denoted by $X_{n,k}$. In addition, we introduce several kinds of k-retracts of $X_{n,k}$, investigate their properties related to several continuities and homeomorphisms in computer topology and study extension problems of these continuities in relation with these k-retracts.

• Journal of Biomedical Engineering Research
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• v.26 no.6
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• pp.365-372
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• 2005

Topology optimization method has a great advantage and capability over a conventional shape optimization technique because it optimizes a topology as well as a shape and size of structure. The purpose of the present study, using topology optimization method with an objective function of minimum compliance as a mechanism of bone remodeling, is to examine which shape factors of femur is strongly related with the curvature of femoral shaft. As is expected, the optimized curvature increased definitely with neck angle among the shape factors and showed a similar trend with the measured curvature to neck angle. Therefore, the topology optimization method can be successfully applied in the analysis of bone remodeling phenomenon in the subsequent studies.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.183-190
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• 2001

Topology optimization. has been evolved into a very efficient conceptual design tool and has been utilized into design engineering processes in many industrial parts. In recent years, topology optimization has become the focus of structural optimization design and has been researched and widely applied both in academy and industry. Traditional topology optimization has been using homogenization method and optimality criteria method. Homogenization method provides relationship equation between structure which includes many holes and stiffness matrix in FEM. Optimality criteria method is used to update design variables while maintaining that volume fraction is uniform. Traditional topology optimization has advantage of good convergence but has disadvantage of too much convergency time and additive checkerboard prevention algorithm is needed. In one way to solve this problem, element remove method is presented. Then, it is applied to many examples. From the results, it is verified that the time of convergence is very improved and optimal designed results is obtained very similar to the results of traditional topology using 8 nodes per element.