• Proceedings of the KIEE Conference
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• 2001.07b
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• pp.768-770
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• 2001

The topology optimizations of electromagnetic systems with the nonlinear and the eddy current effects are studied using the finite element method. The topology design sensitivity formulations of nonlinear magnetostatics and eddy current systems are derived using the adjoint variable method. A computer program is developed using object orient programming and applied to the topology optimization of a C-core actuator. A numerical study shows the effects of saturation and eddy current by comparing results of topology optimizations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.182-189
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• 1996

The focus of this study is on the problem of the design of structure of undetermined topology. This problem has been regarded as being the most challenging of structural optimization problems, because of the difficulty of allowing topology to change. Conventional approaches break down when element sizes approach to zero, due to stiffness matrix singularity. In this study, a novel nonlinear Programming formulation of the topology Problem is developed and examined. Its main feature is the ability to account for topology variation through zero element sizes. Stiffness matrix singularity is avoided by embedding the equilibrium equations as equality constraints in the optimization problem. Although the formulation is general, two dimensional plane elasticity examples are presented. The design problem is to find minimum weight of a plane structure of fixed geometry but variable topology, subject to constraints on stress and displacement. Variables are thicknesses of finite elements, and are permitted to assume zero sizes. The examples demonstrate that the formulation is effective for finding at least a locally minimal weight.

• Wind and Structures
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• v.18 no.1
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• pp.21-35
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• 2014

The latest developments in topology optimization are integrated with Computational Fluid Dynamics (CFD) for the conceptual design of building structures. The wind load on a building is simulated using CFD, and the structural response of the building is obtained from finite element analysis under the wind load obtained. Multiple wind directions are simulated within a single fluid domain by simply expanding the simulation domain. The bi-directional evolutionary structural optimization (BESO) algorithm with a scheme of material interpolation is extended for an automatic building topology optimization considering multiple wind loading cases. The proposed approach is demonstrated by a series of examples of optimum topology design of perimeter bracing systems of high-rise building structures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.4
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• pp.370-377
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• 2004

The density approach and the homogenization design method are representative methods in topology optimization problems. In the topology optimization in magnetic fields, those methods are applied based on the results of the applications In elastic fields. In this study, the density method is modified considering the concept of the homogenization design method. Also, the results of the topology optimization in magnetic fields by the modified density method as well as the homogenization method are compared especially focusing the change of the penalization parameter in the density approach. The effect of the definition of the design domain such as global/local design domain is also discussed.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.7
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• pp.66-77
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• 1996

Optimal topology design is to search the optimal configuration of a structure which can be used as a shape at the conceptual design stage. Our objective is to maximize the stiffness of the structures and ribs under a material usage constraintl. The density of each finite element is the design variable and its relationship with Young's modulus is expressed by quadratic form. The configuration is represented by the entire density distribution, the structural analysis is performed by finite element method and the optimiza- tion is performed by Feasible Direction Method. Feasible Direction Method can handle various problems simultaneously, that is, mult-objectives and multi-constraints. Total computation time can be reduced by the quadratic relationship between the density and the material property and fewer design variables than Homogenization Method. Toplogy optimization technique developed in this research is applied to design the shapes of the ribs.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.19-28
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• 2007

Discrete topology optimization processes of structures start from an initial design domain which is described by the topology of constant material densities. During optimization procedures, the structural topology changes in order to satisfy optimization problems in the fixed design domain, and finally, the optimization produces material density distributions with optimal topology. An introduction of initial holes in a design domain presented by Eschenauer et at. has been utilized in order to improve the optimization convergence of boundary-based shape optimization methods by generating finite changes of design variables. This means that an optimal topology depends on an initial topology with respect to topology optimization problems. In this study, it is investigated that various optimal topologies can be yielded under constraints of usable material, when partial solid phases are deposited in an initial design domain and thus initial topology is finitely changed. As a numerical application, structural topology optimization of a simple MBB-Beam is carried out, applying partial circular solid phases with varying sizes to an initial design domain.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.495-502
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• 2008

We show that free products of finitely generated and residually p-finite nilpotent groups, amalgamating p-closed central subgroups are residually p-finite. As a consequence, we are able to show that generalized free products of residually p-finite abelian groups are residually p-finite if the amalgamated subgroup is closed in the pro-p topology on each of the factors.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.3
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• pp.279-283
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• 2014

Recently, a topology algorithm based on the artificial bee colony algorithm (ABCA) has been proposed for static and dynamic topology optimization. From the results, the convergence rate of the algorithm was determined to be slightly slow. Therefore, we propose a new search method to improve the convergence rate of the algorithm using a chaotic map. We investigate the effect of the chaotic map on the convergence rate of the algorithm in static and dynamic topology optimization. The chaotic map has been applied to three cases, namely, employ bee search, onlooker bee search, and both employ bee as well as onlooker bee search steps. It is verified that the case in which the logistic function of the chaotic map is applied to both employ bee as well as onlooker bee search steps shows the best dynamic topology optimization, improved by 5.89% compared to ABCA. Therefore, it is expected that the proposed algorithm can effectively be applied to dynamic topology optimization to improve the convergence rate.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.327-334
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• 2005

In this paper, using an adjoint variable method, we develop a design sensitivity analysis (DSA) method applicable to 3-Dimensional heat conduction problems in steady state. Also, a topology design optimization method is developed using the developed DSA method. Design sensitivity expressions with respect to the thermal conductivity are derived. Since the already factorized system matrix is utilized to obtain the adjoint solution, the cost for the sensitivity computation is trivial. For the topology design optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of structures and allowable material volume, respectively, Through several numerical examples, the developed DSA method is verified to yield efficiency and accurate sensitivity results compared with finite difference ones. Also, the topology optimization yields physical meaningful results.

• Journal of Mechanical Science and Technology
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• v.14 no.3
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• pp.306-313
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• 2000

The homogenization method and the density function method are common approaches to evaluate the equivalent material properties for design cells composed of matter and void. In this research, using a new topology optimization method based on the homogenized material with a penalty factor and the chessboard prevention strategy, we obtain the optimal layout of a structure for the natural frequency of a designated mode. The volume fraction of nodes of each finite element is chosen as the design variable and a total material usage constraint is imposed. In this paper, the subspace method is used to evaluate the eigenvalue and its corresponding eigenvector of the structure for the designated mode and the recursive quadratic programming algorithm, PLBA algorithm, is used to solve the topology optimization problem.