• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 하계학술대회 논문집 B
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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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1996년도 봄 학술발표회 논문집
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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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• 제18권1호
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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.

• 대한기계학회논문집A
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• 제28권4호
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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.

• 한국정밀공학회지
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• 제13권7호
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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.

• 한국전산구조공학회논문집
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• 제20권1호
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• pp.19-28
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• 2007

이산화 된 구조물의 위상최적화 과정은 균일하게 분포된 재료 밀도의 위상으로 표현되는 초기 설계영역을 시발점으로 한다. 최적화 과정 동안 구조물의 위상은 고정된 설계영역 내에 주어진 최적화 문제를 만족시키는 방향으로 변화하면서, 최종적으로 최적 위상의 재료 밀도 분포를 생산한다. Eschenauer et al.에 의해 제안되었던 설계영역 안에 구멍을 도입하는 개념은 원래 경계면의 최적화 문제에 대해 설계변수의 유한적인 변화를 촉진시켜 최적화의 수렴성 개선을 도모하기 위함이었으나, 위상최적화의 관점에서는 초기 위상의 정의에 따라 다양한 최적 위상이 생산되는 것을 의미한다. 본 연구에서는 초기 설계영역 안에 국소적인 솔리드 상을 도입해 초기 위상에 변화를 주었을 때, 한정된 재료 하에 구조물에 배치 가능한 다양한 최적 위상을 산출할 수 있음을 검증하였다. 수치 예제로서 초기 설계영역 내에 다양한 치수를 가지는 국부적인 원형 솔리드의 고정된 개수를 투입하여 간단한 MBB-보의 위상최적 설계를 수행하였다.

• Kyungpook Mathematical Journal
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• 제48권3호
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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.

• 한국생산제조학회지
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• 제23권3호
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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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2005년도 춘계 학술발표회 논문집
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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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• 제14권3호
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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.