• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.3
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• pp.155-162
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• 2014

Using an isogeometric approach, a continuum-based shape design optimization method is developed for steady state power flow problems at high frequencies. In case the isogeometric method is employed to the shape design optimization, the NURBS basis functions used in CAD geometric modeling are directly utilized to embed the exact geometry into the computational framework so that the design parameterization for shape optimization is much easier than that in the finite element method and consequently provides the enhanced smoothness of design perturbations. Thus, exact geometric models can be used in both the response and the shape sensitivity analyses, where normal vector and curvature are continuous over the whole design space so that enhanced shape sensitivity can be expected. Through numerical examples, the developed isogeometric sensitivity is compared with finite difference one to provide excellent agreement. Also, it turns out that the proposed method works very well in the shape optimization problems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.6
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• pp.1852-1860
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• 1991

A shape design sensitivity of the elastic deformation due to a change of traction boundary condition is presented. The solution of governing equations for a linear elasticity problem is obtained by finite element method and the traction boundary is defined by design variables. The performance functional to be considered involves both the domain and boundary integral. Variations of geometry can be defined as design velocity. Using material derivative concept and adjoint equations, the design sensitivity is derived by Lagrange multiplier method. For a given geometry of a structure, the change of traction boundary is described by the tangential component of the design velocity only. The final result for the shape design sensitivity is formulated as the boundary integral form, the integrand is defined by tangential component of design velocity and first order derivatives of parameters. Numerical implementation of design sensitivity is discussed and is compared with the difference of the actual values.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.3
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• pp.275-281
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• 2010

In this paper, the design optimization of structures with stress constraints is performed using isogeometric shape optimization method. The stress constraints have an important role in design optimization problems since stress concentration could result in structural failure. To represent exact geometry in analysis, the isogeometric analysis method uses the same basis functions as used in the CAD geometry. The geometrically exact model can be used in both stress and design sensitivity analyses so that it can yield more precise optimal design than finite element one. Through numerical examples, the isogeometric approach turns out to be effective in shape optimization problems under stress constraints.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.3
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• pp.427-435
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• 1999

In the field of shape optimum design, much efforts are needed in regridding method and shape design sensitivity analysis. In this paper, Bezier curve is used to make the boundary of a structure and the improved direct differentiation method is used to calculate the shape design sensitivity. To regrid the finite element model, modified displacement field is presented in this paper. The modified displacement field makes more fine grid at large curvature. The purpose of this paper is to obtain the optimum shape of a cantilever with weight and a 3-dimensional journal bearing cap.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.2
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• pp.56.2-56.2
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• 2015

본 연구에서는 미국 맥도날드 천문대 (Mcdonald Observatory)에 있는 82인치 Otto Struve 망원경의 가이드 망원경으로 사용하기 위해 2개의 반사경을 이용해 구경이 100 mm이고 유효초점거리가 800 mm인 비축 반사망원경을 설계하였다. 비축 반사경은 일반적인 축 대칭인 반사경보다 가공이 매우 어렵기 때문에 형상 정밀도의 요구량을 알 수 있다면 비축 반사경을 가공하는 과정에서 시간과 비용을 절약할 수 있다. 광학계가 수차가 잘 보정된 회절한계의 성능이기 때문에 엔서클드 에너지 직경(Encircled Energy Diameter) 분석을 통해 민감도 분석을 하였다. 광학설계 소프트웨어인 CodeV를 사용하여 80 % 에너지가 $20{\mu}m$ 내에 들도록 공차한계로 설정하였으며, 기준 파장은 $587.56{\mu}m$이다. 또한 부경과 초점 면 사이의 거리를 보상자로 설정하여 공차가 광학계의 성능에 미치는 영향을 최소화하였다. 민감도 분석은 반사경의 위치, 회전, 그리고 반사경의 형상 정밀도에 대해 수행하였다. 분석 결과, 반사경의 위치와 각도는 일반적인 제작 및 조립 공차보다 매우 작은 것을 확인하였다. 그리고 형상정밀도는 주경이 부경보다 민감하였으며 자승 제곱 평균제곱근 (root-mean-square) 32 nm로 가장 민감한 결과가 나왔다.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.7
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• pp.18-27
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• 2006

The conventional reliability based design optimization(RBDO) methods require high computational cost compared with the deterministic design optimization(DO) methods, therefore it is hard to apply directly to large-scaled problems such as an aerodynamic shape design optimization. In this study, to overcome this computational limitation the efficient RBDO procedure with the two-point approximation(TPA) and adjoint sensitivity analysis is proposed, that the computational requirement is nearly the same as DO and the reliability accuracy is good compared with that of RBDO. Using this, the 3-D aerodynamic shape design optimization is performed very efficiently.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.5
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• pp.1458-1467
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• 1996

A direct differentiationmethod is presented for the shape design sensitivity analysis of axisymmeetric elastic solids. Based on the exisymmetric boundary integralequaiton formulation, a new boundary ntegral equatio for sensitivity analysis is derived by taking meterial derivative to the same integral identity that was used in the adjoint variable melthod. Numerical implementation is performed to show the applicaiton of the theoretical formulation. For a simple example with analytic solution, the sensitivities by present method are compared with analytic sensitivities. As an application to the shape optimization, an optimal shape of a gas turbine disc toinimize the weight under stress constraints is found by incorporating the sensitivity analysis algorithm in an optimizatio program.

• Proceedings of the KIEE Conference
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• 1999.07a
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• pp.43-45
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• 1999

지금까지 사용된 2차원 유한요소해석은 자계의 프린징(Fringing) 및 누설 자계 등을 무시하기 때문에 정확한 특성을 파악하기 위해서는 3차원 모델을 사용하여야 한다. BLDC 모터의 회전자(자석)의 높이를 고정시킨 상태에서 고정자(Core) 높이의 변화에 따른 코깅(Cogging) 토크의 해석을 통해 높이 비에 대한 2차원과 3차원 유한요소해석 결과 사이에의 상관 오차에 대한 연구를 수행하였다 또한. 정자기의 3차원 형상 설계 민감도 해석 기법을 개발하였다. 개발된 정자기 민감도 프로그램(MAGSEN-magnetic sensitivity)은 유용성과 실용성을 보이기 위하여 BLDC 모터의 코깅토크를 줄이는 형상 최적설계에 적용되었다.

• Journal of the KSME
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• v.31 no.1
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• pp.34-42
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• 1991

복잡한 형상의 서지 탱크를 CAEDS의 GEOMOD를 이용하여 내부의 리보까지 포함한 용기를 모델링하였으며, 설계 부피를 검사하고 GEOMOD와 GFEM 사이의 직접 데이터 교환을 통하여 구조 해석에 필요한 유한요소를 만들었다. 유한요소법에 최적화 이론을 적용하여 서지탱크의 두께 변화에 따른 응력의 설계 민감도를 구하였으며, 민감도를 근거로 보강 위치 및 국부적인 용기의 두께를 결정하였다. 유한요소법 프로그램(IFES, GFEM)과 솔리드 모델러(GEOMOD), 그리고 최적화 기법(IFES-Optimization)을 모두 통합하여, 최적 설계를 수행함으로써 반복되는 실험에 의한 시간과 경비를 줄임과 동시에 신뢰성 있는 설계방법 및 방향을 제시하였다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.497-504
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• 2012

Finite element analysis is to approximate a geometry model developed in computer-aided design(CAD) to a finite element model, thus the conventional shape design sensitivity analysis and optimization using the finite element method have some difficulties in the parameterization of geometry. However, isogeometric analysis is to build a geometry model and directly use the functions describing the geometry in analysis. Therefore, the geometric properties can be embedded in the NURBS basis functions and control points so that it has potential capability to overcome the aforementioned difficulties. In this study, the isogeometric structural analysis and shape design sensitivity analysis in the generalized curvilinear coordinate(GCC) systems are discussed for the curved geometry. Representing the higher order geometric information, such as normal, tangent and curvature, yields the isogeometric approach to be the best way for generating exact GCC systems from a given CAD geometry. The developed GCC isogeometric structural analysis and shape design sensitivity analysis are verified to show better accuracy and faster convergency by comparing with the results obtained from the conventional isogeometric method.