• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집A
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• pp.367-371
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• 2001

In the shape optimization based on the finite element method, the accuracy of finite element analysis of a given structure is important to determine the final shape. In case of a bending dominant problem, finite element solutions by the full integration scheme are not reliable because of the locking phenomenon. Furthermore, in the process of shape optimization, the mesh distortion is large due to the change of the structure outline: therefore, we cannot guarantee the accurate result unless the finite element itself is accurate. We approach to more accurate shape optimization to diminish these inaccuracies by improving the existing finite element. The shape optimization using the modified finite element is applied to a two-dimensional simple beam. Results show that the modified finite element have improved the optimization results.

• 대한기계학회논문집A
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• 제26권7호
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• pp.1408-1415
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• 2002

In this paper, we investigate the effect and the importance of the accuracy of finite element analysis in the shape optimization based on the finite element method and improve the existing finite element which has inaccuracy in some cases. And then, the shape optimization is performed by using the improved finite element. One of the main stream to improve finite element is the prevention of locking phenomenon. In case of bending dominant problems, finite element solutions cannot be reliable because of shear locking phenomenon. In the process of shape optimization, the mesh distortion is large due to the change of the structure outline. So, we have to raise the accuracy of finite element analysis for the large mesh distortion. We cannot guarantee the accurate result unless the finite element itself is accurate or the finite elements are remeshed. So, we approach to more accurate shape optimization to diminish these inaccuracies by improving the existing finite element. The shape optimization using the modified finite element is applied to a two and three dimensional simple beam. Results show that the modified finite element has improved the optimization results.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.216-221
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• 2008

Shape design optimization for linear elasticity problem is performed using isogeometric analysis method. In many design optimization problems for real engineering models, initial raw data usually comes from CAD modeler. Then designer should convert this CAD data into finite element mesh data because conventional design optimization tools are generally based on finite element analysis. During this conversion there is some numerical error due to a geometry approximation, which causes accuracy problems in not only response analysis but also design sensitivity analysis. As a remedy of this phenomenon, the isogeometric analysis method is one of the promising approaches of shape design optimization. The main idea of isogeometric analysis is that the basis functions used in analysis is exactly same as ones which represent the geometry, and this geometrically exact model can be used shape sensitivity analysis and design optimization as well. In shape design sensitivity point of view, precise shape sensitivity is very essential for gradient-based optimization. In conventional finite element based optimization, higher order information such as normal vector and curvature term is inaccurate or even missing due to the use of linear interpolation functions. On the other hands, B-spline basis functions have sufficient continuity and their derivatives are smooth enough. Therefore normal vector and curvature terms can be exactly evaluated, which eventually yields precise optimal shapes. In this article, isogeometric analysis method is utilized for the shape design optimization. By virtue of B-spline basis function, an exact geometry can be handled without finite element meshes. Moreover, initial CAD data are used throughout the optimization process, including response analysis, shape sensitivity analysis, design parameterization and shape optimization, without subsequent communication with CAD description.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.1328-1333
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• 2003

In the present study, an integrated framework of geometric modeling, analysis, and design optimization is proposed. Geometric modeling is based on B-spline surface representation. Geometrically-exact shell finite element is implemented in analysis module. Control points of the surface are selected as design variables for optimization, which can make the interaction easier between analysis and surface representation. Sequential linear programming(SLP) is adopted for the shape optimization of surfaces. For the computation of shape sensitivities, semi-analytical method is used. The developed integrated framework should serve as a powerful tool for the geometric modeling, analysis, and shape design of surfaces.

• 대한전기학회논문지:전기기기및에너지변환시스템부문B
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• 제52권7호
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• pp.307-314
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• 2003

This paper presents a 3D shape optimization algorithm for electromagnetic devices using the design sensitivity analysis with finite element method. The structural deformation analysis based on the deformation theory of the elastic body under stress is used for mesh renewing. The design sensitivity and adjoint variable formulae are derived for the 3D finite element method with edge element. The results of sensitivity analysis are used as the input data of the structural analysis to calculate the relocation of the nodal points. This method makes it possible that the new mesh of analysis region can be obtained from the initial mesh without regeneration. The proposed algorithm is applied to the shape optimization of 3D electromagnet pole to net a uniform flux density at the target region.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 하계학술대회 논문집 A
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• pp.241-243
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• 1998

This paper describes a new method for the faster shape optimization of the electromagnetic devices. In a conventional iterative method of shape design optimization using design sensitivity based on a finite element method, meshes for a new shape of the model are generated and a discretized system equation is solved using the meshes in each iteration. They cause much design time. To save this time, a polynomial approximation of the finite element solution with respect to the geometric design parameters using Taylor expansion is constructed. This approximate state variable expressed explicitly in terms of design parameters is employed in a gradient-based optimization method. The proposed method is applied to the shape design of quadrupole magnet.

• Structural Engineering and Mechanics
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• 제8권1호
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• pp.73-84
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• 1999

This paper is concerned with shape optimization problems by the boundary element method (BEM) emphasizing the use of a reduced basis reanalysis technique proposed recently by the author. Problems of this class are conventionally carried out iteratively through an optimizer; a sequential quadratic programming-based optimizer is used in this study. The iterative process produces a succession of intermediate designs. Repeated analyses for the systems associated with these intermediate designs using an exact approach such as the LU decomposition method are time consuming if the order of the systems is large. The newly developed reanalysis technique devised for boundary element systems is utilized to enhance the computational efficiency in the repeated system solvings. Presented numerical examples on optimal shape design problems in electric potential distribution and elasticity show that the new reanalysis technique is capable of speeding up the design process without sacrificing the accuracy of the optimal solutions.

• Steel and Composite Structures
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• 제33권5호
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• pp.747-753
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• 2019

Metaheuristic algorithm is used to solve the weight minimization problem of truss structures considering shape, and sizing design variables. The cross-sectional areas of the line element in trusses are the design variables for size optimization and the changeable joint coordinates are the shape optimization used in this study. The design of plane and spatial truss structures are optimized by metaheuristic technique named Teaching-Learning-Based Optimization (TLBO). Finite element analyses of structures and optimization process are carried out by the computer program visually developed by the authors coded in MATLAB. The four benchmark problems (trusses 2D ten-bar, 3D thirty-seven-bar, 3D seventy-two-bar and 2D two-hundred-bar) taken from literature are optimized and the optimal solution compared the results given by previous studies.

• 한국전산구조공학회논문집
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• 제21권3호
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• pp.233-238
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• 2008

본 논문에서는 등기하 해석법을 이용하여 선형 탄성문제에 대한 형상 최적설계 기법을 개발하였다. 실용적인 공학문제에 대한 많은 최적설계 문제에서는 초기의 데이터가 CAD 모델로부터 주어지는 경우가 많다. 그러나 대부분의 설계 최적화 도구들은 유한요소법에 기초하고 있기 때문에 설계자는 이에 앞서 CAD 데이터를 유한요소 데이터로 변환해야 한다. 이 변환과정에서 기하 모델의 근사화에 따른 수치적 오류가 발생하게 되고, 이는 응답 해석뿐만 아니라 설계민감도 해석에 있어서도 정확도 문제를 발생시킨다. 이러한 점에서 등기하 해석법은 형상 최적설계에 있어서 유망한 방법론 중 하나가 될 수 있다. 등기하 해석법의 핵심은 해석에 사용되는 기저 함수와 기하 모델을 구성하는 함수가 정확히 일치한다는 것이다. 이러한 기하학적으로 정확한 모델은 설계민감도 해석 및 형상 최적설계에 있어서도 사용된다. 이로 인해 높은 정확도의 설계민감도를 얻을 수 있으며, 이는 설계구배 기반의 최적화에 있어서 매우 중요하게 작용한다. 수치 예제를 통하여 본 논문에서 제시된 등기하 해석 기반의 형상 최적설계 방법론이 타당함을 확인하였다.

• 한국정보통신설비학회:학술대회논문집
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• 한국정보통신설비학회 2009년도 정보통신설비 학술대회
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• pp.45-48
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• 2009

In this paper, we use the optimization design theory based on the finite element method and implement the optimal design of electromagnetic devices using COMSOL interface. COMSOL is one of the commercial EM software. Shape information for the design optimization is extracted by CAD in EM software. To calculate the shape of optimal design, sensitive analysis is applied to the design processing in MATLAB. To achieve the design objective in this paper, objective function is defined. According to the sensitive analysis based on the finite element method, we change the design variable after the sensitivity of the objective function is computed. To verify the proposed method, the results are compared with the initial design.