• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 가을 학술발표회논문집
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• pp.238-245
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• 2000

A general formulation for shape design sensitivity analysis over a plane arch structure is developed based on a variational formulation of curved beam in linear elasticity. Sensitivity formula is derived using the material derivative concept and adjoint variable method for the stress defined at a local segment. Obtained sensitivity expression, which can be computed by simple algebraic manipulation of the solution variables, is well suited for numerical implementation since it does not involve numerical differentiation. Due to the complete description for the shape and its variation of the arch, the formulation can manage more complex design problems with ease and gives better optimum design than before. Several examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. Shape optimization is also conducted with two design problems to illustrate the excellent applicability.

• Journal of Mechanical Science and Technology
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• 제16권8호
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• pp.1102-1108
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• 2002

In this study, a topological design sensitivity of the ai. bearing surface (ABS) is suggested by using an adjoint variable method. The discrete form of the generalized lubrication equation based on a control volume formulation is used as a compatible condition. A residual function of the slider is considered as an equality constraint function, which represents the slider in equilibrium. The slider thickness parameters at all grid cells are chosen as design variables since they are the topological parameters determining the ABS shape. Then, a complicated adjoint variable equation is formulated to directly handle the highly nonlinear and asymmetric coefficient matrix and vector in the discrete system equation of air-lubricated slider bearings. An alternating direction implicit (ADI) scheme is utilized for the numerical calculation. This is an efficient iterative solver to solve large-scale problem in special band storage. Then, a computer program is developed and applied to a slider model of a sophisticated shape. The simulation results of design sensitivity analysis (DSA) are directly compared with those of FDM at the randomly selected grid cells to show the effectiveness of the proposed approach. The overall distribution of DSA results are reported, clearly showing the region on the ABS where special attention should be given during the manufacturing process.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 하계학술대회 논문집 B
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• pp.915-917
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• 2003

In this paper, a 3D shape optimization algorithm which guarantees a smooth optimal shape is presented using parameterized sensitivity analysis. The design surface is parameterized using Bezier spline and the control points of the spline are taken as the design variables. The parameterized sensitivity for the control points are found from that for nodal Points. The design sensitivity and adjoint variable formulae are also derived for the 3D non-linear problems. Through an application to the shape optimization of 3D electromagnet to get a uniform magnetic field, the effectiveness of the proposed algorithm is shown.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• 제3B권1호
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• pp.23-31
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• 2003

A novel 3D shape optimization algorithm is presented for electromagnetic devices carry-ing eddy current. The algorithm integrates the 3D finite element performance analysis and the steepest descent method with design sensitivity and mesh relocation method. For the design sensitivity formula, the adjoint variable vector is defined in complex form based on the 3D finite element method for eddy current problems. A new 3D mesh relocation method is also proposed using the deformation theory of the elastic body under stress to renew the mesh as the shape changes. The design sensitivity f3r the sur-face nodal points is also systematically converted into that for the design variables for the parameterized optimization application. The proposed algorithm is applied to the optimum design of the tank shield model of the transformer and the effectiveness is proved.

• International Journal of Aeronautical and Space Sciences
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• 제8권1호
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• pp.95-104
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• 2007

A new design approach of complex geometries such as wing/body configuration is arranged by using overset mesh techniques under large scale computing environment. For an in-depth study of the flow physics and highly accurate design, several special overlapped structured blocks such as collar grid, tip-cap grid, and etc. which are commonly used in refined drag prediction are adopted to consider the applicability of the present design tools to practical problems. Various pre- and post-processing techniques for overset flow analysis and sensitivity analysis are devised or implemented to resolve overset mesh techniques into the design optimization problem based on Gradient Based Optimization Method (GBOM). In the pre-processing, the convergence characteristics of the flow solver and sensitivity analysis are improved by overlap optimization method. Moreover, a new post-processing method, Spline-Boundary Intersecting Grid (S-BIG) scheme, is proposed by considering the ratio of cell area for more refined prediction of aerodynamic coefficients and efficient evaluation of their sensitivities under parallel computing environment. With respect to the sensitivity analysis, discrete adjoint formulations for overset boundary conditions are derived by a full hand-differentiation. A smooth geometric modification on the overlapped surface boundaries and evaluation of grid sensitivities can be performed by mapping from planform coordinate to the surface meshes with Hicks-Henne function. Careful design works for the drag minimization problems of a transonic wing and a wing/body configuration are performed by using the newly-developed and -applied overset mesh techniques. The results from design applications demonstrate the capability of the present design approach successfully.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.391-396
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• 2008

A level set based topological shape optimization using extended B-spline basis functions is developed for steady state heat conduction problems. The only inside of complicated domain is identified by the level set functions and taken into account in computation. The solution of Hamilton-Jacobi equation leads to an optimal shape according to the normal velocity field determined from the sensitivity analysis, minimizing a thermal compliance while satisfying a volume constraint. To obtain exact shape sensitivity, the precise normal and curvature of geometry need to be determined using the level set and B-spline basis functions. The nucleation of holes is possible whenever and wherever necessary during the optimization using a topological derivative concept.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2002년도 추계학술대회 논문집 전기기기 및 에너지변환시스템부문
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• pp.124-127
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• 2002

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 nonlinear finite element method with edge element. The proposed algorithm is applied to the shape optimization of 3D electromagnet to get a uniform flux density at the air gap.

• 대한기계학회논문집
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• 제11권1호
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• pp.82-87
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• 1987

본 논문에서는 열전달문제 역시 변분형으로 전환될 수 있음에 착안하여 전미 분 개념을 도입해서 전도와 대류가 있는 열전달모델에서 주어진 면적 제한조건을 만족 시키며 지정된 경계에서의 온도가 주어진 온도에 가장 근접할 수 있는 모델의 형상을 찾는 방법을 연구하였다. 어떤 물질의 열전달 상태를 바꾸어 경계에서의 온도를 원 하는 바대로 조정하는 문제는 실제 공정에서 중요한 경우가 많다.해석시 열전달 상 태 방정식과 adjoint식은 6절점 삼각형 등계수 요소의 유한 요소법을 이용하여 해석하 였다.설계민감도의 정확한 계산을 위해서는 임의의 형상변화에 따른 경계에서의 수 치적분이 정확해야 하므로 경계를 곡선으로 표시할 수 있는 등계수 요소가 필요하다. 설계 민감도 해석이 진행된 후에는 최적화 기법의 하나인 미분벡터 투영법(Gradient Projection Method)을 사용하여 최적화를 시도했다. 최적설계 과정중 매번 계산결과 에 의해 형상의 변화가 진행되므로 그때마다 유한 요소 모델을 적절히 변화시켜 주어 야 한다. 모델의 경계는 3차함수로 근사화하여 형상이 부드러운 곡선이 되도록 했 으며 설계변수는 근사화한 3차함수를 결정할 수 있도록 정하면 되나 본 연구에서는 모 델의 변화에 따른 y좌표의 변화는 없다고 가정하여 모델경계의 세점을 취해 그 점들의 x좌표를 설계변수로 했다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1993년도 가을 학술발표회논문집
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• pp.98-105
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• 1993

A method for shape design sensitivity analysis for axisymmetric shells of general shapes is developed. The basic approach is to divide the structures into many segments. For each of the segments, the formula for a shallow arch or shell can be applied and the results assembled. To interconnect those segments, the existing sensitivity formula, obtained for a variation only in the direction perpendicular to the plane on which the structure is mapped, has been extended to include a variation normal to the middle surface. The method follows the adjoint variable approach based on the material derivative concept as established in the literature. Numerical examples are taken to illustrate the method and the applicability to practical design problems.

• 한국전산구조공학회논문집
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• 제28권4호
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• pp.425-431
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• 2015

본 논문에서는 균열 진전문제에 대하여 페리다이나믹스 이론을 이용하여 설계민감도 해석 및 구조 최적설계를 수행하였다. 페리다이나믹스는 해의 불연속성을 다루기 어려웠던 기존의 연속체 이론에 비해 균열 진전문제와 같은 불연속성을 가지는 문제를 자연스럽게 표현할 수 있다는 장점을 가지고 있다. 최적설계를 진행하기 위하여 애조인 변수법으로 설계민감도를 유도하였다. 특히 균열이 진전되더라도 애조인 변수법으로 계산된 변위장과 변형에너지에 대한 설계민감도 값은 유한차분법과 비교하여 매우 정확하고 효율적임을 보였다. 이를 바탕으로 간단한 인장응력 하의 균열진전 문제에 대하여 균열의 분기가 발생하는 위치를 조절하기 위하여 정해진 시간구간에서 변형에너지 값을 줄이는 방향으로 최적설계를 수행하였다. 최적의 재료분포로 해석을 수행한 결과 균열의 분기점을 늦출수 있음을 확인하였다.