• 한국정밀공학회지
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• 제20권8호
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• pp.175-184
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• 2003

A method of the shape design sensitivity analysis based on the boundary integral equation formulation is presented for two-dimensional inhomogeneous thermal conducting solids with multiple domains. Shape variation of the external and interface boundary is considered. A sensitivity formula of a general performance functional is derived by taking the material derivative to the boundary integral identity and by introducing an adjoint system. In numerical analysis, state variables of the primal and adjoint systems are solved by the boundary element method using quadratic elements. Two numerical examples of a compound cylinder and a thermal diffuser are taken to show implementation of the shape design sensitivity analysis. Accuracy of the present method is verified by comparing analyzed sensitivities with those by the finite difference. As application to the shape optimization, an optimal shape of the thermal diffuser is found by incorporating the sensitivity analysis algorithm in an optimization program.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 가을 학술발표회 논문집
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• pp.355-362
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• 2004

An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in various problems. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-to-use features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem and fillet problem are chosen to illustrate the efficiency of the proposed methodology. Implementation issues for the sensitivity analysis and optimization procedure are also addressed in these problems.

• 대한기계학회논문집A
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• 제28권9호
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• pp.1320-1327
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• 2004

An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in supercavitating flow problem. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in potential flow problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design in potential flow problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-to-use features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem is chosen to illustrate the efficiency of the proposed methodology. Implementation issues for the sensitivity analysis and optimization procedure are also addressed in this flow problem.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.1047-1052
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• 2004

An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in supercavitating flow problem. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in potential flow problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design in potential flow problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-touse features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem is chosen to illustrate the efficiency of the proposed methodology. Implementation issues for and optimization procedure are addressed in this flow problem.

• 한국전산구조공학회논문집
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• 제18권3호
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• pp.255-263
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• 2005

본 논문에서는 다양한 문제들의 형상 설계 민감도 해석에 대한 효율적인 경계기반 기법을 제시하였다 우선 문제에서 정의된 일반적인 함수들에 대한 연속체 형태의 식에 근거하여, 경계 적분 형태의 해석적 민감도 식을 유도하였다. 이 식은 다양한 형상 설계 문제들의 경사를 계산하는데 편리하게 사용할 수 있다. 그리고 경계법은 형상 변분 벡터가 전체 도메인이 아닌 경계에서만 요구된다는 장점이 있는데, 여기서 경계 형상 변분은 형상 함수의 복잡한 해석적 미분 대신 형상을 미소 증분시킴으로써 편리하게 계산할 수 있다. 제시한 방법의 효율성을 보이기 위해 포텐셜 유동 문제와 필렛(fillet)에서의 응력 집중 문제에 이를 적용하였다.

• 대한기계학회논문집A
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• 제30권2호
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• pp.149-156
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• 2006

A boundary-based design sensitivity analysis(DSA) technique is proposed for addressing shape optimization issues in the elastostatics problems. Sensitivity formula is derived based on the continuum formulation in a boundary integral form, which consists of the boundary solutions and shape variation vectors. Though the boundary element method(BEM) has been mainly used to obtain the boundary solution, the FEM is used in this paper because this is much more popular, and has greatly improved meshing and computing power recently. The advantage of the boundary DSA is that the shape variation vectors, which are also known as design velocity fields, are needed only on the boundary. Then, the step for determining the design velocity field over the whole domain, which was necessary in the domain-based DSA, is eliminated, making the process easy to implement and efficient. Problem of fillet design is chosen to illustrate the efficiency of the proposed method. Accuracy of the sensitivity is good with this method even by employing the free mesh for the FE analysis.

• 한국멀티미디어학회논문지
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• 제5권3호
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• pp.255-262
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• 2002

윤곽선 시퀀스는 임의 형상을 간단하면서도 정확하게 표현할 수 있는 좋은 표현법이 될 수 있다. 그러나, 형상을 구성하는 화소로부터 쉽게 구할 수 있는 면적, 무게중심, 오리엔테이션 방향, 투영 히스토그램 등과 같은 형상 특징들을 윤곽선 시퀀스로부터 직접 구하기는 어렵기 때문에, 윤곽선 시퀀스를 임의 형상에 대한 표현법으로 잘 사용하지 못하였다. 본 논문에서는 형상 내부의 연속된 화소들로 구성된 수직(또는 수평)의 라인 세그먼트를 의미하는 크로스 섹션 개념을 이용하여, 윤곽선 시퀀스로부터 형상 특징들을 쉽게 구할 수 있음을 보인다. 윤곽선 시퀀스를 한번 순차적으로 탐색함으로써 크로스 섹션을 효율적으로 구할 수 있는 방법을 제안한다. 또한, 이진 영상으로부터 여러 형상의 윤곽선 시퀀스를 자동으로 추출할 수 있는 효율적인 방법도 함께 제안한다. 제안된 방법들은 형상 내부에 홀(hole)이 있는 경우에도 적용할 수 있다. 결과적으로, 윤곽선 시퀀스가 임의 형상 영역에 대한 매우 효과적인 표현이 될 수 있음을 밝힌다.

• Journal of Mechanical Science and Technology
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• 제19권12호
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• pp.2231-2244
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• 2005

An efficient boundary-based optimization technique is applied in the numerical computation of free surface flow problems, by reformulating them into the equivalent optimal shape design problems. While the sensitivity in the boundary method has mainly been calculated using the boundary element method (BEM) as an analysis means, the finite element method (FEM) is used in this study because of its popularity and easy-to-use features. The advantage of boundary method is that the design velocity vectors are needed only on the boundary, not over the whole domain. As such, a determination of the complicated domain design velocity field, which is necessary in the domain method, is eliminated, thereby making the process easy to implement and efficient. Seepage and supercavitating flow problem are chosen to illustrate the accuracy and effectiveness of the proposed method.

• 대한기계학회논문집A
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• 제20권5호
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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.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2008년도 춘계 학술발표회 초청강연 및 논문집
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• pp.1095-1099
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• 2008

Critical state theory involves two state boundary surface. One is Roscoe surface and the other is Hvorslev surface. The shape of these boundary surface was changed because of several parameters : Critical state constant(M), spacing ratio (r) and critical state pore pressure coefficient($\wedge$). As these constants make difference to each model and the way of solution, they may affect the shape of state boundary surface. Specially, spacing ratio (r) is important. On this study, triaxial compression test was performed using remolded weathered mudstone soil and investigated variation of state boundary surface because of spacing ratio. In the results of prediction, critical state point was located highly and the shape of boundary surface was changed more tightly curve as decreasing spacing ratio.