• Journal of computational fluids engineering
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• v.6 no.2
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• pp.9-21
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• 2001

초음속 여객기의 천음속 순항 성능을 개선하기 위하여 날개의 플랩 꺽임각을 최적화하였다. 이를 위하여 3차원 Euler 코드와 adjoint 코드를 이용한 최적설계기법을 적용하였다. 설계변수로서, 앞전플랩 5개, 뒷전 플랩 5개 등 총 10개의 플랩의 꺽임각이 사용되었다. 설계과정중에 격자계 내부격자점의 수정을 위해 타원형방정식법을 이용하였다. 계산 시간의 단축을 위해 내부격자의 민감도는 무시하였다. 또한 본 설계문제에 근사구배기법의 적용가능성 여부를 조사하였다. 충격파가 없는 경우 앞전 플렙에 한하여 근사구배기법을 적용할 수 있음을 알았다. 최적설계기법으로 BFGS기법을 적용하여 항력을 최소화하였으며, 양력 및 날개 표면 마하수에 대한 제약조건을 적용하였다. 앞전 플랩의 최적화 및 앞전과 뒷전 플랩의 최적화 등 두 개의 설계 문제를 고려하였다. 성공적인 결과를 얻음으로써 본 설계방법의 타당성 및 효율성을 확인하였다.

• Smart Structures and Systems
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• v.22 no.3
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• pp.249-257
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• 2018

This study contributes to evaluate multiphase topology optimization design of plate-like elastic structures with constant thickness and Reissner-Mindlin plate theory. Stiffness and adjoint sensitivity formulations linked to Reissner-Mindlin plate potential energy of bending and shear are derived in terms of multiphase design variables. Multiphase optimization problem is solved through alternative active-phase algorithm with Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples verify efficiency and diversity of the present topology optimization method of Reissner-Mindlin elastic plates depending on multiphase and Poisson's ratio.

• Nuclear Engineering and Technology
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• v.3 no.4
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• pp.203-208
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• 1971

Noether's theorem is applied to the one dimensional neutron transport equation. It is obtained the transformation rendering the functional of the one dimensional Boltzmann equation invariant. It is derived the law conserving the product of the directional flux and its adjoint flux. The possible types of the solution of the Boltzmann equation are discussed. The results are compared with the well-known solution.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.61-82
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• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05a
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• pp.93-98
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• 1998

PEN(1)(다항식전개 노달) 해법을 육방형 노심의 과도상태 해석과 Adjoint flux(수반 중성자속)해법에 응용하여 여러가지 Benchmark문제들(3)(4)(5)을 풀고 그 결과를 다른 수치기법 결과와 비교·분석하였다. 2차원 육방형 대형중수로 과도상태 Benchmark문제(5)를 다항식전개 노달해법에 의한 과도상태 해석·검증의 대상으로 삼았으며 그 기준 계산치로서 FX2-TH 코드의 계산결과를 사용하였다 대형중수로 노심의 과도상태 해석 결과, 기준해와 비교해 집합체 낙하시작 3초 후에 집합체가 낙하한 위치에서 Normalized Flux 오차가 0.5% 이내, 집합체가 낙하하지 않은 위치에서 Normalized Flux 오차가 1% 이내의 정확한 결과를 보였다. Adjoint flux 해의 검증을 위해서는 VENTURE 코드(2)의 계산 결과를 기준해로 하였으며, 계산능 검증을 위해 사용된 대부분 의 Benchmark 문제들에서 작은 오차를 보였으나 반사체가 포함된 IAEA 문제에서는 큰 오차를 보였다.

• Steel and Composite Structures
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• v.27 no.2
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• pp.177-184
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• 2018

This study contributes to evaluate multiphase topology optimization design of plate-like structures on elastic foundations by using classic plate theory. Multi-material optimal topology and shape are produced as an alternative to provide reasonable material assignments based on stress distributions. Multi-material topology optimization problem is solved through an alternative active-phase algorithm with Gauss-Seidel version as an optimization model of optimality criteria. Stiffness and adjoint sensitivity formulations linked to thin plate potential strain energy are derived in terms of multiphase design variables and Winkler-Pasternak parameters considering elastic foundation to apply to the current topology optimization. Numerical examples verify efficiency and diversity of the present topology optimization method of elastic thin plates depending on multiple materials and Winkler-Pasternak parameters with the same amount of volume fraction and total structural volume.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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• pp.208-208
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• 2006

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.04a
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• pp.264-265
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• 2009

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.221-226
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• 1988

Using the method of eigenfunction expantion of self adjoint operators, we establish the necessary and sufficient conditions for a reflection positive generalized matrix kernel to be represented in an integral form. This integral converges in the cosidered spaces.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.309-316
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• 2005

In this paper, we develop continuum-based design sensitivity analysis (DSA) methods using both direct differential method (DDM) and adjoint variable method (AVM) for non-shape design problems. The developed DSA method is further utilized for the topology design optimization of 3-dimensional structures. In numerical examples, the analytical DSA results are verified using finite difference ones. The topology optimization method yields very reasonable results in physical point of view.