• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.14 no.2
• /
• pp.159-171
• /
• 2001

평면 아치 구조물에 대해 선형 탄성 변분방정식에 기반을 둔 설계민감도 해석을 위한 일반적 이론을 개발하였다. 아치 구조물내의 임의 마디에 정의된 응력범함수를 고려하였고 이에 대한 설계민감도 공식을 유도하기 위해 전미분(material derivative) 개념과 보조(adjoint) 변수 방법을 도입하였다. 얻어진 민감도 공식은 구조해석 결과를 얻고 나면 이들로부터 단순 대수연산을 통해 계산이 되므로 적용이 간편할 뿐 아니라 해의 정확도가 높은 잇점이 있다. 본 방법은 아치의 형상을 매개변수를 통해 표현하므로 얕은 아치에 국한하지 않고 어떠한 형상도 고려가 가능하며, 나아가서 아치의 형상변화를 형상에 대해 수직뿐 아니라 접선방향도 포함하여 일반적으로 고려하므로 다양한 형상설계가 가능하다. 몇 가지 예제에서 민감도 계산을 수행함으로써 본 방법의 정확도와 효율성을 입증하였으며, 두 가지의 설계최적화 문제를 대상으로 실제로 두께 및 형상최적설계를 수행하였다.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.8 no.4 s.23
• /
• pp.136-145
• /
• 2005

특이응력해석을 위한 일반화된 가역상반일 경계적분식이 섬유강화복합재를 모형화한 직교 이방성 크랙평판의 수치해를 위하여 발전시켰다. 이 적분방정식은 평판경계에서의 탄성변위와 트랙션의 변수로 구성된 경계적분식의 형태로 하중이 없다는 두 크랙면의 경계조건과 유한의 탄성변형에너지의 개념에서 경계적분식에 필요한 특성해를 규정하고 대응되는 보조해를 계산하였다. 대칭모우드 I형의 중앙원공크랙평판 및 복합모우드형의 반원편측크랙 일단고정평판의 응력확대계수가 임의의 섬유방향각에 따라서 계산되었다.

• Water for future
• /
• v.15 no.1
• /
• pp.57-62
• /
• 1982

In order to make a numerical modeling for the one dimensional unsteady flow which expressed by Saint Venant partial differential equations, Preissman's implicit schem was used, and it's stability and accuracy was investigated. By introducing recurrence relations make it possible to use double sweep algorithm. Effective parameters to the result were the values of the C$$ and the Chezy coefticient. In order to get numerical solutions whith enough accuracy, C$$ should not be far from the value of1, and when the criteria of the $\theta$ was 0.6<$\theta$<1.0, the rewult was always stable for any condition. This model should be calibrated by real field data, and expected to be developed for the simulation of the river system and to the long wave analysis for one dimensional coastal zone problem.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.27 no.3
• /
• pp.7-12
• /
• 1990

A rigorous analysis of the scattering problem by the perfectly conducting strip loaded with a dielectric cylinder of different permittivity is presented. By introducing auxiliary electromagnetic fields and applying the reciprocity theorem, integral equations for the unknown electric field are derived. These integral equations are transformed into an equivalent matrix equation of infinite order with proper boundary conditions. By calculating inverse matrix of unknown coefficients from this equation, scattered electric fields are determined. In particular case of the dielectric with the same permittivity, the results of this paper correspond to well-known results.

• Proceedings of the Korea Water Resources Association Conference
• /
• 1982.07a
• /
• pp.27-32
• /
• 1982

In other to make a numerical modeling for the one dimensional unsteady flow which expressed by Saint Venant partial differential equations, Preissman's implicit scheme was used, and it's stability and accuracy was investigated. By introducing recurrence relations make it possible to use double sweep algorithm. Effective parameters to the result were the values df the $$ and the Chezy coefticient. In other to get numberical solutions with enough accuracy, $$ should not be far from the value of1, and when the criteria of the $$ was 0.6<$$<1.0, the result was alaways stable for any condition. This model should be calibrated by real fileld data, and expected to be developed for the simulation of the river system and to the long wave analysis for one dimensional coastal zone problem.

• Journal for History of Mathematics
• /
• v.27 no.3
• /
• pp.165-182
• /
• 2014

After algebraic expressions for the roots of 3rd and 4th degree polynomial equations were given in the mid 16th century, seeking such a formula for the 5th and greater degree equations had been one main problem for algebraists for almost 200 years. Lagrange made careful and thorough investigation of various solving methods for equations with the purpose of finding a principle which could be applicable to general equations. In the process of doing this, he found a relation between the roots of the original equation and its auxiliary equation using permutations of the roots. Lagrange's ingenious idea of using permutations of roots of the original equation is regarded as the key factor of the Abel's proof of unsolvability by radicals of general 5th degree equations and of Galois' theory as well. This paper intends to examine Lagrange's contribution in the theory of polynomial equations, providing a detailed analysis of various solving methods of Lagrange and others before him.

• Geophysics and Geophysical Exploration
• /
• v.11 no.2
• /
• pp.85-92
• /
• 2008

Magnetotelluric (MT) methods are widely applied as an effective exploration technique to geothermal surveys. Two-dimensional (2-D) analysis is frequently used to investigate a complicated subsurface structure in a geothermal region. A 2-D finite-element method (FEM) is usually applied to the MT analysis, but we must pay attention to the accuracy of so-called auxiliary fields. Rodi (1976) proposed an algorithm of improving the accuracy of auxiliary fields, and named it as the MOM method. Because it introduces zeros into the diagonal elements of coefficient matrix of the FEM total equation, a pivoting procedure applied to the symmetrical band matrix makes the numerical solution far less efficient. The MOM method was devised mainly for the inversion analysis, in which partial derivatives of both electric and magnetic fields with respect to model parameters are required. In the case of forward modeling, however, we do not have to resort to the MOM method; there is no need of modifying the coefficient matrix, and the auxiliary fields can be elicited from the regular FEM solution. The computational efficiency of the MOM method, however, can be greatly improved through a sophisticated rearrangement of the total equation.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2022.05a
• /
• pp.372-372
• /
• 2022

스마트시티 하천관리를 위해 선행된 연구에서는 도시하천관련 데이터를 수집-정제-제공하는 도시하천 통합데이터 플랫폼을 개발하였다. 이에 하천 분석을 위한 유역 유출, 하천 흐름 그리고 도시유출 등의 모듈과 하천 환경, 친수, 종합 평가 모델을 연계하여 도시하천관리 연계플랫폼으로 연구개발을 진행하였다. 본 연구에서는 스마트시티 하천관리를 위한 시나리오 기반 제방 파제 시뮬레이션 분석 결과 가시화 모듈에 관한 연구를 진행한다. 부산 EDC 지역을 대상으로 DEM, 항공영상, 위성영상, 하천 지리 정보, 하천 단면도 등의 데이터를 결합하여 하천 및 유역 전산 3D 형상 모델링을 진행한다. 또한 하천 내부 유량 및 파제 제체 모델링, 유동장 격자 모델링을 통해 제방 붕괴 범람 시뮬레이션 대상 지역을 구현한다. 해당 EDC 지역 구현 모델에 연속방정식, 운동량방정식, 수송방정식 등 지배방정식과 삼상 유동 기법 등 수치 해석 기법을 활용하여 제방 파제 시뮬레이션을 수행한다. 시뮬레이션의 침수범위 및 침수심 분포 결과는 위경도를 포함한 ASCII Grid로 반환되며 GeoServer를 통한 좌표계 설정 및 도시하천 연계플랫폼에서 가시화하는 연구를 진행하였다. 제방 파제 시나리오는 제방 높이 2m, 제방 폭 7.5m, 파제 길이 20m로 설정하여 4개의 붕괴 위치를 지정하였고, 지정된 위치에 대한 제방 파제 3D 시뮬레이션을 통해 도출된 Case 별 2D/3D 영상과 침수심 공간 분포에 대한 Raster Graphics를 전처리하여 시나리오별 침수범위-침수심을 도시하천 연계플랫폼 상에서 가시화하는 연구를 진행하였다. 도시하천 연계플랫폼의 시나리오 기반 제방 파제 시뮬레이션 모듈을 통하여 스마트시티의 제방 파제 피해 양상 및 대책 마련 의사결정 보조로 활용할 수 있을 것으로 기대된다.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
• /
• 2005.11a
• /
• pp.169-174
• /
• 2005

In this paper, we proposed a new algorithm of the inverse scattering for the reconstruction of unknown dielectric scatterers using the finite-difference time-domain method and the design sensitivity analysis. We introduced the design sensitivity analysis based on the gradient for the fast convergence of the reconstruction. By introducing the adjoint variable method for the efficient calculation, we derived the adjoint variable equation. As an optimal algorithm we used the steepest descent method and reconstructed the dielectric targets using the iterative estimation. To verify our algorithm we will show the numerical examples for the two-dimensional $TM^2$ cases.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.35 no.6
• /
• pp.367-374
• /
• 2022

This papter presents the use of the automatic differential method based on the backpropagation method to obtain the design sensitivity and its application to topology optimization considering the stress constraints. Solving topology optimization problems with stress constraints is difficult owing to singularities, the local nature of stress constraints, and nonlinearity with respect to design variables. To solve the singularity problem, the stress relaxation technique is used, and p-norm for stress constraints is applied instead of local stresses for global stress measures. To overcome the nonlinearity of the design variables in stress constraint problems, it is important to analytically obtain the exact design sensitivity. In conventional topology optimization, design sensitivity is obtained efficiently and accurately using the adjoint variable method; however, obtaining the design sensitivity analytically and additionally solving the adjoint equation is difficult. To address this problem, the design sensitivity is obtained using a backpropagation technique that is used to determine optimal weights and biases in the artificial neural network, and it is applied to the topology optimization with the stress constraints. The backpropagation technique is used in automatic differentiation and can simplify the calculation of the design sensitivity for the objectives or constraint functions without complicated analytical derivations. In addition, the backpropagation process is more computationally efficient than solving adjoint equations in sensitivity calculations.