• 한국군사과학기술학회지
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• 제21권3호
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• pp.264-278
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• 2018

The support structure of an optical mirror system is the one of the important design elements because the one affects the optical aberrations of the mirror surface. In this paper, Lagrange equation of the moving body of the fast steering mirror system(FSM) has been formulated to use with optimization design. Major goals for optimization are to assign the reasonably flexible stiffness to the structure and to enhance the first natural frequency of the mirror and support system in aid of more affordable control bandwidth for the FSM. Pursuing these purposes with the proposed method, the finite element analysis(FEA), optimization technique and the Zernike polynomial estimation are used for the design effects. It is concluded that the proposed approach for design well guides toward the desired design goals with regards to both structural and optical performances.

• 대한기계학회논문집A
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• 제20권1호
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• pp.35-43
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• 1996

A computer program for automatic deriving the symbolic equations of motion for robots using the programming language MATHEMATICA has been developed. The program, developed based on the Lagrange formalism, is applicable to the closed chain robots as well as the open chain robots. The closed chains are virtually cut open, and the kinematics and dynamics of the virtual open chain robot are analyzed. The constraints are applied to the virtually cut joints. As a result, the spatial closed chain robot can be considered as a tree structured open chain robot with kinematic constraints. The topology of tree structured open chain robot is described by a FATHER array. The FATHER array of a link indicates the link that is connected in the direction of base link. The constraints are represented by Lagrange multipliers. The parallel robot, DELTA, having three-dimensional closed chains is modeled and simulated to illustrate the approach.

• Computers and Concrete
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• 제16권3호
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• pp.429-448
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• 2015

The dams are huge structures storing a large amount of water and failures of them cause especially irreparable loss of lives during the earthquakes. They are named as a group of structures subjected to fluid-structure interaction. So, the response of the fluid and its hydrodynamic pressures on the dam should be reflected more accurately in the structural analyses to determine the real behavior as soon as possible. Different mathematical and analytical modelling approaches can be used to calculate the water hydrodynamic pressure effect on the dam body. In this paper, it is aimed to determine the dynamic response of concrete gravity dams using different water modelling approaches such as Westergaard, Lagrange and Euler. For this purpose, Sariyar concrete gravity dam located on the Sakarya River, which is 120km to the northeast of Ankara, is selected as a case study. Firstly, the main principals and basic formulation of all approaches are given. After, the finite element models of the dam are constituted considering dam-reservoir-foundation interaction using ANSYS software. To determine the structural response of the dam, the linear transient analyses are performed using 1992 Erzincan earthquake ground motion record. In the analyses, element matrices are computed using the Gauss numerical integration technique. The Newmark method is used in the solution of the equation of motions. Rayleigh damping is considered. At the end of the analyses, dynamic characteristics, maximum displacements, maximum-minimum principal stresses and maximum-minimum principal strains are attained and compared with each other for Westergaard, Lagrange and Euler approaches.

• 한국광학회지
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• 제12권2호
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• pp.109-114
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• 2001

광학설계의 최적화에서는 광학수차를 줄이면서 광학계의 제한조건을 유지시켜야하며, 이를 위하여 Lagrange 부정승수법이 사용되고 있다. 이 과정에서 제한조건이 merit function의 error 항보다 우선적으로 보정된다. 본연구에서는 이를 이용하여 merit function에서 절대값이 큰 error의 보정조건을 제한조건으로 변경하여 우선적으로 보정하는 최적화의 능동적 제어법을 제안하고 이를 사진렌즈계의 최적화에 적용하였다.

• 한국전산구조공학회논문집
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• 제24권4호
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• pp.365-373
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• 2011

병렬과 영역분할을 이용한 폭발하중을 받는 철근콘크리트패널의 손상을 분석하였다. 폭풍파는 극도로 짧은시간 동안에 발생되기 때문에 수치해석을 통한 결과값은 폭풍파의 메쉬크기에 영향을 받는다. 그러므로 폭풍파 메쉬크기의 영향을 분석하기 위해 explicit 유한요소해석 프로그램인 AUTODYN을 이용하여 기존 실험결과와 메쉬크기에 따른 해석결과가 비교되었다. 폭발해석결과 메쉬크기가 작을수록 정확도가 높았으나 수행시간이 증가하여 효율성이 떨어졌다. 추가로 수치해석의 효율성을 높이기 위해 영역별 Euler와 Lagrange 기법을 달리하는 병렬해석이 수행되었다. 결과로, 폭풍파영역에서는 영역분할된 Euler 메쉬를 사용하고 구조물영역에서는 영역 분할된 Lagrange 메쉬를 사용하는 것이 구조물영역에서 영역 분할된 Lagrange 메쉬만을 사용한 것보다 수치효율성이 가장 높았다.

• 소성∙가공
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• 제8권1호
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• pp.47-56
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• 1999

The governing functional in plastic deformation has to satisfy the incompressibility constraint. This incompressibility constraint imposed on velocity fields can be removed by introducing either Lagrange multiplier or the penalty constant into the functional. In this study, two-dimensional rigid plastic FEM programs using these schemes were developed. These two programs and DEFORM were applied in a cylinder upsetting and a closed die forging to compare the values of load, local mean stress and volume loss. As the results, the program using Lagrange multiplier obtained a more exact and stable solution, but it took more computational time than the program using the penalty constant. Therefore, according to user's need, one of these two programs can be chosen to simulate a metal forming processes.

• 대한기계학회논문집
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• 제15권2호
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• pp.544-556
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• 1991

The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust and efficient. A general-purpose nonlinear optimization program IDOL (Interactive Design Optimization Library) is developed based on the Augmented Lagrange Mulitiplier (ALM) method. The ideas of selecting a good initial design point, using resonable initial values for Lagrange multipliers, constraints scaling, descent vector restarting, and dynamic stopping criterion are employed for computational enhancement to the ALM method. A descent vector is determined by using the Broydon-Fletcher-Goldfarb-Shanno (BFGS) method. For line search, the Incremental-Search method is first used to find bounds on the solution, then the bounds are reduced by the Golden Section method, and finally a cubic polynomial approximation technique is applied to locate the next design point. Seven typical test problems are solved to show IDOL efficient and robust.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.674-679
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• 2005

This paper is concerned with the application of perturbation method to the dynamic analysis of space structure floating in space. In dealing with the dynamics of space structure, the use of Lagrange's equations of motion in terms of quasi-coordinates were suggested to derive hybrid equations of motion for rigid-body translations and elastic vibrations. The perturbation method is then applied to the hybrid equations of motion along with discretization by means of admissible functions. This process is very tiresome. Recently, a new approach that applies the perturbation method to the Lagrange's equations directly was proposed and applied to the two-dimensional floating structure. In this paper, we propose the application of the perturbation method to the Lagrange's equations of motion in terms of quasi-coordinates. Theoretical derivations show the efficacy of the proposed method.

• 한국해양공학회지
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• 제10권3호
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• pp.96-104
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• 1996

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

• 소음진동
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• 제5권4호
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• pp.503-514
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• 1995

In the case of performing experimental modal analysis(EMA) and finite- element analysis(EFA) for a whole structure of automotive body that is composed of many complex parts, a trouble may arise from the calculation time, the capacity of memory in computers and the experimental conditions, etc. In this paper, for the vibrational analysis of automotive body model, the efficient modal synthesis method by means of dividing the whole structure into two parts and performing EMA and FEA for each part is studied. In addition, the method based on Lagrange interpolation is proposed for approximating rotational degrees-of-freedom information and linking FEA with EMA. In result, by measuring translational degrees-of-freedom information of only few points and adopting only few modes, the linking method based on Lagrange interpolation turned out to be efficient and accurate in the low frequency range.