• 한국정밀공학회지
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• 제16권6호
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• pp.148-159
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• 1999

A numerical method is presented for the dynamic analysis of spur gears rotating with very high angular speeds. For an efficient computation each gear is assumed to consist of a rotating rigid disk and an elastic tooth having mass, and finite element formulations are used for the equations of motion of the tooth. The geometric constraint is imposed between the rigid disk and the elastic tooth to fix them, and contact condition is imposed between the meshing teeth of the gears. At each iteration of each time step the Lagrange multiplier and contact force are revised by using the constraint error vector, and then the whole equations of motion are time integrated with the given Lagrange multiplier and contact force. For the accurate solution the velocity and acceleration constraints as well as the displacement constraint are satisfied by the monotone reductions of the constraint error vectors. Computing procedures associated with the iterative schemes are explained and numerical simulations are conducted with the spur gears.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 2002년도 춘계공동학술발표회요약집
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• pp.231.1-231
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• 2002

• 한국해양공학회지
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• 제25권4호
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• pp.36-41
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• 2011

In the present paper, a direct forcing/fictitious domain (DF/FD) level set method is proposed to simulate the FSI (fluid-solid interaction) in two-phase flow. The main idea is to combine the direct-forcing/fictitious domain (DF/FD) method with the level set method in the Cartesian coordinates. The DF/FD method is a non-Lagrange-multiplier version of a distributed Lagrange multiplier/fictitious domain (DLM/FD) method. This method does not sacrifice the accuracy and robustness by employing a discrete ${\delta}$ (Dirac delta) function to transfer quantities between the Eulerian nodes and Lagrangian points explicitly as the immersed boundary method. The advantages of this approach are the simple concept, easy implementation, and utilization of the original governing equation without modification. Simulations of various water-entry problems have been conducted to validate the capability and accuracy of the present method in solving the FSI in two-phase flow. Consequently, the present results are found to be in good agreement with those of previous studies.

• 한국시뮬레이션학회논문지
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• 제18권2호
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• pp.57-64
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• 2009

물리적 기반의 다이내믹 시뮬레이션에 있어서 안정적이고 효율적인 제한 시스템은 매우 중요한 요소 중 하나이다. 본 논문은 기존에 널리 사용되고 있는 제한 시스템들(Lagrange Multiplier method, Baumgarte stabilization method, Post-stabilization Method, Implicit constraint enforcement method, Fast projection method)에 대한 분석과 평가를 통해 제한 시스템을 사용하고자 하는 사용자들에게 적절한 선택을 할 수 있는 지침을 제공하고자 한다. 본 논문은 기존의 제한 방법들에 대한 수학적 수식들이 설명되어 있고, 제한 오차 비교, 계산 비용, 동적 움직임 분석 등을 통해 기존 제한 시스템들 각각에 대한 평가를 제공한다.

• 대한기계학회논문집A
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• 제29권12권
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• pp.1629-1637
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• 2005

Optimum sensitivity analysis (OSA) is the process to find the sensitivity of optimum solution with respect to the parameter in the optimization problem. The prevalent OSA methods calculate the optimum sensitivity as a post-processing. In this research, a simple technique is proposed to obtain optimum sensitivity as a result of the original optimization problem, provided that the optimum sensitivity of objective function is required. The parameters are considered as additional design variables in the original optimization problem. And then, it is endowed with equality constraints to penalize the additional variables. When the optimization problem is solved, the optimum sensitivity of objective function is simultaneously obtained as Lagrange multiplier. Several mathematical and engineering examples are solved to show the applicability and efficiency of the method compared to other OSA ones.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2005년도 추계학술대회 논문집
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• pp.464-469
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• 2005

Optimum sensitivity analysis (OSA) is the process to find the sensitivity of optimum solution with respect to the parameter in the optimization problem. The prevalent OSA methods calculate the optimum sensitivity as a post-processing. In this research, a simple technique is proposed to obtain optimum sensitivity as a result of the original optimization problem, provided that the optimum sensitivity of objective function is required. The parameters are considered as additional design variables in the original optimization problem. And then, it is endowed with equality constraints to penalize the additional variables. When the optimization problem is solved, the optimum sensitivity of objective function is simultaneously obtained as Lagrange multiplier. Several mathematical and engineering examples are solved to show the applicability and efficiency of the method compared to other OSA ones.

• 대한기계학회논문집A
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• 제24권3호
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• pp.803-809
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• 2000

For the effective analysis of an engineering problem, meshless methods which require only positioning finite points without the element meshing recently have been proposed and being studied extensively. Meshless methods have difficulty in imposing essential boundary conditions directly, because non-interpolate shape functions originated from an approximation process are used. So some techniques, which are Lagrange multiplier method, modified variational principles and coupling with finite elements and so on, were introduced in order to impose essential boundary conditions. In spite of these methods, imposition of essential boundary conditions have still many problems like as non-positive definiteness, inaccuracy and negation of meshless characteristics. In this paper, we propose a new method which modifies shape function. Through numerical tests, convergence, accuracy and validity of this method are compared with the standard EFGM which uses Lagrange multiplier method or modified variational principles. According to this study, the proposed method shows the comparable accuracy and efficiency.

• 조명전기설비학회논문지
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• 제19권1호
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• pp.59-63
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• 2005

전력계통을 효율적으로 운용하려면 관련량을 정확하고 신속히 계산하는 좋은 알고리즘이 필요하다. 최근 IEEE Transaction on Power System에 위상각 이동을 이용한 손실 최적화 알고리즘이 발표되었다. 동일한 손실최적화 문제를 본 논문에서는 Standard method of Lagrange Multiplier 기법을 적용하여 해석하였으며, 그 결과 저자들은 두 가지 방법이 수학적으로 동일함을 증명하였다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권2호
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• pp.179-192
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• 2012

We find the solution minimizing the shortfall risk by using the Lagrange-multiplier method. The conventional duality method in the expected utility maximization problem is used and we get the same results as in the paper [21].

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1997년도 추계학술대회논문집
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• pp.40-44
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• 1997

The governing functional in plastic deformation has to satisfy the incompressible condition. This incompressible condition imposed on the velocity fields can be removed by introducing either the Langrange multiplier or the penalty function into the functional. In the study two-dimensional rigid plastic FEM programs using by Lagrange multiplier and penalty function are developed. A compression of cylinder and a spike forging are simulated to compare the data of loads, local mean stresses and reductions of volume.