• 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.

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.101-114
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• 1995

In this paper we consider the multiple unit root tests both for the regular and seasonal unit roots based on the Lagrange Multiplier(LM) principle. Unlike Li(1991)'s method, by plugging the restricted maximum likelihood estimates of the nuisance parameters in the model, we propose a Lagrange multiplier test which does not depend on the existence of the nuisance parameters. The asymptotic distribution of the proposed statistic is derived and empirical percentiles of the test statistic for selected seasonal periods are provided. The power and size of the test statistic for examined for finite samples through a Monte Carlo simularion.

• 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.

• Journal of Advanced Marine Engineering and Technology
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• 제24권3호
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• pp.106-112
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• 2000

Since the oil crisis, we have been concerned about the energy saving techniques of electric generating systems. As a part of the effort to save energy, automatic electric load sharing device was developed. Usually, ship's electric generating system consists of two or three sets of generator. And, electric generating system is operated as single or parallel operation mode according to the demanded electric power. Therefore, it is important to investigate generators operating mode for the supply of required electric power in the ship in order to decrease the operating cost. So, this paper suggests the method to solve the optimal electric load distribution problem by dynamic programming. And, this thesis indicates that the proposed method is superior to the lagrange multiplier's method in obtaining optimal load distribution solution in the ship's electric generating system.

• 소성∙가공
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• 제11권4호
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• pp.355-362
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• 2002

In this study, an axi-symmetric finite element program for elastic analysis of the die set shrink fitted in cold extrusion was developed. The geometrical constraint according to shrink fit was enforced by employing the Lagrange multiplier method. The numerical results for strain and stress distributions in the die set including single and multi stress rings assembled by shrink fit were compared well with the Lame's equation for thick-walled solution available in the literature. To extend the applicability of the analysis program developed, various cases without or with stress ring and with pre-stress applied on stress ring were numerically investigated as well. This numerical approach enables the optimization study to determine optimal dimensions of die set to improve tool life for practical use in industry.

• Structural Engineering and Mechanics
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• 제41권5호
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• pp.617-632
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• 2012

An isogeometric approach is presented for static analysis of thin plate problems of various geometries. Non-Uniform Rational B-Splines (NURBS) basis function is applied for approximation of the thin plate deflection, as for description of the geometry. The governing equation based on Kirchhoff plate theory, is discretized using the standard Galerkin method. The essential boundary conditions are enforced by the Lagrange multiplier method. Several typical examples of thin plate and thin plate on elastic foundation are solved and compared with the theoretical solutions and other numerical methods. The numerical results show the robustness and efficiency of the proposed approach.

• 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.

• 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].

• 오토저널
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• 제11권2호
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• pp.24-33
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• 1989

본 고에서는 이러한 추세에 따라서, 보다 효율적인 optimization program에 대해서 소개하고자 한다. 사용한 최적화 알고리즘은 ALM(augmented lagrange multiplier) 방법을 적용해서 구속조건이 있는 문제를 구속조건이 없는 문제로 변환한 후, self-scaling BFGS(broydon-flecher-goldfarb-schanno)를 적용한다. BFGS의 각 descent 방향에서의 step 길이는, sequential search로 unimodal point를 구해서, golden section 방법으로 refine을 한후, cubic approximation을 적용해서 구한다.

• Journal of Advanced Marine Engineering and Technology
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• 제26권3호
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• pp.313-319
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• 2002

Since the oil crisis in 1970, a great deal of effort has been made to develop automatic electric load sharing systems as a part of the efforts to save energy. A large scale electric generating system composes more than two generators whose characteristics may be different. When such a system is operated individually or in parallel, the lagrange multiplier's method has difficulty in achieving optimal load distribution because generators usually have the limitations of the operating range with inequality constraints. Therefore, a suitable operating mode of generators has to be decided according to the selection of the generators to meet electric power requirements at the minimum cost. In this study, a method which solves the optimal electric load distribution problem using the dynamic programming technique is proposed. This study also shows that the dynamic programming method has an advantage in dealing with the optimal load distribution problem under the limitations of the operating range with inequality constraints including generator operation mode. In this study, generator operating cost curve of second order equation by shop trial test results of diesel generators are used. The results indicate that the proposed method can be applied to the ship's electric generating system.