• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.196-220
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• 2021

This study formulates a new geometric parameterization scheme to effectively address numerical analysis subject to the variation of the fiber radius of a square unit cell. In particular, the proposed mesh-morphing approach may lead to a parameterized weak form whose bilinear and linear forms are affine in the geometric parameter of interest, i.e. the fiber radius. As a result, we may certify the reduced basis analysis of a square unit cell model for any parameters in a predetermined parameter domain with a rigorous a posteriori error bound. To demonstrate the utility of the proposed geometric parameterization, we consider a two-dimensional, steady-state heat conduction analysis dependent on two parameters: a fiber radius and a thermal conductivity. For rapid yet rigorous a posteriori error evaluation, we estimate a lower bound of a coercivity constant via the min-θ method as well as the successive constraint method. Compared to the corresponding finite element analysis, the constructed reduced basis analysis may yield nearly the same solution at a computational speed about 29 times faster on average. In conclusion, the proposed geometric parameterization scheme is conducive for accurate yet efficient reduced basis analysis.

• Structural Engineering and Mechanics
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• 제20권6호
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• pp.609-630
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• 2005

A reliability analysis method is proposed in this paper through a combination of the advantages of the response surface method (RSM), finite element method (FEM), first order reliability method (FORM) and the importance sampling updating method. The accuracy and efficiency of the method is demonstrated through several numerical examples. Then the method is used to estimate the serviceability reliability of cable-stayed bridges. Effects of geometric nonlinearity, randomness in loading, material, and geometry are considered. The example cable-stayed bridge is the Second Nanjing Bridge with a main span length of 628 m built in China. The results show that the cable sag that is part of the geometric nonlinearities of cable-stayed bridges has a major effect on the reliability of cable-stayed bridge. Finally, the most influential random variables on the reliability of cable-stayed bridges are identified by using a sensitivity analysis.

• 대한기계학회논문집A
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• 제36권2호
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• pp.165-171
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• 2012

본 연구는 3 축 공작기계에 있어 기하학적 오차가 체적 오차에 미치는 영향을 해석적 방법으로 분석하는데 목적이 있다. 먼저 기하학적 오차가 공작기계의 체적 오차에 미치는 영향을 제시하는 수학적 모델인 오차합성모델에 대해 분석한다. 민감도 분석은 분산 기반의 방법(Variance based method)을 사용하였으며 해석적 방법으로 분석하기 위해 평균 및 분산에 대해 목적 함수의 유형별로 그 해를 제시한다. 마지막으로 3 축 공작기계의 예를 들어 민감도 분석을 하였다.

• 대한기계학회논문집A
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• 제27권2호
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• pp.262-267
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• 2003

Error of the geometric series expansion method for the structural sensitivity analysis is estimated. Although the semi-analytic method has several advantages, accuracy of the method prevents it from practical application. One of the promising remedies is the use of geometric series formula for the matrix inversion. Its result of the sensitivity analysis converges that of the global difference method which is known as reliable one. To reduce computational efforts and to obtain reliable results, it is important to know how many terms need to expand. In this paper, the error formula is presented and Its usefulness is illustrated through numerical experiments.

• 한국정밀공학회지
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• 제25권5호
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• pp.69-76
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• 2008

Inner diameter of bearing race is automatically measured by complete inspection system after grinding process. Contact type three points supporting method is widely applied to automatic inner diameter measurement because of its excellent stability. However, the geometric consideration regarding three points supporting method is not sufficient. In this study, the error equation from geometric error analysis of three points supporting method is found. The effect of factors in the error equation is also investigated. The error equation is linear for difference of diameter in sample and master on range of tolerance. An error becomes more and more larger, when the distance of two supporting balls or the diameter of supporting ball are increased. In the result, some considerations are proposed for measurement of inner diameter by the three points supporting method.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 1998년도 춘계학술대회 논문집
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• pp.239-244
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• 1998

ESP(Electronic Speckle Pattern Interferometry) is an optical technique to measure deforamtion of engineering components and materials in industrial areas. ESPI, a non-contact and non-destructive measuring method, is capable of providing full-field results with high spatial resolution and high speed. One of important application aspects using electronic speckle pattern interferometry is to generate contours of a diffuse object in order to provide data for 3-D shape analysis and topography measurement. The electronic speckle contouring is suitable for providing measurement range from millimeters to several centimeters. In this study, we introduce the contouring method by modified dual-beam speckle pattern interferometer and a shift of the two illumination beams through optical fiber in order to obtain the contour fringe patterns. Before the experiments, we performed the geometric analysis for dual-beam-shifted ESPI contouring. And by this geometric analysis, we performed the electronic speckle contouring experiment. We used 4-frame phase shifting method with PZT for quantitative analysis of contour fringes. Finally, we showed good agreements between the geometric analysis and experimental results.

• 한국기계가공학회지
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• 제3권4호
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• pp.13-19
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• 2004

This paper deals with the analysis of geometric error and the optimization of process parameters in surface grinding. Taguchi method which is one of the design of experiments has been introduced in achieving the aims. The process parameters were the grain size, the wheel speed, the depth of cut and the table speed. The effect of the process parameters on the geometric error was examined and an optimal set of the parameters was selected to minimize the geometric error within the controllable range of the used grinding machine. The reliability of the results was evaluated by the ANOVA.

• 대한기계학회논문집
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• 제17권8호
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• pp.2051-2060
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• 1993

A finite element program using degenerated shell element was developed to solve the geometric, material and combined nonlinear behaviors of composite laminated shell. The total Lagrangian method was implemented for geometric nonlinear analysis. The material nonlinear behavior was analyzed by considering the matrix degradation due to the progressive failure in the matrix and matrix-fiber interface after initial failure. The result of the geometric nonlinear analysis showed good agreement with the other exact and numerical solutions. The results of the combined analyses considered both geometric and material nonlinear analyses were compared with the experiments in which internal pressure was applied to the filament wound antisymmetric tubes.

• 한국정밀공학회지
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• 제19권9호
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• pp.34-40
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• 2002

Machining accuracy is affected by quasi-static errors of machining center. Since machine errors have a direct influence upon both the surface finish and geometric shape of the finished workpiece, it is very important to measure the machine errors and to compensate these errors. The laser measurement method for identifying geometric errors of machine tool has the disadvantages such as high cost, long calibration time and usage of volumetric error synthesis model. Accordingly, this paper deals with analysis of the geometric errors of a machine tool using ball bar test without using complicated error synthesis model. Statistical analysis method was adopted in this paper for deriving geometric errors using hemispherical helix ball bar test. As a result of experiment, geometric errors of the vertical machining center are compensated by 88%.

• 전산구조공학
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• 제10권1호
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• pp.173-183
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• 1997

본 논문에서는 랜덤한 축대칭 기하학적 초기결함을 갖는 원통이 축방향 충격하중을 받는 경우의 반경방향 변위가 임계기준치를 최초로 통과하는 확률론적 충격좌굴 파괴시간을 해석할 수 있는 방법을 제시하였다. 랜덤한 기하학적 초기결함의 생성을 위해 초기결함의 평균함수 및 상관함수를 이용하여 확률장을 형성하는 방법을 사용하였다. 본 논문에서 제시된 방법은 실제적인 기하학적 초기결함이 갖는 불확실성을 취급하는데 적절하고 실용적이므로 이를 고려한 원통의 구조안전도해석에 이용할 수 있다.