• 대한화학회지
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• 제22권3호
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• pp.128-132
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• 1978

산화환원 전위차 적정에 있어, 수치미분법으로 얻은 적정곡선의 2차 미분이 0이 되는 점을 얻어 종말점으로 삼을 때, 그 오차의 성격을 전자계산기를 사용하여 계산하였다. 그 결과로부커 당량점이 포함되는 시약첨가량의 어느 부분에 당량점이 존재하는 가에 따라 종말점의 오차가 변화함을 알 수 있다. 오차는 그 중심점에서 당량점이 벗어남에 따라 증가하여 최대 오차는 첨가량의 약 1/2이다. 따라서 수치미분법으로 영 2차미분점을 얻는 경우에는 적정곡선의 최대 기울기의 점을 얻어 두 값을 비교해 보는 것이 바람직스럽다. 또 종말점 부근에서는 묽은 시약을 사용하여 적정하는 방법으로 오차를 작게 할 수 있다.

• Journal of Mechanical Science and Technology
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• 제19권spc1호
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• pp.350-356
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• 2005

A method of dynamic analysis of mechanical systems considering probabilistic properties is proposed in this paper. Probabilistic properties that result from manufacturing tolerances can be represented by means and standard deviations (or variances). The probabilistic characteristics of dynamic responses of constrained multi-body systems are obtained by two ways : the proposed analytical approach and the Monte Carlo simulation. The formerpaper, necessitates sensitivity information to calculate the standard deviations. In this a direct differentiation method is employed to find the sensitivities of constrained multi-body systems. To verify the accuracy of the proposed method, numerical examples are solved and the results obtained by using the proposed method are compared to those obtained by Monte Carlo simulation.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 봄 학술발표회논문집
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• pp.177-186
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• 2000

An improved multi-level（IML) optimization algorithm using automatic differentiation (AD) for multi-objective optimum design of framed structures is proposed in this paper. In order to optimize the steel frames under seismic load, two main objective functions need to be considered for minimizing the structural weight and maximizing the strain energy. For the efficiency of the proposed algorithm, multi-level optimization techniques using decomposition method that separately utilizes both system-level and element-level optimizations and an artificial constraint deletion technique are incorporated in the algorithm. And also to save the numerical efforts, an efficient reanalysis technique through approximated structural responses such as moments, frequencies, and strain energy with respect to intermediate variables is proposed in the paper. Sensitivity analysis of dynamic structural response is executed by AD that is a powerful technique for computing complex or implicit derivatives accurately and efficiently with minimal human effort. The efficiency and robustness of the IML algorithm, compared with a plain multi-level (PML) algorithm, is successfully demonstrated in the numerical examples.

• Smart Structures and Systems
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• 제19권4호
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• pp.431-439
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• 2017

This investigation is aimed to develop a model of experimental-computation determination of a support moment of a cantilever beam loaded with concentrated force at its end including the optimal choice of coordinates of deflection data points and parameters of transformation of deflection data in case of insufficient accuracy of the assignment of initial parameters (support settlement, angle of rotation of the bearing section) and cantilever beam length. The influence of distribution and characteristics of sensors on the cantilever beam on the accuracy of determining the support moment which improves in the course of transition from the uniform distribution of sensors to optimal non-uniform distribution is shown. On the basis of the theory of inverse problems the method of transformation reduction at numerical differentiation of deflection functions has been studied. For engineering evaluation formulae of uncertainty estimate to determine a support moment of a cantilever beam at predetermined uncertainty of measurements using sensors have been obtained.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.523-538
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• 1999

A new preconditioning method is investigated to reduce the roundoff error in computing derivatives using Chebyshev col-location methods(CCM). Using this preconditioning causes ration of roundoff error of preconditioning method and CCm becomes small when N gets large. Also for accuracy enhancement of differentiation we use a domain decomposition approach. Error analysis shows that for this domain decomposition method error reduces proportional to the length of subintervals. Numerical results show that using domain decomposition and preconditioning simultaneously gives super accu-rate approximate values for first derivative of the function and good approximate values for moderately high derivatives.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1992년도 하계학술대회 논문집 B
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• pp.567-569
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• 1992

Design sensitivity analysis is proposed for the optimal shape design of three dimensional magnetostatic problems. The direct differentiation method is introduced for design sensitivity analysis and the boundary element method with reduced magnetic scalar potential as the state variable is used to analyze the magnetic characteristics. In the direct differentiation method, the design sensitivity, defined as the total derivative of the objective function with respect to the design variables, is calculated based on the variation of the state variable with respect to the design variable. And the variation of He state variable is calculated by differentiating the both sides of the system matrix equation obtained by applying boundary element method. Through the numerical example with simple electromagnet, the usefullness is proved.

• 대한기계학회논문집A
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• 제20권5호
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• pp.1458-1467
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• 1996

A direct differentiationmethod is presented for the shape design sensitivity analysis of axisymmeetric elastic solids. Based on the exisymmetric boundary integralequaiton formulation, a new boundary ntegral equatio for sensitivity analysis is derived by taking meterial derivative to the same integral identity that was used in the adjoint variable melthod. Numerical implementation is performed to show the applicaiton of the theoretical formulation. For a simple example with analytic solution, the sensitivities by present method are compared with analytic sensitivities. As an application to the shape optimization, an optimal shape of a gas turbine disc toinimize the weight under stress constraints is found by incorporating the sensitivity analysis algorithm in an optimizatio program.

• 대한전기학회논문지
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• 제41권8호
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• pp.850-857
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• 1992

Design sensitivity analysis is proposed for the optimal shape design of three-dimensional magnetostatic problems. The direct differentiation method is introduced for design sensitivity analysis and the boundary element method with reduced magnetic scalar potential as the state variable is used to analyze the magnetic characteristics. In the direct differentiation method, the design sensitivity, defined as the total derivative of the objective function with respect to the design variables, is calculated based on the variation of the state variable with respect to the design variable. And the variation of the state variable is calculated by differetiating the both sides of the system matrix equation obtained by applying boundary element method. Through the numerical example with simple electromagnet, the usefulness is proved.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.418-423
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• 2008

Among various sensitivity evaluation techniques, semi-analytical method is quite popular since this method is more advantageous than analytical method and global finite difference method. However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, the adjoint variable method combined with complex variable is proposed to obtain the shape and size sensitivity for structural optimization. The complex variable can present accurate results regardless of the perturbation size as well as easy to be implemented. Through a few numerical examples of the static problem for the structural sensitivity, the efficiency and reliability of the adjoint variable method combined with complex variable is demonstrated.

• Interaction and multiscale mechanics
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• 제2권4호
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• pp.333-352
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• 2009

We introduce a radial basis collocation method to solve axially moving beam problems which involve $2^{nd}$ order differentiation in time and $4^{th}$ order differentiation in space. The discrete equation is constructed based on the strong form of the governing equation. The employment of multiquadrics radial basis function allows approximation of higher order derivatives in the strong form. Unlike the other approximation functions used in the meshfree methods, such as the moving least-squares approximation, $4^{th}$ order derivative of multiquadrics radial basis function is straightforward. We also show that the standard weighted boundary collocation approach for imposition of boundary conditions in static problems yields significant errors in the transient problems. This inaccuracy in dynamic problems can be corrected by a statically condensed semi-discrete equation resulting from an exact imposition of boundary conditions. The effectiveness of this approach is examined in the numerical examples.