• Proceedings of the KSME Conference
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• 2001.06a
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• pp.686-691
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• 2001

Structural optimization often require the evaluation of design sensitivities. The Semi Analytic method(SAM) is popular for shape optimization because this method has several advantages. But when relatively large rigid body motions are identified for individual elements, the SA method shows severe inaccuracy. In this paper, the improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes. Moreover, the error of the SA method caused by numerical difference scheme is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.2
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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.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05a
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• pp.131-136
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• 1996

An analytic nodal expansion method has been derived for the multigroup neutron diffusion equation in 2-D cylindrical(R-Z) coordinate. In this method we used the second order Legendre polynomials for source, and transverse leakage, and then the diffusion eqaution was solved analytically. This formalism has been applied to 2-D LWR model. $textsc{k}$$_{eff}$, power distribution, and computing time have been compared with those of ADEP code(finite difference method). The benchmark showed that the analytic nodal expansion method in R-Z coordinate has good accuracy and quite faster than the finite difference method. This is another merit of using R-Z coordinate in that the transverse integration over surfaces is better than the linear integration over length. This makes the discontinuity factor useless.s.

• Progress in Medical Physics
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• v.8 no.1
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• pp.75-82
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• 1997

The human physiological systems are so complex and irregular dynamics. Dynamics of peripheral blood vessel, in particular, have quite sensitive and complex. Before, the linear analytic method have been used to analyze the system. But, the method have many problems to predict the following results. In the other hand, the nonlinear analytic method, chaotic time series analysis method, is suitable for measuring complex, vary system. In this study, the scalar data of the blood flow of peripheral blood vessel of rabbits, in accordance with injection of glucose, was obtained and redefined as multi-dimensional vectors, with time-series analytic methods. This study also intended to confirm that the peripheral blood flow is chaotic dynamics and evaluate the availability of non-linear analytic method. As a result, the existing FFT, and mean could show the difference of blood flow of peripheral blood vessel by injection of glucose, but the nonlinear analytic method could show the definite difference. The hemodynamics is a chaotic phenomenon.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.37 no.1
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• pp.83-91
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• 2017

In case of estimation of settlement for the piled-raft foundation, it is necessary to consider interaction among raft, piles and soil. But, simple analytic methods usually are not applicable to considering this complicated interaction. In this study, a computer-based approximate analytic method, HDPR, was developed in consideration of above mentioned interaction in order to analysis of settlement for the piled-raft foundation. The finite element method was applied to raft analysis by means of the Mindlin plate theory, and soil and piles were modeled as springs which were connected with their raft. The linear spring which can consider multi layered soil and the non-linear spring were applied to soil springs and pile springs, respectively. The raft-piles-soil interaction was reflected to each spring. In order to verify the developed analytic method, it was compared and analyzed with 3D FEM analysis, existing approximate analytic method and site monitoring data. As a result, the developed analytic method showed reasonable results of settlement estimations of raft and piles for each case. From a practical point of view, it is confirmed that this analytic method is able to apply for analysis and design of the piled-raft foundation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.593-600
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• 2003

Structural optimization often requires the evaluation of design sensitivities. The Semi Analytic Method(SAM) fur computing sensitivity is popular in shape optimization because this method has several advantages. But when relatively large rigid body motions are identified for individual elements. the SAM shows severe inaccuracy. In this study, the improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes. Moreover. the error of the SAM caused by numerical difference scheme is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms. Finally the present study shows that the refined SAM including the iterative method improves the results of sensitivity analysis in dynamic problems.

• Transactions of the Korean Society of Automotive Engineers
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• v.7 no.5
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• pp.141-153
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• 1999

A finite element procedure for the analysis of rubber-like hyperelastic material is developed. The volumetric incompressiblity conditions of the rubber deformation is included in the formulation by using penalty method. In this paper, the behavior of the rubber deformation is represented by hyperelastic constitutive relations based on a generalized Mooney-Rivlin model. The principle of virtual work is used to derive nonlinear finite element equation for the large displacement problem and presented in total-Lagrangian description. The finite element procedure using analytic differentiation resulted in very close solution to the result of the well known commercial packages NISAII AND ABAQUS. Numerical tests show that the results from the numerical differentiation method coincide very well with those from the analytic method and the well known commercial packages in static analysis. The convergency of rubber usingν iteration method is also discussed.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.16 no.8
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• pp.683-690
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• 2004

A modified rectangular fin is analyzed by two-dimensional analytic method and finite difference method. Relative error of heat loss from the modified rectangular fin between analytic method and finite difference method is presented. Comparisons of fin effectiveness and heat loss between a modified rectangular fin and a plane rectangular fin are made as a function of the non-dimensional fin length and wing height for different positions of wings by using analytic method. The ratio of the incremental rate of heat loss to that of the area of a modified rectangular fin is shown as a function of the wing height. One of the results shows that performance of a modified fin is more improved as the wing approaches the fin root.

• Journal of Industrial Technology
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• v.8
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• pp.65-70
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• 1988

The intensity of ultrasound in liquid is calculated by improved analytic method. Helmholtz equation or Rayleigh's proposition does not offer the analytic solution. Considering a bounded medium, the use of the image source method in electromagnetic thoery gives a new way of calculating the total ultrasonic intensity in liquid. Some methods of measuring the intensities are also mentioned.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.12
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• pp.549-555
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• 2002

While the z-transform method is a basic mathematical tool to relate the imput/output signals only at the sampling instants in analyzing and designing sampled-data control systems, the modified z-transform which is a variation of the z-transform is widely used to represent the details of continuous signals between the sampling instants. To relate the modified z-transform to the corresponding regular z-transform, some properties were established regarding the modified z-transform method. This paper will show that these properties, in their current forms, cause come analytic problems, when they are applied to the signals with discontinuities at the sampling instants, which accordingly limit their applications significantly. In this paper, those analytic problems will be investigated, and the theorems of the modified z-transform will be revised by adopting new notations on the z-transform so that those can be correctly interpreted and used without any analytic problems. Also some additional useful schemes of applying the modified z-transform will be developed.