• Journal of Power Electronics
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• v.10 no.6
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• pp.680-685
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• 2010

Although LLC resonant converters have the advantages of a wide operation range and high efficiency, the lack of an analytical solution for the peak gain makes it difficult to optimize the resonant tank design, when considering not only the normal condition but also the holdup time requirement. In this paper, based on a mathematical analysis of a LLC resonant converter at the peak gain point, an analytical solution for the peak gain has been developed. By using the developed analytical solution, the peak gain with given resonant tank parameters can be obtained. To confirm the validity of the developed analytical solution, simulations and experimental results are compared.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.905-908
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• 2009

In the management of groundwater in coastal areas, saltwater intrusion associated with extensive groundwater pumping, is an important problem. The groundwater optimization model is an advanced method to study the aquifer and decide the optimal pumping rates or optimal well locations. Cheng and Park gave the analytical solutions to the optimization problems basing on Strack's analytical solution. However, the analytical solutions have some limitations of the property of aquifer, boundary conditions, and so on. A simulation-optimization numerical method presented in this study can deal with non-homogenous aquifers and various complex boundary conditions. This simulation-optimization model includes the sharp interface solution which solves the same governing equation with Strack's analytical solution, therefore, the freshwater head and saltwater thickness should be in the same conditions, that can lead to the comparable results in optimal pumping rates and optimal well locations for both of the solutions. It is noticed that the analytical solutions can only be applied on the infinite domain aquifer, while it is impossible to get a numerical model with infinite domain. To compare the numerical model with the analytical solutions, calculation of the equivalent boundary flux was planted into the numerical model so that the numerical model can have the same conditions in steady state with analytical solutions.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.458-463
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• 2000

The mechanical structures generally have discontinuous parts such as the cracks, notches and holes owing to various reasons. In this paper, in order to analyze effectively these singularity problems using the finite element method, a mixed analysis method which an analytical solution and finite element solutions are simultaneously used is newly proposed. As the analytical solution is used in the singularity region and the finite element solutions are used in the remaining regions except this singular zone, this analysis method reasonably provides for the numerical solution of a singularity problem. Through various numerical examples, it is shown that the proposed analysis method is very convenient and gives comparatively accurate solution.

• Geomechanics and Engineering
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• v.28 no.3
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• pp.225-237
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• 2022

Settlement evaluation is important for shallow tunnels in big cities to estimate the settlement that occurs due to the excavation of twin tunnels. The majority of earlier research on analytical solutions, on the other hand, concentrated on calculating the settlement for a single tunnel. This research introduces a procedure to evaluate the settlement induced by the excavation of twin tunnels (two parallel tunnels). In this study, a series of numerical analysis were performed to validate the analytical solution results. Two geological conditions were considered to derive the settlement depending on each case. The analytical and numerical methods were compared, which involved considering many sections and conducting a parametric study; the results have good agreement. Moreover, a comparison of the 3D flat model and 2D (FEM) with the analytical solution shows that in the fill soil, the maximum settlement values were obtained by the analytical solution. In contrast, the values obtained by the analytical solution in the rock is more conservative than those in the fill. Finally, this method was shown to be appropriate for twin tunnels dug side by side by utilizing finite element analysis 3D and 2D (PLAXIS 3D and PLAXIS 2D) to verify the analytical equations. Eventually, it will be possible to use this approach to predict settlement troughs over twin tunnels.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2001.09a
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• pp.79-82
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• 2001

Analytical solutions have been derived to delineate the capture zone created by pumping wells for the remediation design of contaminated groundwater. These previous analytical solutions are often restricted to pumping wells only, specific well locations, a limited number of wells, and an isotropic aquifer. Analytical solution was developed to deal with arbitrarily located multi injection-pumping wells in an anisotropic homogeneous aquifer. The solution presented in this study provides a simple, easy method for determining tile complex flow field caused by multi injection-pumping wells at different rates, and will consequently be useful in pump-and-treat design.

• Journal of the Korean Society of Hazard Mitigation
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• v.11 no.3
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• pp.111-116
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• 2011

Analytical solutions for laterally loaded piles were derived. Critical pile length which can be considered as the length for behaving as long pile was investigated varying with densities of sandy soils. Lateral behaviors obtained from analytical solution and numerical solution were also investigated. Non-dimensional critical pile lengths obtained from analytical solutions for three types of pile head boundary conditions were 2.3~3.2. By comparing analytical solutions with numerical solutions, distribution of pile deflection and that of moment were similar and it can be seen that pile head deflection obtained by analytical method is conservative. And the values of moments were not too different between analytical solution and numerical solution.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.3
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• pp.228-236
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• 2007

An analytical solution for long waves propagating over an asymmetric trench is derived. The water depth inside the trench varies in proportion to a power of distance from the center of the trench. The mild-slope equation, governing equation, is transformed into second order ordinary differential equation with variable coefficients by using the long wave assumption and then the analytical solution is obtained by using the power series technique. The analytical solution is confirmed by comparison with the numerical solution. After calculating the analytical solution under various conditions, the results are analyzed.

• Geomechanics and Engineering
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• v.13 no.6
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• pp.1027-1044
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• 2017

Membrane penetration is the most important factor influencing the measurement of volume change for triaxial consolidated-drained shear test for coarse-grained soil. The effective pressure p, average particle size $d_{50}$, thickness $t_m$ and elastic modulus $E_m$ of membrane, contact area between membrane and soil $A_m$ as well as the initial void ratio e are the major factors influencing membrane penetration. According to the membrane deformation model given by Kramer and Sivaneswaran, an analytical solution of the membrane penetration considering the initial void ratio is deduced using the energy conservation law. The basic equations from theory of plates and shells and the elastic mechanics are employed during the derivation. To verify the presented solution, isotropic consolidation tests of a coarse-grained soil are performed by using the method of embedding different diameter of iron rods in the triaxial samples, and volume changes due to membrane penetration are obtained. The predictions from presented solution and previous analytical solutions are compared with the test results. It is found that the prediction from presented analytical solution agrees well with the test results.

• Geotechnical Engineering
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• v.13 no.2
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• pp.169-184
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• 1997

A semi -analytical solution is derived to solve the elastic-plastic behavior of the axisymmetric tunnels in Drucker-Prager medium. Based on this analytical solution, a computer program FDAXP. is developed. Parametric studies are carried out to verify the FDAXP program, and the results were found to be satisfactory. This simple solution could be incorporated into the preliminary design, analysis of deep underground tunnel as well as tunnels with unfavourable geotechnical conditions. The program provided a useful means of checking the Drucker-Eraser model and iris associated computational algorithms in other tunnel programs.

• Structural Engineering and Mechanics
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• v.38 no.5
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• pp.549-571
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• 2011

This paper presents analytical solutions for skewed thick plates under transverse loading that have previously been unreported in the literature. The thick plate solution is obtained in a framework of an oblique coordinate system. The governing equation is first derived in the oblique coordinate system, and the solution is obtained using deflection and rotation as partial derivatives of a potential function developed in this research. The solution technique is applied to three illustrative application examples, and the results are compared with numerical solutions in the literature and those derived from the commercial finite element analysis package ANSYS 11. These results are in excellent agreement. The present solution may also be used to model skewed structures such as skewed bridges, to facilitate efficient routine design or evaluation analyses, and to form special elements for finite element analysis. At the same time, the analytical solution developed in this research could be used to develop methods to address post-buckling and dynamic problems.