• 한국도로학회논문집
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• 제18권3호
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• pp.21-32
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• 2016

PURPOSES : In this paper, the analytical solutions suggested to simulate the behavior of rheological fluids were rigorously re-derived and investigated for fixed conditions to evaluate the applicability for the solutions on a mini-cone slump test of cement paste. The selected solutions with proper boundary conditions can be used as reference solutions to evaluate the performance of numerical simulation approaches, such as the discrete element method. METHODS : The slump, height, and spread radius for the given boundary and yield stress conditions that are determined by five different analytical solutions are compared. RESULTS : The analytical solution based on fluid mechanics for pure shear flow shows similar results to that for intermediate flow at low yield stresses. The fluid mechanics-based analytical solution resulted in a very similar trend to the geometry-based analytical solution. However, it showed a higher slump at high yield stress and lower slump at low yield stress ranges than the geometry-based analytical model. The analytical solution based on the mini-cone geometry was not significantly affected by the yield criteria, such as von Mises and Tresca. CONCLUSIONS : Even though differences among the analytical solutions in terms of slump and spread radius existed, the difference can be considered insignificant when the solutions were used as reference to evaluate the appropriateness of numerical approaches, such as the discrete element method.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2009년도 학술발표회 초록집
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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.

• 전기학회논문지
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• 제61권8호
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• pp.1115-1122
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• 2012

This paper analyzes eddy-current loss induced in magnets of surface-mounted permanent magnet (SPM) machines by using an analytical method such as a space harmonic method. First, on the basis of a two-dimensional (2D) polar coordinate system and a magnetic vector potential, the analytical solutions for the flux density produced by armature winding current are obtained. By using derived field solutions, the analytical solutions for eddy current density distribution are also obtained. Finally, analytical solutions for eddy current loss induced in rotor magnets are derived by using equivalent electrical resistance calculated from magnet volume and analytical solutions for eddy-current density distribution. In particular, the influence of time harmonics in armature current on the eddy current loss is fully investigated and discussed. All analytical results are validated extensively by finite element analysis (FEA).

• Structural Engineering and Mechanics
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• 제86권1호
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• pp.69-83
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• 2023

Analytical solutions to problems are crucial because they provide high-quality comparison data for assessing the accuracy of numerical solutions. Benchmark analytical solutions for the vibrations of cracked functionally graded material (FGM) plates are not available in the literature because of the high level of complexity of such solutions. On the basis of first-order shear deformation plate theory (FSDT), this study proposes analytical series solutions for the vibrations of FGM rectangular plates with side or internal cracks parallel to an edge of the plates by using Fourier cosine series and the domain decomposition technique. The distributions of FGM properties along the thickness direction are assumed to follow a simple power law. The proposed analytical series solutions are validated by performing comprehensive convergence studies on the vibration frequencies of cracked square plates with various crack lengths and under various boundary condition combinations and by performing comparisons with published results based on various plate theories and the theory of three-dimensional elasticity. The results reveal that the proposed solutions are in excellent agreement with literature results obtained using the Ritz method on the basis of FSDT. The paper also presents tabulations of the first six nondimensional frequencies of cracked rectangular Al/Al2O3 FGM plates with various aspect ratios, thickness-to-width ratios, crack lengths, and FGM power law indices under six boundary condition combinations, the tabulated frequencies can serve as benchmark data for assessing the accuracy of numerical approaches based on FSDT.

• Journal of Electrical Engineering and Technology
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• 제2권2호
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• pp.221-230
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• 2007

This paper deals with analytical prediction for electromagnetic characteristics of a tubular linear actuator with Halbach array using transfer relations, namely, Melcher's methodology. Using transfer relations derived in terms of magnetic vector potential and a two-dimensional (2-d) cylindrical coordinate system, this paper derives analytical solutions for magnetic vector potential due to permanent magnets (PMs) and stator winding currents. On the basis of these analytical solutions, this paper also achieves analytical solutions for the magnetic fields distribution produced by PMs, stator windings current and axial thrust. The analytical results are validated extensively by finite element (FE) analyses. In particular, test results such as thrust measurements are given to confirm the analysis. Finally, this paper estimates control parameters using analytical solutions and test results such as thrust, back-emf, inductance and resistance measurements.

• Journal of Magnetics
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• 제19권1호
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• pp.84-89
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• 2014

This paper presents an analytical prediction and experimental verification of the electromagnetic performance of a parallel magnetized surface-mounted permanent magnet (SPM) motor having a fractional number of slots per pole combination. On the basis of a two-dimensional (2-D) polar coordinate system and a magnetic vector potential, analytical solutions for flux density produced by the permanent magnets (PMs) and stator windings are derived. Then, analytical solutions for back-electromotive force (emf) and electromagnetic torque are derived from these field solutions. The analytical results are thoroughly validated with 2-D nonlinear finite element (FE) analysis results. Finally, the experimental back-emf and electromagnetic torque measurements are presented to test the validity of the analysis.

• Journal of Electrical Engineering and Technology
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• 제9권3호
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• pp.926-931
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• 2014

This paper presents the torque calculation and parametric analysis of synchronous permanent magnet couplings (SPMCs). Based on a magnetic vector potential, we obtained the analytical magnetic field solutions produced by permanent magnets (PMs). Then, the analytical solutions for a magnetic torque were obtained. All analytical results were extensively validated with the non-linear a two-dimensional (2D) finite element analysis (FEA). In particular, test results such as torque measurements are presented that confirm the analysis. Finally, using the derived analytical magnetic torque solutions, we carried out a parametric analysis to determine the influence of the design parameters on the SPMC's behavior.

• 자원환경지질
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• 제53권1호
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• pp.11-21
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• 2020

본 연구는 대수층과 저투수층이 존재하는 단일시스템에서 trichloroethylene (TCE)과 tetrachloroethylene (PCE)의 거동에 대해 1차원 확산 해석해를 사용하여 저투수층의 농도 분포, 대수층과 저투수층의 경계면에서 확산 선속, 그리고 역확산에 의한 대수층의 오염 지속성을 모델링하였다. 모델링에 사용된 해석해는 이전 연구에서 많이 사용되었던 저투수층의 두께가 무한한 조건의 해석해와 본 연구에서 제시한 저투수층의 두께가 유한한 조건을 고려한 해석해를 모두 사용하였다. 제시된 해석해의 타당성을 평가하기 위해 저투수층의 두께가 무한한 조건의 해석해와 Yang et al.(2015)이 개발한 1차원 확산 해석해의 결과를 Nash-Sutcliffe 유효계수(NSE)로 비교하였다. 저투수층의 농도 분포, 확산 선속, 그리고 대수층의 오염 지속성 등 모든 결과에서 무한한 조건의 해석해를 이용하였을 때 과소평가되는 결과를 나타내었다. 그리고 본 연구에서 제시한 해석해의 결과와 Yang et al. (2015)이 개발한 해석해의 결과는 높은 일치성(NSE = 0.99)을 보였다. 본 연구에서 제시한 해석해를 실제 오염된 부지에 효율적으로 적용하기 위해 유효확산계수, 저투수층의 두께, 그리고 확산된 시간을 이용하여 확산 거리(Z_d)라는 용어를 소개하였다. 확산 거리가 0.7 보다 작은 경우 저투수층의 두께가 무한한 조건의 해석해를 사용할 수 있으며, 확산 거리가 0.7 보다 큰 경우 저투수층의 두께가 유한한 확산 해석해를 사용하여야 모델링의 신뢰성을 높일 수 있을 것으로 사료된다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집B
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• pp.57-64
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• 2000

The present work investigates the heat transfer characteristics for laminar fully developed forced convection in an internally finned tube with axially uniform heat flux and peripherally uniform temperature through analytical models of convection in a porous medium. Using the Brinkman-extended Darcy flow model and the two equation model fur heat transfer, analytical solutions fur fluid flow and heat transfer are obtained and compared with the exact solution for fluid flow and the numerical solutions for conjugate heat transfer to validate the porous medium approach. Using the analytical solutions, parameters of engineering importance are identified and their effects on fluid flow and heat transfer are studied. Also, the expression fur total thermal resistance is derived from the analytical solutions and minimized in order to optimize the thermal performance of the internally finned tubes.

• Structural Engineering and Mechanics
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• 제56권3호
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• pp.461-472
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• 2015

In this paper, the nonlinear static response of curled cantilever beam actuators subjected to the one-sided electrostatic field is focused on. By assuming the deflection function of electrostatically actuated beam, analytical approximate solutions are established via using Galerkin method to solve the equilibrium equation. The Pull-In voltages which determine the stability of the curled beam actuators are also obtained. These approximate solutions show excellent agreements with numerical solutions obtained by the shooting method and the experimental data for a wide range of beam length. Expressions of these analytical approximate solutions are brief and could easily be used to derive the effects of various physical parameters on MEMS structures.