• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.3
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• pp.251-260
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• 2003

A three dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of deep, tapered rods and beams with circular cross section. Unlike conventional rod and beam theories, which are mathematically one-dimensional (1-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sup r/, u/sub θ/ and u/sub z/, in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in , and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the rods and beams are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rods and beams. Novel numerical results are tabulated for nine different tapered rods and beams with linear, quadratic, and cubic variations of radial thickness in the axial direction using the 3D theory. Comparisons are also made with results for linearly tapered beams from 1-D classical Euler-Bernoulli beam theory.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.2 no.2
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• pp.39-46
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• 1982

A model of substrate removal by rotating discs has been developed for a better understanding of the process, and the performance of the system has been evaluated under steady and unsteady state. The model was constructed based upon mass transfer of the substrate from the bulk solution to the biofilm and a simultaneous removal of the substrate by the biomass. The model is composed of a few sets of differential equations representing mass balance within the elements of a liquid film and a biofilm, and in the bulk solution. Substrate removal efficiency of the process is largely dependent on a diffusion coefficient of the substrate within the biofilm and a maximum rate of substrate removal of the biomass. The efficiency is affected to a greater extent when the substrate concentration is low and the maximum substrate removal rate is high. The efficiency increases proportionally with increasing film depth when the biofilm is shallow, however, the rate of increase gradually decreases with an increase of the film depth. As the film reaches a limiting depth, the efficiency remains constant. Unlike the steady state, the effluent quality is affected by the tank volume under dynamic state. Increasing tank volume decreases peak concentration of the effluent under peak loading. Additional tank volume provides a buffer capacitya.gainst a peak loading and the holding tank behaves like an equalization tank.

• Journal of the Korea Concrete Institute
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• v.15 no.2
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• pp.225-233
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• 2003

Even though a lot of advanced researches on analysis, design, and performance evaluation of reinforced concrete (RC) under seismic action have been carried out, there has been only a few study on seismic analysis of underground RC structures surrounding soil medium. Since the underground RC structures interact with surrounding soil medium, a path-dependent soil model which can predict the soil response is necessary for analyzing behavior of the structure inside soil medium. The behavior of interfacial zone between the RC structure and the surrounding medium should be also considered for more accurate seismic analysis of the RC structure. In this paper, an averaged constitutive model of concrete and reinforcing bars for RC structure and path-dependent Ohsaki's model for soil are applied, and an elasto-plastic interface model having thickness is proposed for seismic analysis of underground RC structures. A finite element analysis technique is developed by applying aforementioned constitutive equations and is verified by predicting both static and dynamic behaviors of RC structures. Then, failure mechanisms of underground RC structure under seismic action are numerically derived through seismic analysis of underground RC station structure under different seismic forces. Finally, the changes of failure mode and the damage level of the structures are also analytically derived for different design cases of underground RC structures.

• KSTLE International Journal
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• v.7 no.2
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• pp.27-34
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• 2006

Knudsen number is the ratio of molecular mean free path versus mm thickness and the criterion to determine the flow form. When its value is lower than 0.01, the flow can be assumed to has no slip boundary condition. And in the case that the value is between 0.01 and 10, then the flow has slip boundary condition at both the adjacent walls. The condition of the air flow between the rotating journal and top foil in the air foil bearing is determined by the rotating speed and load, and the Knudsen number is also varied by those values. Because the molecular mean free path is variable to the pressure and temperature, more exact formulation is necessary to understand and analyze the flow regime. In this study, the analysis considering Knudsen number formulated with those variables (pressure, temperature and mm thickness) was executed. The approximate value was examined using the equation to confirm whether the flow has the slip or no-slip boundary condition. From the analytic investigation, it was decided to range approximately 0.01 to 1.0 and the flow can be supposed to have the slip boundary condition. Under the condition of the slip flow, the static characteristics of the air foil bearing were examined using modified Reynolds equations. The results were compared with those considering no slip condition. It shows that the slip condition makes the flow decelerates and the load carrying capacity decreases compared with no slip condition. And as the bearing number and eccentricity ratio increase, the load carrying capacity also increased at both the cases. From this result, it can be supposed that the bearing torque also increases. In the analysis of the dynamic characteristics, the perturbed Knudsen number was taken into consideration. Because the Knudsen number is expressed as the terms of each variable, the perturbed equation can be simply derived. The results of both cases considering and not considering Knudsen number were compared each other. In the case of the direct terms of the stiffness and damping coefficients, the difference between both cases was little and increased as the bearing number and eccentricity ratio increased. And the cross terms have less or more differences.

• Journal of Biomedical Engineering Research
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• v.20 no.2
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• pp.173-182
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• 1999

Contrast-enhanced CT has an important role in assessing liver lesions, the optimal protocol to get most effective result is not clear. The mein goal when deciding injention protocol is to optimize lesion detectability with rapid scanning when lesion to liver contrast is maximum. For this purpose, we developed a physiological model of the contrast medium enhancement based on the compartment modeling and pharmacokinetics. Blood supply to liver is achieved in two paths. This dual supply characteristic distinguishes the CT enhancement of liver from that of the other organs. The first path is by hepatic artery and to second, by portal vein. However, it is assumed that only gepatic artery can supply blood to hepatocellular carcinoma(HCC) compartment, thus, the difference of contrast enhancement is resulted between normal liver tissue and hepatic tumor. By solving differential equations for each compartment simultaneously using the computer program Matlab, CT contrast-enhancement curves were simulated. The simulated enhancement curves for aortic, hepatic, portal vein, and HCC compartments were compared with the mean enhancement curves from 24 patients exposed to the same protocols as the simulation. These enhancement curves showed a good agreement. Furthermore, we simulated lesion-to-liver curves for various injection protocols, and the effects were analyzed. The variables to be considered in the injection protocol were injection rate, dose, and concentration of contrast material. These data may help to optimize scanning protocols for better diagnosis.

• Journal of the Society of Naval Architects of Korea
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• v.33 no.3
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• pp.35-47
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• 1996

A surface panel method treating a boundary-value problem of the Dirichlet type is presented to design a three dimensional body with free surface corresponding to a prescribed pressure distribution. An integral equation is derived from Green's theorem, giving a relation between total potential of known strength and the unknown local flux. Upon discretization, a system of linear simultaneous equations is formed including free surface boundary condition and is solved for an assumed geometry. The pseudo local flux, present due to the incorrect positioning of the assumed geometry, plays a role f the geometry corrector, with which the new geometry is computed for the next iteration. Sample designs for submerged spheroids and Wigley hull and carried out to demonstrate the stable convergence, the effectiveness and the robustness of the method. For the calculation of the wave resistance, normal dipoles and Rankine sources are distributed on the body surface and Rankine sources on the free surface. The free surface boundary condition is linearized with respect to the oncoming flow. Four-points upwind finite difference scheme is used to compute the free surface boundary condition. A hyperboloidal panel is adopted to represent the hull surface, which can compensate the defects of the low-order panel method. The design of a 5500TEU container carrier is performed with respect to reduction of the wave resistance. To reduce the wave resistance, calculated pressure on the hull surface is modified to have the lower fluctuation, and is applied as a Dirichlet type dynamic boundary condition on the hull surface. The designed hull form is verified to have the lower wave resistance than the initial one not only by computation but by experiment.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.2
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• pp.119-129
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• 2004

A three dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular and annular plates with nonlinear thickness variation along the radial direction. Unlike conventional plate theories, which are mathematically two dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components u/sub s/, u/sub z/, and u/sub θ/ in the radial, thickness, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the s and z directions. Potential (strain) and kinetic energies of the plates are formulated, and the Ritz method is used to solve the eigenvalue problem thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the plates. Numerical results we presented for completely free, annular and circular plates with uniform linear, and quadratic variations in thickness. Comparisons are also made between results obtained from the present 3D and previously published thin plate (2D) data.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.4
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• pp.419-429
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• 2003

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of thick, hyperboloidal shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sub r/, u/sub θ/, u/sub z/ in the radial, circumferential, and axial directions, respectively, we taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z directions. Potential(strain) and kinetic energies of the hyperboloidal shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the hyperboloidal shells of revolution. Numerical results are tabulated for eighteen configurations of completely free hyperboloidal shells of revolution having two different shell thickness ratios, three variant axis ratios, and three types of shell height ratios. Poisson's ratio (ν) is fixed at 0.3. Comparisons we made among the frequencies for these hyperboloidal shells and ones which ate cylindrical or nearly cylindrical( small meridional curvature. ) The method is applicable to thin hyperboloidal shells, as well as thick and very thick ones.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.6
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• pp.529-538
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• 2016

The simplified plate theory is presented for static and free vibration analysis of power-law(P) and sigmoid(S) Functionally Graded Materials(FGM) plates. This theory considers the parabolic distribution of the transverse shear stress, and satisfies the condition that requires the transverse shear stress to be zero on the upper and lower surfaces of the plate, without the shear correction factor. The simplified plate theory uses only four unknown variables and shares strong similarities with classical plate theory(CPT) in many aspects such as stress-resultant expressions, equation of motion and boundary conditions. The material properties of the plate are assumed to vary according to the power-law and sigmoid distributions of the volume fractions of the constituents. The Hamilton's principle is used to derive the equations of motion and Winkler-Pasternak elastic foundation model is employed. The results of static and dynamic responses for a simply supported FGM plate are calculated and a comparative analysis is carried out. The results of the comparative analysis with the solutions of references show relevant and accurate results for static and free vibration problems of FGM plates. Analytical solutions for the static and free vibration problems are presented so as to reveal the effects of the power law index, elastic foundation parameter, and side-to-thickness ratio.

• Journal of Korea Water Resources Association
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• v.45 no.1
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• pp.39-52
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• 2012

Surface-subsurface interactions are an intrinsic component of the hydrologic response within a watershed. In general, these interactions are considered to be one of the most difficult areas of the discipline, particularly for the modeler who intends simulate the dynamic relations between these two major domains of the hydrological cycle. In essence, one major complexity is the spatial and temporal variations in the dynamically interacting system behavior. The proper simulation of these variations requires the need for providing an appropriate coupling mechanism between the surface and subsurface components of the system. In this study, an approach for modelling surface-subsurface flow and transport in a fully intergrated way is presented. The model uses the 2-dimensional diffusion wave equation for sheet surface water flow, and the Boussinesq equation with the Darcy's law and Dupuit-Forchheimer's assumption for variably saturated subsurface water flow. The coupled system of equations governing surface and subsurface flows is discretized using the finite volume method with central differencing in space and the Crank-Nicolson method in time. The interactions between surface and subsurface flows are considered mass balance based on the continuity conditions of pressure head and exchange flux. The major module consists of four sub-module (SUBFA, SFA, IA and NS module) is developed.