• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.311-334
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• 2020

The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that arises in the elliptic interface problems are very complex. In this article we propose an exponentially accurate nonconforming spectral element method for these problems based on [7, 18]. A geometric mesh is used in the neighbourhood of the singularities and the auxiliary map of the form z = ln ξ is introduced to remove the singularities. The method is essentially a least-squares method and the solution can be obtained by solving the normal equations using the preconditioned conjugate gradient method (PCGM) without computing the mass and stiffness matrices. Numerical examples are presented to show the exponential accuracy of the method.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.309-320
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• 2010

With taking the geometric nonlinearity of bridge structure into account, a framework is presented for predicting the dynamic responses of a long-span suspension bridge subjected to running train and turbulent wind. The nonlinear dynamic equations of the coupled train-bridge-wind system are established, and solved with the Newmark numerical integration and direct interactive method. The corresponding linear and nonlinear processes for solving the system equation are described, and the corresponding computer codes are written. The proposed framework is then applied to a schemed long-span suspension bridge with the main span of 1120 m. The whole histories of the train passing through the bridge under turbulent wind are simulated, and the dynamic responses of the bridge are obtained. The results demonstrate that the geometric nonlinearity does not influence the variation tendency of the bridge displacement histories, but the maximum responses will be changed obviously; the lateral displacement of bridge are more sensitive to the wind than the vertical ones; compared with wind velocity, train speed affects the vertical maximum responses a little more clearly.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.3
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• pp.415-425
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• 1996

This study presents an analytical method of solving the behaviors of arc plasma in a nozzle constricting transferred-type torch and purposes to obtain the basic data for the design of a plasma torch, which can be obtained from the temperature, pressure, velocities and voltage distributions. We have to solve some conservation equations simultaneously and need to know the exact thermal gas properties in order to obtain the correct behaviors of arc plasma. It is also necessary to give the relevant physical or geometric boundary conditions. For the simplicity of analysis, we assumed that (a) the plasma flow is laminar, (b)the local thermodynamic equilibrium, i.e. LTE, prevails over the entire arc column region. The electrode sheath effects were neglected and the nozzle area was excluded from the analysis by assuming that the current flow into the nozzle is zero. We solved the momentum transfer equation including the self-magnetic pinch effect, and obtained the temperature distribution from the energy conservation equation. From this temperature, we could get arc voltage distribution. (author). refs., figs., tabs.

• Korean Journal of Computational Design and Engineering
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• v.12 no.5
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• pp.330-343
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• 2007

In this paper, we present a new surface content completion system that can effectively repair both shape and appearance from scanned, incomplete point set inputs. First, geometric holes can be robustly identified from noisy and defective data sets without the need for any normal or orientation information. The geometry and texture information of the holes can then be determined either automatically from the models' context, or manually from users' selection. After identifying the patch that most resembles each hole region, the geometry and texture information can be completed by warping the candidate region and gluing it onto the hole area. The displacement vector field for the exact alignment process is computed by solving a Poisson equation with boundary conditions. Out experiments show that the unified framework, founded upon the techniques of deformable models and PDE modeling, can provide a robust and elegant solution for content completion of defective, complex point surfaces.

• Structural Engineering and Mechanics
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• v.43 no.5
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• pp.583-605
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• 2012

This paper presents a spatial catenary cable element for the nonlinear analysis of cable-supported structures. An incremental-iterative solution based on the Newton-Raphson method is adopted for solving the equilibrium equation. As a result, the element stiffness matrix and nodal forces are determined, wherein the effect of self-weight and pretension are taken into account. In the case of the initial cable tension is given, an algorithm for form-finding of cable-supported structures is proposed to determine precisely the unstressed length of the cables. Several classical numerical examples are solved and compared with the other available numerical methods or experiment tests showing the accuracy and efficiency of the present elements.

• 유체기계공업학회:학술대회논문집
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• 2004.12a
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• pp.65-69
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• 2004

In the present work, characteristics of an axial flow fan haying distorted inlet flow produced by hub cap are investigated. The distorted inlet flow is generated by the shape of hub cap installed in front of the axial flow fan. Two different cases of hub cap geometry are analyzed to verify the influence of flow distortion. The flow fields are analyzed numerically by solving steady form of three-dimensional Reynolds-averaged Wavier-Stokes equation and standard k-$\epsilon$ model is used for a turbulence closure. The results obtained from the numerical simulation are compared to those from experimental measurements. It is found that the overall performance of the axial flow fan is increased by reducing the flow distortion at the hub. Detailed characteristics of the flow fields of two different geometric conditions are also discussed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.6
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• pp.502-511
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• 2013

Noise performance of small wind turbines is critical since these are generally installed near the community. In this study, flow noise characteristics of Savonius wind turbines are numerically investigated. Flow field around the turbine are computed by solving unsteady RANS equation using CFD techniques and the radiated noise are predicted by applying acoustic analogy to the computed flow data. Parametric study is then carried out to investigate the effects of operating conditions and geometric design factors of the Savonius wind turbine. Tonal noise components with higher harmonic frequency than the BPF are identified in the predicted noise spectra from a Savonius wind turbine. The end-plates and helical blades are shown to reduce overall noise levels. These results can be used to design low-noise Savonius wind turbines.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1331-1343
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• 2017

A curve ${\gamma}$ immersed in the three-dimensional sphere ${\mathbb{S}}^3$ is said to be a slant helix if there exists a Killing vector field V(s) with constant length along ${\gamma}$ and such that the angle between V and the principal normal is constant along ${\gamma}$. In this paper we characterize slant helices in ${\mathbb{S}}^3$ by means of a differential equation in the curvature ${\kappa}$ and the torsion ${\tau}$ of the curve. We define a helix surface in ${\mathbb{S}}^3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in ${\mathbb{S}}^3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in ${\mathbb{S}}^3$ are exactly the geodesics of helix surfaces.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.660-665
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• 2006

This paper presents a finite element method to analyze the free and forced vibration of a hard disk drive (HDD) considering the flexibility of a spinning disk-spindle with fluid dynamic bearings (FDBs), an actuator with pivot bearings, an air bearing between head-disk interface and the base with complicated geometry. Finite element equation of each component is consistently derived with the satisfaction of the geometric compatibility of the internal boundary between each component. The spinning disk, hub and FDBs are modeled by annular sector elements, beam elements and stiffness and damping elements, respectively. The actuator am, E-block, suspension and base plate are modeled by tetrahedral elements. The pivot bearing in the actuator and the air bearing between head-disk interfaces are modeled by the stiffness element with five degrees of freedom and the axial stiffness, respectively. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem with the restarted Arnoldi iteration method. Modal and shock testing are performed to show that the proposed method well predicts the vibration characteristics of a HDD.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.1
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• pp.24-30
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• 2016

The accuracy of small and low-cost CCD cameras is insufficient to provide data for precisely tracking unmanned aerial vehicles (UAVs). This study shows how a quad rotor UAV can hover on a human targeted tracking object by using data from a CCD camera rather than imprecise GPS data. To realize this, quadcopter UAVs need to recognize their position and posture in known environments as well as unknown environments. Moreover, it is necessary for their localization to occur naturally. It is desirable for UAVs to estimate their position by solving uncertainty for quadcopter UAV hovering, as this is one of the most important problems. In this paper, we describe a method for determining the altitude of a quadcopter UAV using image information of a moving object like a walking human. This method combines the observed position from GPS sensors and the estimated position from images captured by a fixed camera to localize a UAV. Using the a priori known path of a quadcopter UAV in the world coordinates and a perspective camera model, we derive the geometric constraint equations that represent the relation between image frame coordinates for a moving object and the estimated quadcopter UAV's altitude. Since the equations are based on the geometric constraint equation, measurement error may exist all the time. The proposed method utilizes the error between the observed and estimated image coordinates to localize the quadcopter UAV. The Kalman filter scheme is applied for this method. Its performance is verified by a computer simulation and experiments.