• Proceedings of the Korea Water Resources Association Conference
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• 2007.05a
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• pp.1392-1396
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• 2007

The governing equations in generalized curvilinear coordinates for 3D laminar flow are the Incompressible Navier-Stokes (INS) equations with the artificial dissipative terms. and continuity equation discretized using a second-order accurate, finite volume method on the nonstaggered computational grid. This method adopts a dual or pseudo time-stepping Artificial Compressibility (AC) method integrated in pseudo-time. Multigrid methods are also applied because solving the equations on the coarse grids requires much less computational effort per iteration than on the fine grid. The algorithm yields practically identical velocity profiles and secondary flows that are in excellent overall agreement with an experimental measurement (Humphrey et al., 1977).

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.371-384
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• 2022

Fix an integer n ≥ 1. Then the simplex Π_n, Birkhoff polytope Ω_n, and Latin square polytope Λ_n each yield projective geometries obtained by identifying antipodal points on a sphere bounding a ball centered at the barycenter of the polytope. We investigate conditions for homogeneous coordinates of points in the projective geometries to locate exact vertices of the respective polytopes, namely crisp distributions, permutation matrices, and quasigroups or Latin squares respectively. In the latter case, the homogeneous conditions form a crucial part of a recent projective-geometrical approach to the study of orthogonality of Latin squares. Coordinates based on the barycenter of Ω_n are also suited to the analysis of generalized doubly stochastic matrices, observing that orthogonal matrices of this type form a subgroup of the orthogonal group.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.8 s.239
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• pp.1123-1131
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• 2005

In this paper, a formulation for a spatial sliding joint, which a general multibody can move along a very flexible cable, is derived using absolute nodal coordinates and non-generalized coordinate. The large deformable motion of a spatial cable is presented using absolute nodal coordinate formulation, which is based on the finite element procedures and the general continuum mechanics theory to represent the elastic forces. And the non-generalized coordinate, which is neither related to the inertia forces nor external forces, is used to describe an arbitrary position along the centerline of a very flexible cable. In the constraint equation for the sliding joint, since three constraint equations are imposed and one non-generalized coordinate is introduced, one constraint equation is systematically eliminated. Therefore, there are two independent Lagrange multipliers in the final system equations of motion associated with the sliding joint. The development of this sliding joint is important to analyze many mechanical systems such as pulley systems and pantograph/catenary systems for high speed-trains.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1974-1984
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• 1994

This paper presents a relative coordinate formulation for constrained mechanical systems. Relative coordinates are defined along degrees of freedom of a joint. Graph theoretic analyses are performed to identify topological paths in mechanical systems. Cut constraints are generated to handle closed loop systems. Equations of motion are derived in the Cartesian space and transformed to the joint space. Relative generalized coordinates are corrected to satisfy the cut constraints by a parametrizatiom method.

• International Journal of Precision Engineering and Manufacturing
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• v.5 no.4
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• pp.50-60
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• 2004

A very flexible beam can be used to model various types of continuous mechanical parts such as cables and wires. In this paper, the dynamic properties of a very flexible beam, included in a multibody system, are analyzed using absolute nodal coordinates formulation, which is based on finite element procedures, and the general continuum mechanics theory to represent the elastic forces. In order to consider the dynamic interaction between a continuous large deformable beam and a rigid multibody system, a combined system equations of motion is derived by adopting absolute nodal coordinates and rigid body coordinates. Using the derived system equation, a computation method for the dynamic stress during flexible multibody simulation is presented based on Euler-Bernoulli beam theory, and its reliability is verified by a commercial program NASTRAN. This method is significant in that the structural and multibody dynamics models can be unified into one numerical system. In addition, to analyze a multibody system including a very flexible beam, formulations for the sliding joint between a very deformable beam and a rigid body are derived using a non-generalized coordinate, which has no inertia or forces associated with it. In particular, a very flexible catenary cable on which a multibody system moves along its length is presented as a numerical example.

• Journal of Mechanical Science and Technology
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• v.15 no.6
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• pp.693-698
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• 2001

The analysis of actuating forces (or torques) and joint reaction forces (or moments) are essential to determine the capacity of actuators, to control the system and to design the components. This paper presents an inverse dynamic analysis algorithm for flexible multibody systems with closed-loops in the relative joint coordinate space. The joint reaction forces are analyzed in Cartesian coordinate space using the inverse velocity transformation technique. The joint coordinates and the deformation modal coordinates are used as the generalized coordinates of a flexible multibody system. The algorithm is verified through the analysis of a slider-crank mechanism.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.1
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• pp.68-74
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• 1999

The Green function method is widely used for the analysis of waves in a harbor with a constant depth. In extending this method to a wave field over arbitrary depth, a generalized and convenient method is needed to obtain unit solutions for waves emerging from a point source. For this purpose, a parabolic wave equation is derived to approximate the mild-slope equation written in terms of polar coordinates. Usefulness of the equation obtained is examined through trial computations.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.333-333
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• 2000

When the generalized singular perturbation method is used for model reduction, the state variables of the original system is reconstructed from the reduced order model. The state reduction error is defined, which shows how well the reconstructed state variables approximate the state variables of the original system equation.

• The Korean Journal of Applied Statistics
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• v.37 no.1
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• pp.73-86
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• 2024

A radial chart of Excel is very useful graphical method in delivering information for numerical data. However, it is not easy to discriminate or classify many individuals. In this case, after shaping each individual of a radial chart, we need to apply shape analysis. For a radial chart, since landmarks for shaping are formed as many as the number of variables representing the characteristics of the object, we consider a shape that connects them to a line. If the shape becomes complicated due to the large number of variables, it is difficult to easily grasp even if visualized using a radial chart. Principal component analysis (PCA) is performed on variables to create a visually effective shape. The classification table and classification rate are checked by applying the techniques of traditional discriminant analysis, support vector machine (SVM), and artificial neural network (ANN), before and after principal component analysis. In addition, the difference in discrimination between the two coordinates of generalized procrustes analysis (GPA) coordinates and Bookstein coordinates is compared. Bookstein coordinates are obtained by converting the position, rotation, and scale of the shape around the base landmarks, and show higher rate than GPA coordinates for the classification rate.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.516-523
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• 2009

The artificial compressibility (AC) method for the incompressible Navier-Stokes equations in the generalized curvilinear coordinates using the primitive form is implemented. The main advantage of the AC approach is that the resulting system of equations resembles the system of compressible N-S equations and can thus be integrated in time using standard, well-established time-marching methods. The errors, which are the odd-even oscillation, for pressure field in using the artificial compressibility can be eliminated by using the $4^{th}$ order artificial dissipation term which is explicitly included. Even though this paper focuses exclusively on 2D laminar flows to validate and assess the performance of this solver, this numerical method is general enough so that it can be readily extended to carry out 3D URANS simulation of engineering flows. This algorithm yields practically identical velocity profiles and primary vortex and secondary vortices that are in excellent overall agreement with the results of the vorticity-stream function formulation (Ghia et al., 1982). However, the grid resolution have to be required to be large enough to express the various vortices.