• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.561-577
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• 2002

In this paper, a two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular background interpolation mesh is developed for analysing the evolution of the saltwater intrusion into single and multiple coastal aquifer systems. The model formulation consists of a ground-water flow equation and a salt transport equation. These coupled and non-linear partial differential equations are transformed by FVUM into a system of differential/algebraic equations, which is solved using backward differentiation formulas of order one through five. Simulation results are compared with previously published solutions where good agreement is observed.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.4
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• pp.64-71
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• 2002

Recently, mechanical systems such as a high-speed vehicles and railway trains moving on flexible beam structures have become a very important issue to consider. Using the general approach proposed in the first part of this paper, it is possible to predict motion of the constrained mechanical system and the elastic structure, with various kinds of foundation supporting conditions. Combined differential-algebraic equation of motion derived from both multibody dynamics theory and finite element method can be analyzed numerically using a generalized coordinate partitioning algorithm. To verify the validity of this approach, results from the simply supported elastic beam subjected to a moving load are compared with the exact solution from a reference. Finally, parametric study is conducted for a moving vehicle model on a simply supported 3-span bridge.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.04a
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• pp.252-259
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• 1999

One of the most important factors for a proper design of a slender compression member may be the exact determination of the elastic critical load of that member. In the cases of non-prismatic compression member, however, there are times when the exact critical load becomes impossible to determinate if one relies on the neutral equilibrium method or energy principle. Here in this paper, the approximate critical loads of symmetrically or non-symmetrically tapered members are computed by finite element method. The two parameters considered in this numerical analysis are the taper parameter, $\alpha$ and the sectional property parameters, m. The computed results for each sectional property parameter, m are presented in an algebraic equation which agrees with those by F.E.M The algebraic equation can be easily used by structural engineers, who are engaged in structural analysis and design of non-prismatic compression member.

• Structural Engineering and Mechanics
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• v.5 no.3
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• pp.283-295
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• 1997

This paper presents a high precision integration method for the dynamic response analysis of structures with holonomic constraints. A detail recursive scheme suitable for algebraic and differential equations (ADEs) which incorporates generalized forces is established. The matrix exponential involved in the scheme is calculated precisely using $2^N$ algorithm. The Taylor expansions of the nonlinear term concerned with state variables of the structure and the generalized constraint forces of the ADEs are derived and consequently, their particular integrals are obtained. The accuracy and effectiveness of the present method is demonstrated by two numerical examples, a plane truss with circular slot at its tip point and a slewing flexible cantilever beam which is currently interesting in optimal control of robot manipulators.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.10
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• pp.1166-1172
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• 1988

This paper presents an efficient method of analyzing linear time-varying systems via Taylor polynomials. While the approach suggested by Sparis and Mouroutsos gives an implicit form for unknown state vector and requires to solve a linear algebraic equation with large dimension when the number of terms increases, the method proposed in this paper shows an explicit form and has no need to solve any linear algebraic equation.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.38-42
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• 1997

A multiblock grid generation has been applied to a Navier-Stokes design procedure of a axial-flow compressors. A multiblock structure simplifies the creation of structured H-grids about complex turbomachinery geometries and facilitate the creation of a grid in the tip flow region. The numerical algorithm adopts the combination of the algebraic and elliptic method to create the internal grids efficiently and quickly. The input module is made of the results of the preliminary design, i.e., flow-path, aerodynamic conditions along the spanwise direction, and the blade profile data. The final grids generated from each module of the system are used as the preprocessor for the performance prediction of the sectional blade, the blade-stacking process and the three-dimensional flow simulation inside the blade passage. Application to the blade design of the LP compressor was demonstrated to be very reliable and practical in support of design activities. This customized system are coupled strongly with the design procedure of the turbomachinery cascades using the Navier-Stokes technique.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.93-108
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• 2004

In this article we study on various proofs of the Steiner-Lehmus theorem(any triangle that has two equal angle bisectors is isosceles). We suggest 6 geometric proofs and 3 algebraic proofs of the theorem in detail, analyze these proofs, extract related theorems, proof ideas.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.11
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• pp.3227-3233
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• 2009

A method for performing Boolean resubstitution is proposed. This method is efficiently implemented using division matrix. It begins by creating an algebraic division matrix from given two logic expressions. By introducing Boolean properties and adding literals into the algebraic division matrix, we make the Boolean division matrix. Using this extended division matrix, Boolean substituted expressions are found. Experimental results show the improvements in the literal counts over well-known logic synthesis tools for some benchmark circuits.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.45-53
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• 2009

As the point sampling technology evolves rapidly, there has been increasing need in generating tool path from dense point set without creating intermediate models such as triangular meshes or surfaces. In this paper, we present a new tool path generation method from point set using Euclidean distance fields based on Algebraic Point Set Surfaces (APSS). Once an Euclidean distance field from the target shape is obtained, it is fairly easy to generate tool paths. In order to compute the distance from a point in the 3D space to the point set, we locally fit an algebraic sphere using moving least square method (MLS) for accurate and simple calculation. This process is repeated until it converges. The main advantages of our approach are : (1) tool paths are computed directly from point set without making triangular mesh or surfaces and their offsets, and (2) we do not have to worry about no local interference at concave region compared to the other methods using triangular mesh or surface model. Experimental results show that our approach can generate accurate enough tool paths from a point set in a robust manner and efficiently.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.151-156
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• 1998

In this paper, we present new control method for robot manipulators. The design objective can be the implementation of minimax controller with H$_{\infty}$ performance via LMI approach to guarantee the robustness and to obtain the exact tracking performance for robot manipulators with system parameter uncertainty and exogenous disturbance. We show that the Algebraic Riccati equation (ARE) which is needed for the construction of H$_{\infty}$ controller can be recast into the Algebraic Riccati Inequality (ARI) and the optimal control gain can be obtained by convex optimization method. Then, we will apply the proposed controller to rigid robot manipulators for verifying the performance of our controller.