• 대한수학회지
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• 제44권6호
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• pp.1313-1327
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• 2007

We review the algebraic structure of $\mathbb{H}{\sharp}$ and show that $\mathbb{H}{\sharp}$ has a scalar product that allows as to identify it with semi Euclidean ${\mathbb{E}}^4_2$. We show that a pair q and p of unit split quaternions in $\mathbb{H}{\sharp}$ determines a rotation $R_{qp}:\mathbb{H}{\sharp}{\rightarrow}\mathbb{H}{\sharp}$. Moreover, we prove that $R_{qp}$ is a product of rotations in a pair of orthogonal planes in ${\mathbb{E}}^4_2$. To do that we call upon one tool from the theory of second ordinary differential equations.

• Journal of Mechanical Science and Technology
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• 제16권10호
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• pp.1276-1286
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• 2002

The numerical techniques are presented to solve the static and dynamic contact problems of deformable bodies having large rotations of the contact surfaces. The contact conditions on the possible contact surfaces are enforced by using the contact error vector, and an iterative scheme similar to augmented Lagrange multiplier method is employed to reduce the contact error vector monotonically. For dynamic contact problems using implicit time integration, a contact error vector is also defined by combining the displacement, velocity, and acceleration on the contact surface. The suggested iterative technique is implemented to ABAQUS by using the UEL subroutine UEL. In this work, after the computing procedures to solve the frictional contact problems are explained, the numerical examples are presented to compare the present solutions with those obtained by ABAQUS.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1999년도 추계 학술대회논문집
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• pp.145-151
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• 1999

An Interactive grid generation program(KGRID) with graphical user interface(GUI) has been improved. KGRID works on the UNLX environment and GUI has been implemented with OSF/Motif and X Toolkit and the graphics language is Open GL for visualization of the 3D objects. It supports more convenient user environment to generate 2D and 3D multi-block structured grid systems. It provides various useful field grid generation methods, which are the algebraic methods, the elliptic partial differential equations method and the predictor-corrector method. It also supports 3D surface grid generation with NURBS(Non-Uniform Rational B-Spline) and various stretching functions to control grid points distribution on curves and surfaces. And some menus are added to perform flexible management, for the objects. We generated surface and field grid system about full aircraft configuration using KGRID. The performance and stability of the KGRID is verified through the generation of the grid system about a complex shape.

• 한국자동차공학회논문집
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• 제10권2호
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• pp.159-165
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• 2002

Numerical analysis of dynamic contact and stress developing in the high-speed driven valve of an internal combustion engine is presented. The valve is modeled by finite element techniques, and the dynamic contact between the valve and the valve seat is analyzed by the solution strategies of differential algebraic equations. Also an iterative scheme similar to the augmented Lagrange multiplier method is employed to enforce the contact constraints. It is shown that the contact and separation between the valve and the valve seat can be computed by the finite element techniques without assuming the artificial springs, and the efficiency and accuracy of the solution are demonstrated by the numerical examples.

• 한국자동차공학회논문집
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• 제11권2호
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• pp.31-39
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• 2003

Numerical analysis for valve train dynamics of an internal combustion engine is presented. The components of the valve train are modeled by finite element techniques, and the dynamic contacts between the components are analyzed by the solution strategies of differential algebraic equations. Also an iterative scheme similar to the augmented Lagrange multiplier method is employed to enforce the contact constraints. It is shown that the contact and separation between the components of the valve train can be computed by the finite element techniques, and the numerical examples are presented to demonstrate the efficiency of the solution.

• Structural Engineering and Mechanics
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• 제54권3호
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• pp.419-432
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• 2015

The free vibration of rotating Euler-Bernoulli beams with the thickness and/or width of the cross-section vary linearly along the length is investigated by using the Adomian modified decomposition method (AMDM). Based on the AMDM, the governing differential equation for the rotating tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and the closed form series solution of the corresponding mode shapes can be easily obtained simultaneously. The computed results for different taper ratios as well as different offset length and rotational speeds are presented in several tables and figures. The accuracy is assured from the convergence and comparison with the previous published results. It is shown that the AMDM provides an accurate and straightforward method of free vibration analysis of rotating tapered beams.

• Advances in aircraft and spacecraft science
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• 제1권2호
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• pp.145-175
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• 2014

The results of a series of numerical experiments are presented to verify some of the important developments made in the first part of this paper. Firstly, the static solution of an algebraic system obtained through Strong Formulation Finite Element Method (SFEM) is presented. Secondly, the stress and strain recovery procedure is descripted for the present technique. It will be clear that the present approach is suitable for any strong formulation finite element methodology, due to the presented general approach based on the unknown displacements and on the elasticity equations. Thirdly, the numerical solutions for some classical and other numerical results found in literature are exposed. Finally, an arbitrarily shaped composite plate is solved and good agreement is observed for all the presented cases.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1994년도 추계학술대회 논문집 학회본부
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• pp.6-8
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• 1994

In this paper an attempt is made to understand the voltage stability when the power system networks are represented by the differential-algebraic equations (DAEs) form. The problem is analyzed by interpreting the shape of constraint manifold, based on the singular perturbation model. The global picture or constraint manifold is given to show how the local shape or constraint manifold can be used to guess for the system behavior. The gradient analysis is used systematically to obtain a local shape or the constraint manifold.

• Journal of Welding and Joining
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• 제16권3호
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• pp.141-147
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• 1998

Design sensitivity analysis of a vehicle system is an essential tool for design optimization and trade-off studies. Most optimization algorithms require the derivatives of cost and constraint function with respect to design in order to calculate the next improved design. This paper presents an efficient algorithm application for the design sensitivity analysis, using the direct differentiation method. A mounting area of suspension that welded on chassis frame is analyzed to show the validity and the efficiency of the proposed method. A mounting area of suspension that welded on chassis frame is analyzed to show the validity and the efficiency of the proposed method.

• Structural Engineering and Mechanics
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• 제85권2호
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• pp.207-216
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• 2023

Three time-discontinuous Galerkin quadrature element methods (TDGQEMs) are developed for structural dynamic problems. The weak-form time-discontinuous Galerkin (TDG) statements, which are capable of capturing possible displacement and/or velocity discontinuities, are employed to formulate the three types of quadrature elements, i.e., single-field, single-field/least-squares and two-field. Gauss-Lobatto quadrature rule and the differential quadrature analog are used to turn the weak-form TDG statements into a system of algebraic equations. The stability, accuracy and numerical dissipation and dispersion properties of the formulated elements are examined. It is found that all the elements are unconditionally stable, the order of accuracy is equal to two times the element order minus one or two times the element order, and the high-order elements possess desired high numerical dissipation in the high-frequency domain and low numerical dissipation and dispersion in the low-frequency domain. Three fundamental numerical examples are investigated to demonstrate the effectiveness and high accuracy of the elements, as compared with the commonly used time integration schemes.