• Structural Engineering and Mechanics
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• 제23권5호
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• pp.525-542
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• 2006

On the basis of equilibrium equations for static electric and magnetic fields, two unknown functions related to electric and magnetic fields were firstly introduced to rewrite the governing equations, boundary conditions and initial conditions for mechanical field. Then by introducing a dependent variable and a special function satisfying the inhomogeneous mechanical boundary conditions, the governing equation for a new variable with homogeneous mechanical boundary conditions is obtained. By using the separation of variables technique as well as the electric and magnetic boundary conditions, the dynamic problem of a functionally graded magneto-electro-elastic hollow sphere under spherically symmetric deformation is transformed to two Volterra integral equations of the second kind about two unknown functions of time. Cubic Hermite polynomials are adopted to approximate the two undetermined functions at each time subinterval and the recursive formula for solving the integral equations is derived. Transient responses of displacements, stresses, electric and magnetic potentials are completely determined at the end. Numerical results are presented and discussed.

• 한국해안해양공학회지
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• 제6권4호
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• pp.459-471
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• 1994

쇄파작용에 기인한 준 3차원적 연안류 순환 모델의 수치 기법을 제시한다. 지배 방정식은 근사 factorization 기법과 fractional step method를 사용하여 음해법으로 수치해석 되었고 분할된 식은 유한 체적법으로 차분된다. 계산된 3차원적 연안류 패턴의 한 예로서 Gourlay(1974)의 실험자료와 비교하여 간접적으로 모델의 타당성을 검증한다.

• 품질경영학회지
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• 제27권1호
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• pp.46-58
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• 1999

The exact distributions of the sample variance $(S^2_n)$ and the estimator ($\hat{C}_p$) of the process capability index are not easily obtained in general. In this paper, the approximations using saddlepoint techniques to the distributions of these statistics are suggested and compared with the other approximation methods. For comparisons, the exact values obtained by extensive Monte-Carlo (simulation) studies are also given. As a result, the suggested approximation methods are very accurate even in moderate or small sample sizes and are easy to use. Also, the suggested methods can be adapted to approximate the distributions of more complicated statistics, including $\hat{C}_pk$ ,$\hat{C}_pm$, etc.

• 한국수자원학회논문집
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• 제30권5호
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• pp.487-493
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• 1997

본 논문에서는 단일파의 최대 처오름높이에 관하여 연구하였다. 경계요소법을 이용한 수치모형으로 고립파와 N-파의 처오름높이를 계산하였으며, 수치모형에서는 바닥마찰저항 효과를 고려하였다. 계산된 최대 처오름높이는 기존의 수리모형실험 관측자료, 다른 수치모형 및 근사 해석에 의한 결과와 비교하였으며, 경계요소법에 의해 계산된 처오름높이는 다른 결과들과 매우 잘 일치한다.

• 한국정밀공학회지
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• 제3권2호
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• pp.28-38
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• 1986

An analytical and experimental investigation is made to the dynamic responese of a cantilever with a tip mass that models some of the basic phenomena involved in the response of a flexible manipulator with a tip mass on its free end under the given rotating motion. The system equation is derived from the Hamilton's principle on the basis of the Euler-Bernoulli hypothesis and an approximate solution is obtained from model analysis using Galerkin's method for the vibation response of the system subjected to a sudden stop after an impulsive rotation. Experiment was performed to verify the validity of the theoretical analysis. Results are given for the vibration amplitude of the free end with respect to tip mass ratio, non-dimensionalized rotating velocity, rotating angle and non- dimensionalized hub length. The rotating condition to minimize the vibration amplitude of the free end can be determined for the given basic paramenters.

• 한국수학교육학회지시리즈A:수학교육
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• 제42권4호
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• pp.541-559
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• 2003

This paper considers learning and teaching of mathematical analysis in teachers college. It concentrates on showing a way how learning and teaching of mathematical analysis should be considered for mathematical teachers training. It is composed of five chapters including Chapter I as an introduction and Chapter Vasa concluding remarks. Chapter II deals with goal and contents of global mathematical analysis. The main Chapter, named Chapter III, demonstrates exhibition of contents, way of operations, and contents of teaching and learning of mathematical real analysis. Chapter IV shows an example of learning and teaching of mathematical real analysis concerning to fixed points and approximate solutions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권4호
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• pp.405-416
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• 2009

In this study we are concerned with the problem of approximating a locally unique solution of an equation in a Banach space setting using Newton's and modified Newton's methods. We provide weaker convergence conditions for both methods than before [5]-[7]. Then, we combine Newton's with the modified Newton's method to approximate locally unique solutions of operator equations. Finer error estimates, a larger convergence domain, and a more precise information on the location of the solution are obtained under the same or weaker hypotheses than before [5]-[7]. The results obtained here improve our earlier ones reported in [4]. Numerical examples are also provided.

• 대한수학회논문집
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• 제31권4호
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• pp.869-878
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• 2016

This paper presents an ecient fractional shifted Legendre polynomial method to solve the fractional Volterra's model for population growth model. The fractional derivatives are described based on the Caputo sense by using Riemann-Liouville fractional integral operator. The theoretical analysis, such as convergence analysis and error bound for the proposed technique has been demonstrated. In applications, the reliability of the technique is demonstrated by the error function based on the accuracy of the approximate solution. The numerical applications have provided the eciency of the method with dierent coecients of the population growth model. Finally, the obtained results reveal that the proposed technique is very convenient and quite accurate to such considered problems.

• Bulletin of the Korean Chemical Society
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• 제18권8호
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• pp.841-850
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• 1997

A simple molecular theory of mixtures is formulated based on the nonrandom two-fluid lattice-hole theory of fluids. The model is applicable to mixtures over a density range from zero to liquid density. Pure fluids can be completely characterized with only two molecular parameters and an additional binary interaction energy is required for a binary mixture. The thermodynamic properties of ternary and higher order mixtures are completely defined in terms of the pure fluid parameters and the binary interaction energies. The Quantitative prediction of vapor-liquid, and solid-vapor equilibria of various mixtures are demonstrated. The model is useful, in particular, for mixtures whose molecules differ greatly in size. For real mixtures, satisfactory agreements are resulted from experiment. Also, the equation of state (EOS) is characterized well, even the liquid-liquid equilibria behaviors of organic mixtures and polymer solutions with a temperature-dependent binary interaction energy parameter.

• Structural Engineering and Mechanics
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• 제22권1호
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• pp.107-130
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• 2006

The paper deals with the numerical solution of the dynamic problem of masonry structures. Masonry is modelled as a non-linear elastic material with zero tensile strength and infinite compressive strength. Due to the non-linearity of the adopted constitutive equation, the equations of the motion must be integrated directly. In particular, we apply the Newmark or the Hilber-Hughes-Taylor methods implemented in code NOSA to perform the time integration of the system of ordinary differential equations obtained from discretising the structure into finite elements. Moreover, with the aim of evaluating the effectiveness of these two methods, some dynamic problems, whose explicit solutions are known, have been solved numerically. Comparisons between the exact solutions and the corresponding approximate solutions obtained via the Newmark and Hilber-Hughes-Taylor methods show that in the cases under consideration both numerical methods yield satisfactory results.