• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1999년도 가을 학술발표회 논문집
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• pp.421-428
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• 1999

The elastic critical load of a slender compression member plays an important role when the proper design of that member is required. For the tapered compression members, however, there are cases when the conventional neutral equililbrium or energy method can't be applied to the determination of critical loads of those members. In this paper, finite element method is applied to the approximate determination of the symmetrically tapered bars. Here in this paper, the bars are assumed to take sinusoidally changing shapes along their axes. The parameters considered in this study are taper parameter, $\alpha$ and the sectional property parameter, m. The computed results by finite element method are represented in the forms of algebraic equations. Regression technique is employed to determine the coefficients of algebraic equations. The critical loads estimated by the proposed algebraic equations coincide fairly well with those of finite element method.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 가을 학술발표회논문집
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• pp.299-306
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• 2000

The elastic critical load of a slender compression member plays an important role when the proper design of that member is required. For tapered compression members, however, there are cases when the conventional neutral equilibrium or energy method can't be applied to the determination of critical loads. In this paper, the finite element method is applied to the approximate determination of the linearly tapered members. In this paper, the bars are assumed to be tapered linearly along their axes. The parameters considered in this study are taper parameter, α and the sectional property parameter, m. The member ends are either hinged or fixed. The computed results using the finite element method are represented in the forms of algebraic equations. The regression technique is employed to determine the coefficients of the algebraic equations. Critical loads estimated by the proposed algebraic equations coincide flirty well with those employing the finite element method.

• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.383-393
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• 2021

In this paper, numerical techniques are presented for solving initial value problems of fractional differential equations with variable coefficients. The method is derived by applying a Taylor vector approximation. Moreover, the operational matrix of fractional integration of a Taylor vector is provided in order to transform the continuous equations into a system of algebraic equations. Furthermore, numerical examples demonstrate that this method is applicable and accurate.

• 대한기계학회논문집A
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• 제26권12호
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• pp.2647-2655
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 춘계학술대회논문집
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• pp.181-189
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness in a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time-varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i= 1,2,3..).

• 한국수학교육학회지시리즈C:초등수학교육
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• 제14권3호
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• pp.261-275
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• 2011

본 연구는 방정식을 배우지 않은 초등학교 5학년 학생들이 일차방정식을 조작적으로 해결하는 과정에서 자신의 분수scheme과 조작을 어떻게 사용하고 있으며 계수와 상수가 복잡해짐에 따라 어떠한 분수scheme과 조작을 사용하는지 알아봄으로써 산술과 대수 사이의 간격을 줄이고 대수적 사고와 산술과의 연결성을 강화하고자 하였다. 초등학교 5학년 학생 두 명을 사례연구하여 일차방정식을 조작적으로 해결하는 과정을 면밀하게 분석하였다. 분석결과 학생들은 계수와 상수에 따라 다양한 조작과 분수 scheme를 사용하였으며 특히, 일차방정식의 해결에서 핵심전략인 동시에 대수적 사고와 연결되는 미지수와 주어진 량 사이의 동치관계를 세우는 데 반복 분수 scheme이 필요했다. 그리고 동치관계를 세우고 나서 미지수를 찾는데 동치분수가 중요한 역할을 하였다.

• Journal of Mechanical Science and Technology
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• 제15권7호
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• pp.889-894
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• 2001

In this study, the performances of various turbulence closure models are evaluated in the calculation of a transonic flow over axisymmetric bump. k-$\varepsilon$, explicit algebraic stress, and two Reynolds stress models, i.e., GL model proposed by Gibson & Launder and SSG model proposed by Speziale, Sarkar and Gatski, are chosen as turbulence closure models. SSG Reynolds stress model gives best predictions for pressure coefficients and the location of shock. The results with GL model also show quite accurate prediction of pressure coefficients down-stream of shock wave. However, in the predictions of mean velocities and turbulent stresses, the results are not so satisfactory as in the prediction of pressure coefficients.

• 한국공간구조학회논문집
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• 제7권5호
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• pp.83-87
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• 2007

비대칭 및 대칭 변단면 압축재( = m)의 임계하중을 수치 해석법의 하나인 유한 요소법으로 결정하였다. 해석에서 고려한 변수는 taper parameter(=a) 와 단면 성능 변수 m이다. 구조설계 및 구조의 안전 검토에 임하는 구조 기술자들의 편의를 위하여 유한요소법으로 결정한 임계하중의 계수 변화는 하나의 대수식으로 표시하였다. 대수식에 나타나는 계수들은 회귀분석법으로 결정하였다.

• Structural Engineering and Mechanics
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• 제43권1호
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• pp.105-126
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• 2012

Based on the first-order shear deformation theory (FSDT), and the virtual work principle, an elastic analysis for axisymmetric clamped-clamped Pressurized thick truncated conical shells made of functionally graded materials have been performed. The governing equations are a system of nonhomogeneous ordinary differential equations with variable coefficients. Using the matched asymptotic method (MAM) of the perturbation theory, these equations could be converted into a system of algebraic equations with variable coefficients and two systems of differential equations with constant coefficients. For different FGM conical angles, displacements and stresses along the radius and length have been calculated and plotted.

• Structural Engineering and Mechanics
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• 제22권3호
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• pp.331-349
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• 2006

The stresses and deflections in a laminated rectangular plate under thermal vibration are determined by using the moving least squares differential quadrature (MLSDQ) method based on the first order shear deformation theory. The weighting coefficients used in MLSDQ approximation are obtained through a fast computation of the MLS shape functions and their partial derivatives. By using this method, the governing differential equations are transformed into sets of linear homogeneous algebraic equations in terms of the displacement components at each discrete point. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Solving this set of algebraic equations yields the displacement components. Then substituting these displacements into the constitutive equation, we obtain the stresses. The approximate solutions for stress and deflection of laminated plate with cross layer under thermal load are obtained. Numerical results show that the MLSDQ method provides rapidly convergent and accurate solutions for calculating the stresses and deflections in a multi-layered plate of cross ply laminate subjected to thermal vibration of sinusoidal temperature including shear deformation with a few grid points.