• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.04a
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• pp.137-144
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• 1999

The finite element method was adopted to find out the natural frequencies of a sinusoidally tapered beam with simply supported boundary conditions. The parameters considered in the numerical analysis are the taper parameter, $\alpha$ ($\alpha$=0.0, 0.1, ~ , 2.0) and the sectional property parameters, m and n [(m, n):(0, 2), (1, 3), (2, 4)]. It is generally known that the results of the numerical analysis corresponding to each pair of sectional property parameters, (m, n) are represented by second order polynominals of $\alpha$ . The coefficients of a in the polynominals are determined by using the regression technique, which reveals small m in most cases of given sectional property parameters (m, n).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1995.04a
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• pp.334-339
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• 1995

COSINE 급수를 이용한 유한 길이 원통형 셀의 유체 영향계수에 대한 해석결과를 양단 단순지지 조건(Simply-supported condition)을 갖는 해석모델에서 이용한 SINE 급수를 적용한 해석 결과와 비교, 검토한 결과 유사한 경향을 보이고 있으며, 무차원 파수 ka 값이 커질수록 Reactance는 0으로 접근하고 Resistance는 .rho.c 값으로 접근하는 경향을 가지고 있어 타당한 해석방법임을 알 수 있었다. 따라서 양단에 끝막이 판을 갖고 있는 원통형 셀에 대한 음압복사 현상을 해석하는데 COSINE 급수를 이용하는 것이 가능함을 본 연구를 통하여 확인하였다. 또한 본 연구에서 유도한 Z$_{mm}$값을 이용하면 양단에 끝막이 판을 갖고 있는 원통형 셀에서의 유체 효과를 용이하게 해석할 수 있다.

• Journal of Korean Society of Steel Construction
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• v.8 no.3 s.28
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• pp.79-87
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• 1996

본 논문에서는 단순지지된 일정체적의 정다각형 단면을 갖는 변단면 기둥의 정확탄성곡선(elastica)을 산출할 수 있는 수치해석법을 개발하였다. 정확탄성곡선의 미분방정식은 Bernoulli-Euler 보 이론으로 유도하였고, 미분방정식의 수치적분은 Runge-Kutta method를 이용하였다. 미분방정식의 고유치인 지점의 단면회전각은 Regula-Falsi method를 이용하여 계산하였다. 변단면의 단면 깊이의 변화식으로는 직선식, 포물선식 및 정현식의 3가지 함수식을 채택하였다. 또한 유도된 미분방정식을 이용하여 대상기둥의 좌굴하중을 산출하고 이로부터 최강기둥의 단면비와 좌굴하중을 결정하였다.

• Journal of the Korean Society of Safety
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• v.12 no.4
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• pp.220-229
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• 1997

The differential quadrature method (DQM) is applied to computation of the eigenvalues of the equations governing in plane and out-of-plane buckling. In-plane buckling and twist-buckling under uniformly distributed radial loads are investigated by this method. Critical loads are calculated for various end conditions and opening angles. Results are compared with existing exact solutions where available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used. New results are given for two sets of boundary conditions not previously considered for this problem clamped-clamped and clamped simply supported ends.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.9
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• pp.720-729
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported Euler-Bernoulli beam with the moving mass. The influences of the depth and the position of the crack in the beam have been studied on the dynamic behavior of the simply supported beam system by numerical method. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. As the depth of the crack is increased the frequency of the simply supported beam with the moving mass is increased.

• Magazine of the Korean Society of Agricultural Engineers
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• v.41 no.1
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• pp.106-114
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• 1999

This paper explores the geometrical non-linear behavior of the simply supported tapered beams subject to the trapezoidal distributed load and end moments. In order to apply the Bernoulli -Euler beam theory to this tapered beam, the bending moment equation on any point of the elastical is obtained by the redistribution of trapezoidal distributed load. On the basis of the bending moment equation and the BErnoulli-Euler beam theory, the differential equations governging the elastical of such beams are derived and solved numerically by using the Runge-Jutta method and the trial and error method. The three kinds of tapered beams (i.e. width, depth and square tapers) are analyzed in this study. The numerical results of non-linear behavior obtained in this study from the simply supported tapered beams are appeared to be quite well according to the results from the reference . As the numerical results, the elastica, the stress resultants and the load-displacement curves are given in the figures.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.2
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• pp.1-14
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• 1991

A computer program for the linear elastic buckling anlalysis of thin walled members is developed using a 3-node triangular shell element. The element has real stiffness value for a kinematic degree of freedom associated with rotation about the surface normal at each node. The validity of the present computer program is demonstrated through the plate buckling analysis and the lateral-torsional buckling analysis of a straight beam. Then, simply supported circular arches subjected to uniform bending are analyzed and the results are compared with existing solutions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.4
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• pp.381-387
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• 2016

In this paper, the methodology applied to the improvement of stress analyses is extended to free vibration and buckling analyses. The essence of the methodology is the Saint-Venant's principle that is applicable to beam and plate models. The principle allows one to dimensionally reduce three-dimensional elasticity problems. Thus the methodology can be employed to vibration and buckling as well as stress analysis. First, the principle is briefly revisited, and then the formations of classical beam theories are presented. To improve the predictions, the perturbed terms (unknowns) are introduced together with the warping functions that are calculated by stress equilibrium equations. The unknowns are then calculated by applying the equivalence of stress resultants (i.e., Saint-Venant's principle). As numerical examples, cantilever and simply supported beams are analytically solved. The results obtained are compared with those of the classical beam theories. It is shown that the methodology can be used to improve the predictions without introducing shear correction factors.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.7
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• pp.2858-2864
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• 2012

The differential quadrature method (DQM) is applied to computation of the eigenvalues of in-plane buckling of the curved beams. Critical moments and loads are calculated for the beam subjected to equal and opposite bending moments and uniformly distributed radial loads with various end conditions and opening angles. Results are compared with existing exact solutions where available. The DQM gives good accuracy even when only a limited number of grid points is used. More results are given for two sets of boundary conditions not considered by previous investigators for in-plane buckling: clamped-clamped and simply supported-clamped ends.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.7
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• pp.555-561
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported Euler-Bernoulli beams with the moving masses. The influences of the velocities of moving masses, the distance between the moving masses and a crack have been studied on the dynamic behavior of a simply supported beam system by numerical method. The Presence of crack results In large deflection of beam. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. Totally, as the velocity of the moving masses and the distance between the moving masses are increased, the mid-span deflection of simply supported beam with the crack is decreased.