• Journal of KSNVE
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• v.6 no.5
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• pp.587-594
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• 1996

The differential equation governing both the free vibrations and buckling loads of tapered beam-columns of regular polygon cross-section with constant volume were derived and solved numerically. The parabolic and sinusoidl tapers were chosen as the variable depth of cross-section for the tapered beam-column. In numerical examples, the clamped-clamped, hinged-clamped and hinged-hinged end constraints were considered. The variations of frequency parameters and first buckling load parameters with the non-dimensional system parameters are reported in figures, and typical vibrating mode shapes are presented. Also, the configurations of strongest columns were determined.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.3A
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• pp.533-538
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• 2006

This study deals with the static and dynamic stability analyses of simple tapered columns with constant volume. The crosssections of column taper are the regular polygons whose depths are varied with the parabolic functional fashion. The hingedhinged end constraint is chosen as the boundary condition of the column. The non-dimensional ordinary differential equation governing free vibrations of such column subjected to an axial load is derived and solved numerically. From numerical results, the relationships between natural frequencies and section ratios are obtained, from which the configurations of dynamic optimal shapes of columns and the strongest columns are extracted.

• Journal of Korean Society of Steel Construction
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• v.9 no.2 s.31
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• pp.221-228
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• 1997

The main purpose of this paper is to determine the dynamic optimal shapes of simple beam-columns with the constant volume. The parabolic function is chosen as the variable equation for the depth of regular polygon cross-section. The ordinary differential equation including the effect of axial load is applied to calculate the natural frequencies. The Runge-Kutta and Regula-Falsi methods are used to integrate the differential equation and compute the frequencies, respectively. Then the dynamic optimal shape whose lowest natural frequency is highest is determined by reading the critical value of the frequency versus section ratio curve plotted by the frequency data. In the numerical examples, the simple beam-columns are analysed and the numerical results of this study are shown in tables and figures.

• Journal of Korean Society of Steel Construction
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• v.13 no.6
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• pp.683-691
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• 2001

Numerical methods are developed for solving the elastica and buckling load of tapered columns with shear deformation, subjected to a compressive end load. The linear, parabolic and sinusoidal tapers with the regular polygon cross-sections are considered, whose material volume and span length are always held constant. The differential equations governing the elastica of buckled column are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine the rotation at left end and the buckling load, respectively. The numerical methods developed herein for computing the elastica and the buckling loads of the columns are found to be efficient and reliable.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5A
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• pp.477-486
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• 2009

This paper deals with the strongest static arches with the solid regular polygon cross-section. Both span length and volume of arch are always held constant regardless the shape functions of cross-sectional depth of regular polygon. The normal stresses acting on such arches are calculated when both static vertical and horizontal point loads are subjected. By using the calculating results of stresses, the optimal shapes of strongest static arches are obtained, under which the maximum normal stress become to be minimum. For determining the redundant of such indeterminate arches, the least work theorem is adopted. As the numerical results, the configurations, i.e. section ratios, of the strongest static arches are reported in tables and figures. The results of this study can be utilized in the field of the minimum weight design of the arch structures.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.2
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• pp.144-152
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• 2010

This paper deals with free vibrations of the tapered circular arches with constant volume, whose cross sectional shape is the solid regular polygon. Volumes of the objective arches are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear, parabolic and sinusoidal ones. Ordinary differential equations governing free vibrations of such arches are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various arch parameters such as rise ratio, section ratio, side number, volume ratio and taper type are reported in tables and figures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.417-422
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• 2002

The main purpose of this paper is to determine the dynamic optimal shapes of tapered column with constant volume. The linear, parabolic and sinusoidal tapers with the regular polygon cross-section are considered, whose material volume and span length are always held constant. The ordinary differential equation including the effect of axial load is applied to calculate the natural frequencies. The Runge-Kutta method and Regula-Falsi methods are used to integrate the differential equation and compute the frequencies, respectively. Then the dynamic optimal shape whose lowest natural frequency is highest is determined by reading the critical value of the frequency versus section ratio curve plotted by the frequency data. In the numerical examples, the tapered columns are analysed and the numerical result of this study are shown in table and figures.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1992.04a
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• pp.74-78
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• 1992

외부가 비축대칭인 튜브의 수방압출은 자동차와 항공기등의 복잡한 부품을 만드는데 많이 사용된다. 이런 후방압출 제품의 변형 상태는 저자들의 논문에서 이미 밝힌 바와 같이 복잡하다. 그래서, 외부가 비출대칭인 튜브형상의 후방압출은 근래에 와서 연구되었다. 본 연구에서는 저자들의 논문 에서 제시된 동적가용속도장을 수정하여 비축대칭인 소재에서 내부가 원형인 튜브의 후방압출의 최종 단계를 해석하 고자 한다. 해석의 적용예로서는 정다각형 소재와 모서리가 둥근 직사각형(rounded rectangle)소재를 택하였다 제시된 속도장으로부터 단면 감소율과 형상비(aspect ratio)에 대하여 압출 하중과 압출된 소재의 평균 높이가 결정된다. 이론적인 결과와 비교하기 위하여 퓰림처리된 AIST-2024 알루미늄 소재로 실험하였다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.5
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• pp.581-592
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• 2007

This paper deals with the elastica of deflected cantilever column with the constant volume. The columns are subjected to combined loads consisted of an axial compressive load and a couple moment at the free end. Differential equations governing the elastica of such column are derived, in which both the effects of taper type and shear deformation are included. Three kinds of taper types are considered: linear, parabolic and sinusoidal tapers. Differential equations are solved numerically to obtain the elastica of objective columns. The effects of various system parameters on the elastica are investigated extensively. Experimental studies were carried out in order to verify the theoretical results of non-linear behavior of the elasticas.