Browse > Article

Static and Dynamic Optimal Shapes of Both Clamped Columns with Constant Volume  

Lee, Byoung Koo (원광대학교 토목환경공학과)
Kim, Suk Ki (단국대학교 토목환경공학과)
Publication Information
Journal of Korean Society of Steel Construction / v.19, no.1, 2007 , pp. 99-106 More about this Journal
Abstract
This paper deals with the static and dynamic optimal shapes of both clamped columns with constant volume. The parabolic taper with the regular polygon cross-section is considered, whose material volume and column length are held constant. Numerical methods are developed for solving natural frequencies and buckling loads of columns subjected to an axial compressive load. Differential equations governing the free vibrations of such column are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine natural frequencies and buckling loads, respectively. From the numerical results, dynamic stability regions, dynamic optimal shapes and configurations of strongest columns are presented in figures and tables.
Keywords
natural frequency; buckling load; both clamped column; constant volume; stability region; optimal shape;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 문지호, 윤기용, 조영래, 이학은 (2006) 고정지점 포물선 아치의 면내 좌굴강도, 한국강구조학회 논문집, 제18권, 제3호, pp.301-310
2 Haftka, R.T., Grudal, Z. and Kamat, M.P. (1990) Element of structural optimization, Klüver Academic Publisher
3 Lee, B.K., Carr, A.J., Lee, T.E. and Ahn, D.S. (2005) Elasticas and buckling loads of shear deformable tapered columns, International Journal of Structural Stability and Dynamics, Vol. 5, No. 3, pp. 317-335   DOI
4 Lee, B.K., Carr, A.J., Lee, T.E. and Kim, I.J. (2006) Buckling loads of columns with constant volume, Journal of Sound and Vibration, Vol. 294, pp. 381-387   DOI   ScienceOn
5 Niordson, F.I. (1965) On the optimal design of a vibrating beam, Quarterly Applied Mechanics, Vol. 23, pp. 47-53
6 Pedersen, P. (1977) Inference of boundary conditions on the stability of a column under the nonconservative load, International Journal of Solids and Structures, Vol. 13, pp. 445-455   DOI   ScienceOn
7 윤기용, 강영종 (1998) 유한요소법을 이용한 수평곡선 I형교의 자유진동해석, 한국강구조학회 논문집, 제10권, 제1호, pp. 47-61
8 이병구, 오상진, 이태은, 강희종 (2005) 자유단 집중질량 및 스프링을 갖는 변단면 Beck 기둥의 안정해석, 대한토목학회논문집, 제25권, 제6A호, pp. 1157-1162
9 Lee, B.K. and Oh, S.J. (2000) Elasticas and buckling loads of simple tapered columns with constant volume, International Journal of Solids and Structures, Vol. 37, pp. 2507-2518   DOI   ScienceOn
10 Taylor, J.E. (1987) The strongest column - An energy approach, Journal of Applied Mechanics, ASME, Vol. 29, pp. 159-164
11 Kamat, M.P. and Simites, G.J. (1973) Optimal beam frequencies by the finite element displacement method, International Journal of Solids and Structures, Vol. 9, pp. 415-419   DOI   ScienceOn
12 이병구, 김석기 (2006) 일정체적 단순지지 변단면 기둥의 정,동적 안정해석, 대한토목학회 논문집, 제26권, 제3A호, pp. 533∼538
13 Sato, K. (1996) Instability of a clamped-elastically restrained Timoshenko columns carrying a tip load subjected to a follower force, Journal of Sound and Vibration, Vol. 194, pp. 623-630   DOI   ScienceOn
14 정진섭, 이병구, 김권식, 김종웅 (2005) 자유단 집중질량을 갖는 변단면 캔틸레버 기둥의 임계하중, 한국강구조학회 논문집, 제17권, 제6호, pp. 699-706
15 Kamat, M.P. and Simites, G.J. (1975) Effect of shear deformation and rotatory inertia on optimal beam frequencies, International Journal of Numerical Methods in Engineering, Vol. 9, pp. 51-62   DOI   ScienceOn
16 Bokaian, A. (1988) Natural frequencies of beams under compressive axial load, Journal of Sound and Vibration, Vol. 126, pp. 49-65   DOI   ScienceOn
17 Kupta, A.K. (1985) Vibration of tapered beam, Journal of Structural Engineering, ASCE, Vol. 113, pp. 1244-1247
18 Carnahan, B., Luther, H.A. and Wilkes, J.O. (1969) Applied numerical method, John Wiley & Sons, USA