Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Geometrical Non-linear Analyses of Tapered Cantilever Column Subjected to Sub-tangential Follower Force

경사 종동력을 받는 변단면 기하 비선형 캔틸레버 기둥의 수치해석

  • Lee, Byoung-Koo (Department of Civil and Environmental Engineering, Wonkwang University) ;
  • Oh, Sang-Jin (Department of Civil and Environmental Engineering, Jeonnam Provincial College) ;
  • Lee, Tae-Eun (Department of Civil and Environmental Engineering, Wonkwang University)
  • 이병구 (원광대학교 토목환경공학과) ;
  • 오상진 (전남도립대학 토목환경과) ;
  • 이태은 (원광대학교 토목환경공학과)
  • Received : 2012.05.08
  • Accepted : 2012.12.13
  • Published : 2013.02.28
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Abstract

This paper deals with geometrical non-linear analyses of the tapered cantilever column subjected to the sub-tangential follower force at the free end. Cross-sections of the column whose flexural rigidities are functionally varied with the axial coordinate. The differential equations governing the elastica of such column are derived on the basis of the large deformation theory. These differential equations have three unknown parameters of the vertical and horizontal deflections and rotation at the free end. These differential equations are numerically solved by the iteration technique for obtaining three unknowns and elastica of the deformed column. For validating theories developed herein, laboratory scaled experiments are conducted.

이 연구는 자유단에 경사 종동력을 받는 변단면 기하 비선형 캔틸레버 기둥의 수치해석에 관한 연구이다. 기둥의 단면은 휨 강성이 부재축을 따라 함수적으로 변화하는 변단면으로 선택하였다. 이러한 기둥의 정확탄성곡선을 지배하는 미분방정식을 대변형 이론을 이용하여 유도하였다. 이 미분방정식은 자유단 수직변위, 수평변위 및 회전각의 3개의 미지변수를 갖는다. 이 미분방정식을 반복법으로 수치해석하여 기둥의 미지변수와 정확탄성곡선을 산정하였다. 이 연구의 이론을 검증하기 위하여 실험실 규모의 실험을 실행하였다.

Keywords

References

  1. Beck, M. (1952) Die Knicklast Des Einseitig Eigenspannten, Tangential Gedruckten Stabes. Zeitschrift fur Angewandte Mathematik und Physik, 3, pp. 225-228. https://doi.org/10.1007/BF02008828
  2. Carnahan, B., Luther, H.A., Wilkes, J.O. (1969) Applied Numerical Methods, John Wiley and Sons, USA.
  3. Chen, L.W., Ku, D.M. (1992) Eigenvalue Sensitivity in Stability Analysis of Beck's Column with a Concentrated Mass at the Free End, Journal of Sound and Vibration, 153, pp.403-411. https://doi.org/10.1016/0022-460X(92)90373-6
  4. Gere, J.M., Timoshenko, S.P. (1997) Mechanics of Materials, PWS Publishing Company, USA.
  5. Gupta, A.K. (1985) Free Vibrations of Tapered Beam, Journal of the Structural Division, ASCE, 11(1), pp.19-36.
  6. Koiter, W.T. (1996) Unrealistic Follower Forces, Journal of Sound and Vibration, 194, pp.403-411.
  7. Kounadis, A., Katsikadelis, J.T. (1976) Shear and Rotatory Inertia Effects on Beck's Column, Journal of Sound and Vibration, 49, pp.171-178. https://doi.org/10.1016/0022-460X(76)90494-6
  8. Kuo, S.R., Yang, Y.B. (1994) Critical Load Analysis of Undamped Non-conservative Systems using Bi-eigenvalue Curves, AIAA Journal, 32 pp.2462-2468. https://doi.org/10.2514/3.12314
  9. Langthjem, A., Sugiyama, Y. (1999) Optimal Shape Design Against Flutter of a Cantilevered Column with an End-mass of Finite Size Subjected to a Non-conservative Load, Journal of Sound and Vibration, 226, pp.1-23. https://doi.org/10.1006/jsvi.1999.2211
  10. Lee, B.K., Carr, A.J., Lee, T.E., Kim. I.J. (2005) Buckling Loads of Columns with Constant Volume, International Journal of Structural Stability and Dynamics. 296, pp.381-387.
  11. Lee, B.K., Oh, S.J., Lee, T.E. (2012a) Geometrical Non-linear Analyses of Tapered Variable-Arc-Length Beam subjected to Combined Load, Journal of the Computational Structural Engineering Institute of Korea, 25(2), pp.129-138. https://doi.org/10.7734/COSEIK.2012.25.2.129
  12. Lee, B.K., Oh, S.J., Lee, T.E. (2012b) Novel Method for Numerical Analyses of Tapered Geometrical Non-linear Beam with Three Unknown Parameters, Journal of the Korean Society of Civil Engineers, 33(1), pp.13-22. https://doi.org/10.12652/Ksce.2013.33.1.013
  13. Lee, B.K., Oh, S.J., Lee, T.E., Kang, H.J. (2005) Stability Analysis of Tapered Beck Columns with a Tip Mass and an Elastic Spring at the Free End, Journal of the Korean Society of Civil Engineers, 25(6A), pp.1157-1162.
  14. Pedersen, P. (1977) Influence of Boundary Conditions on the Stability of a Column Under Nonconservative Load, International Journal of Solids and Structures, 13, pp.445-455. https://doi.org/10.1016/0020-7683(77)90039-7
  15. Ryu, B.J., Sugiyama, Y., Lee, G.S. (1997) The Influence of an Intermediate Support on the Dynamic Stability of Cantilevered Timoshenko Beams Subjected to Sub-tangential Forces, Proceedings of Asia-Pacific Vibration Conference '97, Kyoungju, Korea, pp.163-168.
  16. Sankaran, G.V., Rao, G.V. (1976) Stability of Tapered Cantilever Columns Subjected Follower Forces, Computer & Structures, 6, pp.217-220. https://doi.org/10.1016/0045-7949(76)90033-X
  17. Sato, K. (1996) Instability of an Clamped-elastically Restrained Timoshenko Column Carrying a Tip Load Subjected to a Follower Force, Journal of Sound and Vibration, 194, pp.623-630. https://doi.org/10.1006/jsvi.1996.0381
  18. Sugiyama, Y., Langthjem, M.A., Ryu, B.J. (1999) Realistic Follower Forces, Journal of Sound and Vibration, 225, pp.779-782. https://doi.org/10.1006/jsvi.1998.2290
  19. Wilson, J.F. (1993) Experiments of the Strength of Solids, McGraw Hill, Inc., USA.