Structural Engineering and Mechanics

  • 제33권5호
  • /
  • Pages.621-633
  • /
  • 2009
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Numerical comparison of the beam model and 2D linearized elasticity

  • 투고 : 2008.05.17
  • 심사 : 2009.09.22
  • 발행 : 2009.11.30
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper we compare the solution of the one-dimensional beam model and the numerical solution of the two-dimensional linearized elasticity problem for rectangular domain of the beam-like form. We first derive the beam model starting from the two-dimensional linearized elasticity, the same way it is derived from the three-dimensional linearized elasticity. Then we present the numerical solution of the two-dimensional problem by finite element method. As expected the difference of two approximations becomes smaller as the thickness of the beam tends to zero. We then analyze the applicability of the one-dimensional model and verify the main properties of the beam modeling for thin beams.

키워드

참고문헌

  1. Aganovi , I. and Tutek, Z. (1986), 'A justification of the one-dimensional linear model of elastic beam', Math. Method. Appl. Sci., 8, 1-14 https://doi.org/10.1002/mma.1670080102
  2. Albarracín, C.M. and Grossi, R.O. (2005), 'Vibrations of elastically restrained frames', J. Sound Vib., 285, 467-476 https://doi.org/10.1016/j.jsv.2004.09.013
  3. Andreuzzi, F. and Perrone, A. (2001), 'Analytical solution for upheaval bucklingin burried pipeline', Comput. Meth. Appl. Mech. Eng., 190, 5081-5087 https://doi.org/10.1016/S0045-7825(00)00366-2
  4. Chen, D.W. and Liu, T.L. (2006), 'Free and forcedvibrations ofa tapered cantilever beam carrying multiple point masses', Struct. Eng. Mech., 23(2), 209-216 https://doi.org/10.12989/sem.2006.23.2.209
  5. Ciarlet, P.G. (1990), Mathematical Elasticity, Vol. II: Theory of Plates, North-Holland
  6. Ciarlet, P.G. (1997), Mathematical Elasticity, Vol. III: Theory of Shells, North-Holland
  7. Ciarlet, P.G. and Destuynder, P. (1979), 'A justification of the two dimensional linear plate model', J. M$\dot{e}$canique, 18, 315-344
  8. Gu, U.C. and Cheng, C.C. (2004), 'Vibration analysis of a high-speed spindle under the action of a moving mass', J. Sound Vib., 278, 1131-1146 https://doi.org/10.1016/j.jsv.2003.10.034
  9. Hecht, F., Pironneau, O., Le Hyaric, A. and Ohtsuka, K. (2005), Freefem++ manual, http://www.freefem.org/ff++
  10. Hili, M.A., Fakhfakh, T. and Haddar, M. (2007), 'Vibration analysis of a rotating exible shaft-disk system', J. Eng. Math., 57, 351-363 https://doi.org/10.1007/s10665-006-9060-3
  11. Igawaa, H., Komatsub, K., Yamaguchia, I. and Kasaia, T. (2004), 'Wave propagation analysis of frame structures using the spectral element method', J. Sound Vib., 277, 1071-1081 https://doi.org/10.1016/j.jsv.2003.11.026
  12. Iimura, S. (2004), 'Simplified mechanical model for evaluating stress in pipeline subject to settlement', Constr. Build. Mater., 18, 469-479 https://doi.org/10.1016/j.conbuildmat.2004.01.002
  13. Jurak, M. and Tamba a, J. (1999), 'Derivation and justification of a curved rod model', Math. Model. Meth. Appl. Sci., 9(7), 991-1014 https://doi.org/10.1142/S0218202599000452
  14. Jurak, M. and Tamba a, J. (2001), 'Linear curved rod model. General curve', Math. Model. Meth. App. Sci., 11(7), 1237-1252 https://doi.org/10.1142/S0218202501001318
  15. Kim, J.T. (2004), 'Identification of prestress-loss in PSC beams using modal information', Struct. Eng. Mech., 17(3-4), 467-482 https://doi.org/10.12989/sem.2004.17.3_4.467
  16. Li, G.Q. and Guo, S.X. (2008), 'Analysis of restrained steel beams subjected to heating and cooling. Part I: Theory', Steel Compos. Struct., 8(1), 1-18
  17. Lu, Z.R., Liu, J.K. and Law, S.S. (2008), 'Identification of prestress force in a prestressed Timoshenko beam', Struct. Eng. Mech., 29(3), 241-258 https://doi.org/10.12989/sem.2008.29.3.241
  18. Rafii-Tabar, H. (2004), 'Computational modelling of thermo-mechanical and transport properties of carbon nanotubes', Phys. Rep., 390, 235-452 https://doi.org/10.1016/j.physrep.2003.10.012
  19. Rajasekaran, S. and Varghese, S.P. (2005), 'Damage detection in beams and plates using wavelet transforms', Comput. Concrete, 2(6), 481-498 https://doi.org/10.12989/cac.2005.2.6.481
  20. Trabucho, L. and Via o, J.M. (1996), Mathematical Modelling of Rods, in Handbook of Numerical Analysis, Vol. IV, Eds. P.G. Ciarlet, J. L. Lions, North-Holland
  21. Vanegas Useche, L.V., Abdel Wahab, M.M. and Parker, G.A. (2007), 'Dynamics of an unconstrained oscillatory flicking brush for road sweeping', J. Sound Vib., 307, 778-801 https://doi.org/10.1016/j.jsv.2007.07.010
  22. Yoon, J., Ru, C.Q. and Mioduchowski, A. (2003), 'Vibration of an embedded multiwall carbon nanotube', Compos. Sci. Technol., 63, 1533-1542 https://doi.org/10.1016/S0266-3538(03)00058-7

피인용 문헌

  1. Nonlinear analysis of finite beam resting on Winkler foundation with consideration of beam-soil interface resistance effect vol.38, pp.5, 2009, https://doi.org/10.12989/sem.2011.38.5.573