Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Static and dynamic analysis of circular beams using explicit stiffness matrix

  • Received : 2015.11.29
  • Accepted : 2016.07.12
  • Published : 2016.10.10
⟨ Previous Next ⟩

Abstract

Two new elements with six degrees of freedom are proposed by applying the equilibrium conditions and strain-displacement equations. The first element is formulated for the infinite ratio of beam radius to thickness. In the second one, theory of the thick beam is used. Advantage of these elements is that by utilizing only one element, the exact solution will be obtained. Due to incorporating equilibrium conditions in the presented formulations, both proposed elements gave the precise internal forces. By solving some numerical tests, the high performance of the recommended formulations and also, interaction effects of the bending and axial forces will be demonstrated. While the second element has less error than the first one in thick regimes, the first element can be used for all regimes due to simplicity and good convergence. Based on static responses, it can be deduced that the first element is efficient for all the range of structural characteristics. The free vibration analysis will be performed using the first element. The results of static and dynamic tests show no deficiency, such as, shear and membrane locking and excessive stiff structural behavior.

Keywords

References

  1. Ashwell, D.G. and Sabir, A.B. (1971), "Limitations of certain curved finite elements when applied to arches", Int. J. Mech. Sci., 13, 133-139. https://doi.org/10.1016/0020-7403(71)90017-8
  2. Benedetti, A. and Tralli, A. (1989), "A new hybrid F.E. model for arbitrarily curved beam-i. linear analysis", Comput. Struct., 33(6), 1437-1449. https://doi.org/10.1016/0045-7949(89)90484-7
  3. Choi, J.K. and Lim, J.K. (1993), "Simple curved shear beam elements", Commun. Numer. Meth. Eng., 9, 659-669. https://doi.org/10.1002/cnm.1640090805
  4. Choi, J.K. and Lim, J.K. (1995), "General curved beam elements based on the assumed strain fields", Comput. Struct., 55(3), 379-386. https://doi.org/10.1016/0045-7949(95)98865-N
  5. Dawe, D.J. (1974), "Curved finite elements for the analysis of shallow and deep arches", Comput. Struct., 4, 559-580. https://doi.org/10.1016/0045-7949(74)90007-8
  6. Eisenberger, M. and Efraim, E. (2001), "In-plane vibrations of shear deformable curved beams", Int. J. Numer. Meth. Eng., 52, 1221-1234. https://doi.org/10.1002/nme.246
  7. Gimena, L., Gonzaga, P. and N. Gimena, F. (2010), "Forces, moments, rotations, and displacements of polynomial-shaped curved beams", Int. J. Struct. Stab. Dyn., 10(1), 77-89. https://doi.org/10.1142/S0219455410003336
  8. Gonzaga, P., Gimena, F.N. and Gimena, L. (2014), "Stiffness and transfer matrix analysis in global coordinates of a 3D curved beam", J. Struct. Stab. Dyn., 14(7), 1450019. https://doi.org/10.1142/S0219455414500199
  9. Heppler, G.R. (1992), "An element for studying the vibration of unrestrained curved Timoshenko beams", J. Sound Vib., 158(3), 387-404. https://doi.org/10.1016/0022-460X(92)90416-U
  10. Ishaquddin, M., Raveendranath, P. and Reddy, J.N. (2013), "Coupled polynomial field approach for elimination of flexure and torsion locking phenomena in the Timoshenko and Euler-Bernoulli curved beam elements", Finite Elem. Anal. Des., 65, 17-31. https://doi.org/10.1016/j.finel.2012.10.005
  11. Jafari, M. and Mahjoob, M.J. (2010), "An exact three-dimensional beam element with nonuniform cross section", J. Appl. Mech., 77(6), 061009. https://doi.org/10.1115/1.4002000
  12. Kim, J.G. and Kim, Y.Y. (1998), "A new higher-order hybrid-mixed curved beam element", Int. J. Numer. Meth. Eng., 43, 925-940. https://doi.org/10.1002/(SICI)1097-0207(19981115)43:5<925::AID-NME457>3.0.CO;2-M
  13. Kim, J.G. and Lee, J.K. (2008), "Free-vibration analysis of arches based on the hybrid-mixed formulation with consistent quadratic stress functions", Comput. Struct., 86, 1672-1681. https://doi.org/10.1016/j.compstruc.2007.07.002
  14. Kim, J.G. and Park, Y.K. (2008), "The effect of additional equilibrium stress functions on the three-node hybrid-mixed curved beam element", J. Mech. Sci. Tech., 22, 2030-2037. https://doi.org/10.1007/s12206-008-0752-7
  15. Kim, J.G., Lee, J.K. and Yoon, H.J. (2014), "On the effect of shear coefficients in free vibration analysis of curved beams", J. Mech. Sci. Tech., 28(8), 3181-3187. https://doi.org/10.1007/s12206-014-0727-9
  16. Krishnan, A. and Suresh, Y.J. (1998), "A simple cubic linear element for static and free vibration analyses of curved beams", Comput. Struct., 68, 473-489. https://doi.org/10.1016/S0045-7949(98)00091-1
  17. Lee, P.G. and Sin, H.C. (1994), "Locking-free curved beam element based on curvature", Int. J. Numer. Meth. Eng., 37, 989-1007. https://doi.org/10.1002/nme.1620370607
  18. Leung, A.Y.T. and Zhu, B. (2004), "Fourier p-elements for curved beam vibrations", Thin Wall. Struct., 42, 39-57. https://doi.org/10.1016/S0263-8231(03)00122-8
  19. Litewka, P. and Rakowski, J. (1998), "The exact thick arch finite element", Comput. Struct., 68, 369-379. https://doi.org/10.1016/S0045-7949(98)00051-0
  20. Litewka, P. and Rakowski, J. (2001), "Free vibrations of shear-flexible and compressible arches by FEM", Int. J. Numer. Meth. Eng., 52, 273-286. https://doi.org/10.1002/nme.249
  21. Meck, H.R. (1980), "An accurate polynomial displacement function for finite ring elements", Comput. Struct., 11, 265-269. https://doi.org/10.1016/0045-7949(80)90076-0
  22. Pandian, N., Appa Rao, T.V.S.R. and Chandra, S. (1989), "Studies on performance of curved beam finite elements for analysis of thin arches", Comput. Struct., 31(6), 997-1002. https://doi.org/10.1016/0045-7949(89)90284-8
  23. Raveendranath, P., Singh, G. and Pradhan, B. (1999), "A two-noded locking-free shear flexible curved beam element", Int. J. Numer. Meth. Eng., 44, 265-280. https://doi.org/10.1002/(SICI)1097-0207(19990120)44:2<265::AID-NME505>3.0.CO;2-K
  24. Raveendranath, P., Singh, G. and Rao, G.V. (2001), "A three-noded shear flexible curved beam element based on coupled displacement field interpolations", Int. J. Numer. Meth. Eng., 51, 85-101. https://doi.org/10.1002/nme.160
  25. Reddy, J.N. (1993), An Introduction to the Finite Element Method, McGraw-Hill, Inc.
  26. Sabir, A.B. and Ashwell, D.G. (1971), "A comparison of curved beam finite elements when used in vibration problems", J. Sound Vib., 18(4), 555-563. https://doi.org/10.1016/0022-460X(71)90106-4
  27. Stolarski, H. and Belytschko, T. (1982), "Membrane locking and reduced integration for curved beams", J. Appl. Mech., 49, 172-176. https://doi.org/10.1115/1.3161961
  28. Yang, F., Sedaghati, R. and Esmailzadeh, E. (2008), "Free in-plane vibration of general curved beams using finite element method", J. Sound Vib., 318, 850-867. https://doi.org/10.1016/j.jsv.2008.04.041
  29. Yang, S.Y. and Sin, H.C. (1995), "Curvature-based beam elements for the analysis of Timoshenko and shear-deformable curved beams", J. Sound Vib., 18, 7569-84.
  30. Zhu, Z.H. and Meguid, S.A. (2008), "Vibration analysis of a new curved beam element", J. Sound Vib., 309, 86-95. https://doi.org/10.1016/j.jsv.2007.04.051

Cited by

  1. Nonlinear vibration analysis of carbon nanotube reinforced composite plane structures vol.30, pp.6, 2016, https://doi.org/10.12989/scs.2019.30.6.493