Structural Engineering and Mechanics

  • 제63권1호
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  • Pages.11-21
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  • 2017
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Novel techniques for improving the interpolation functions of Euler-Bernoulli beam

  • Chekab, Alireza A. (Civil Engineering Department, Mashhad Branch, Islamic Azad University) ;
  • Sani, Ahmad A. (Civil Engineering Department, Ferdowsi University of Mashhad)
  • 투고 : 2016.05.16
  • 심사 : 2017.06.09
  • 발행 : 2017.07.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the efficiency and the accuracy of classical (CE) and high order (HE) beam element are improved by introducing two novel techniques. The first proposed element (FPE) provides an alternative for (HE) by taking the mode shapes of the clamped-clamped (C-C) beam into account. The second proposed element (SPE) which could be utilized instead of (CE) and (HE) considers not only the mode shapes of the (C-C) beam but also some virtual nodes. It is numerically proven that the eigenvalue problem and the frequency response function for Euler-Bernoulli beam are obtained more accurate and efficient in contrast to the traditional ones.

키워드

참고문헌

  1. Abbas, B.A.H. (1984), "Vibrations of timoshenko beams with elastically restrained ends", J. Sound Vib., 97(4), 541-548. https://doi.org/10.1016/0022-460X(84)90508-X
  2. Abu-Hilal, M. (2003), "Forced vibration of Euler-Bernoulli beams by means of dynamic green functions", J. Sound Vib., 267(2), 191-207. https://doi.org/10.1016/S0022-460X(03)00178-0
  3. Akgoz, B. and Civalek, O. (2014), "A new trigonometric beam model for buckling of strain gradient microbeams", Int. J. Mech. Sci., 81, 88-94. https://doi.org/10.1016/j.ijmecsci.2014.02.013
  4. Akgoz, B. and Civalek, O. (2015), "A novel microstructuredependent shear deformable beam model", Int. J. Mech. Sci., 99, 10-20. https://doi.org/10.1016/j.ijmecsci.2015.05.003
  5. Anton, H. and Rorres, C. (2005), Elementary linear algebra with applications, (9th Edition), John wiley & Sons.
  6. Augarde, C.E. (1998), "Generation of shape functions for straight beam elements", Comput. Struct., 68(6), 555-560. https://doi.org/10.1016/S0045-7949(98)00071-6
  7. Bishop, J.E. (2014), "A displacement‐based finite element formulation for general polyhedra using harmonic shape functions", Int. J. Numer. Method. Eng., 97(1), 1-31. https://doi.org/10.1002/nme.4562
  8. Carrera, E., Pagani, A. and Petrolo, M. (2015), "Refined 1D finite elements for the analysis of secondary primary, and complete civil engineering structures", J. Struct. Eng., 141(4), 04014123. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001076
  9. Civalek, O. (2004), "Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns", Eng. Struct., 26(2), 171-186. https://doi.org/10.1016/j.engstruct.2003.09.005
  10. Civalek, O., Korkmaz, A. and Demir, C. (2010), "Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on twoopposite edges", Adv. Eng. Softw., 41(4), 557-560. https://doi.org/10.1016/j.advengsoft.2009.11.002
  11. Cook, R.D., Malkus, D.S. and Plesha, M.E. (1989), Concepts and Applications of Finite Element Analysis, (3rd Edition), John Wiley & Sons, Singapore.
  12. Dukic, E.P., Jelenic, G. and Gacesa, M. (2014), "Configurationdependent interpolation in higher-order 2D beam finite elements," Finite Element Anal. Des., 78, 47-61. https://doi.org/10.1016/j.finel.2013.10.001
  13. Greif, R. and Mittendorf, S.C. (1976), "Structural vibrations and fourier series", J. Sound Vib., 48(1), 113-122. https://doi.org/10.1016/0022-460X(76)90375-8
  14. Gunda, J.B. and Ganguli, R. (2008), "New rational interpolation functions for finite element analysis of rotating beams", Int. J. Mech. Sci., 50(3), 578-588. https://doi.org/10.1016/j.ijmecsci.2007.07.014
  15. Hashemi, S.M. and Richard, M.J. (1999), "A new Dynamic Finite Element (DFE) formulation for lateral free vibrations of Euler-Bernoulli spinning beams using trigonometric shape functions", J. Sound Vib., 220(4), 578-588.
  16. Hughes, T.J.R. (1987), Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, New Jersey.
  17. Inaudi, J.A. (2013), "Adaptive frequency-dependent shape functions for accurate estimation of modal frequencies", J. Eng. Mech., 139(12),1844-1855. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000609
  18. Kazakov, K.S. (2012), "Elastodynamic infinite elements based on modified bessel shape functions, applicable in the finite element method", Struct. Eng. Mech., 42(3), 353-362. https://doi.org/10.12989/sem.2012.42.3.353
  19. Kim, H.K. and Kim, M.S. (2001), "Vibration of beams with generally restrained boundary conditions using Fourier series", J. Sound Vib., 245(5), 771-784. https://doi.org/10.1006/jsvi.2001.3615
  20. Kim, H.G. (2014), "A study on the development of shape functions of polyhedral finite elements", J. Comput. Struct. Eng. Inst. Korea, 27(3), 183-189. https://doi.org/10.7734/COSEIK.2014.27.3.183
  21. Li, T., Qi, Z., Ma, X. and Chen, W. (2015), "Higher-order assumed stress quadrilateral element for the Mindlin plate bending problem", Struct. Eng. Mech., 54(3), 393-417. https://doi.org/10.12989/sem.2015.54.3.393
  22. Liu, G.R. and Wu, T.Y. (2001), "Vibration analysis of beams using the generalized differential quadrature rule and domain decomposition", J. Sound Vib., 246(3), 461-481. https://doi.org/10.1006/jsvi.2001.3667
  23. Macbai, J.C. and Genin, J. (1973), "Natural frequencies of a beam considering support characteristics", J. Sound Vib., 27(2), 197-206. https://doi.org/10.1016/0022-460X(73)90061-8
  24. Milsted, M.G. and Hutchinson, J.R. (1974), "Use of trigonometric terms in the finite element method with application to vibrating membranes", J. Sound Vib., 32(3), 327-346. https://doi.org/10.1016/S0022-460X(74)80089-1
  25. Rao, C.K. and Mirza, S. (1989), "A note on vibrations of generally restrained beams", J. Sound Vib., 130(3), 453-465. https://doi.org/10.1016/0022-460X(89)90069-2
  26. Rao, S.S. (2011), The Finite Element Method in Engineering, (5th Edition), Elsevier, Boston.
  27. Reddy, J.N. (2006), An Introduction to the Finite Element Method, (3rd Edition), McGraw-Hill, Singapore.
  28. Wang, J.T.S. and Lin, C.C. (1996), "Dynamic analysis of generally supported beams using Fourier series", J. Sound Vib., 196(3), 285-293. https://doi.org/10.1006/jsvi.1996.0484
  29. Wang, X. and Yuan, Z. (2017), "Discrete singular convolution and taylor series expansion method for free vibration analysis of beams and rectangular plates with free boundaries", Int. J. Mech. Sci., 122, 184-191. https://doi.org/10.1016/j.ijmecsci.2017.01.023