Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A general solution to structural performance of pre-twisted Euler beam subject to static load

  • Huang, Ying (School of Civil Engineering, Xi'an University of Architecture and Technology) ;
  • Chen, Chang Hong (School of Mechanics and Civil Engineering, Northwestern Polytechnical University) ;
  • Keer, Leon M. (Civil and Environmental Engineering, Northwestern University) ;
  • Yao, Yao (School of Mechanics and Civil Engineering, Northwestern Polytechnical University)
  • Received : 2017.03.30
  • Accepted : 2017.07.03
  • Published : 2017.10.25
⟨ Previous Next ⟩

Abstract

Based on the coupled elastic bending deformation features and relationships between the internal force and deformation of pre-twisted Euler beam, the generalized strain, the equivalent constitutive equation and the equilibrium equation of pre-twisted Euler beam are developed. Based on the properties of the dual-antisymmetric matrix, the general solution of pre-twisted Euler beam is obtained. By comparison with ANSYS solution by using straight Beam-188 element based on infinite approach strategy, the results show that the developed method is available for pre-twisted Euler beam and also provide an accuracy displacement interpolation function for the subsequent finite element analysis. The effect of pre-twisted angle on the mechanical property has been investigated.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China, China Scholarship Council, Shaanxi National Science Foundation of China

References

  1. Banerjee, J.R (2001), "Free vibration analysis of a twisted beam using the dynamic stiffness method", Int. J. Solid. Struct., 38(38), 6703-6722. https://doi.org/10.1016/S0020-7683(01)00119-6
  2. Banerjee, J.R (2004), "Development of an exact dynamic stiffness matrix for free vibration analysis of a twisted Timoshenko beam", J. Sound Vib., 270(1), 379-401. https://doi.org/10.1016/S0022-460X(03)00633-3
  3. Berdichevskii, V.L. and Starosel'skii, L.A. (1985), "Bending, extension, and torsion of naturally twisted rods", J. Appl. Math. Mech., 49(6), 746-755. https://doi.org/10.1016/0021-8928(85)90012-7
  4. Chen, C.H., Yao, Y. and Huang, Y. (2014), "Elastic flexural and torsional buckling behaviour of pre-twisted bar under axial load", Struct. Eng. Mech., 49(2): 273-283. https://doi.org/10.12989/sem.2014.49.2.273
  5. Chen, C.H., Zhu, Y.F., Yao, Y. and Huang, Y. (2016), "The finite element model research of the pre-twisted thin-walled beam", Struct. Eng. Mech., 57(3), 389-402. https://doi.org/10.12989/sem.2016.57.3.389
  6. Chen, W.R. (2010), "On the vibration and stability of spinning axially loaded pre-twisted Timoshenko beams", Finite Elem. Anal. Des., 46(11), 1037-1047. https://doi.org/10.1016/j.finel.2010.07.020
  7. Chen, W.R. and Keer, L.M. (1993), "Transverse vibrations of a rotating twisted Timoshenko beam under axial loading", J. Vib. Acoust., 115(3), 285-294. https://doi.org/10.1115/1.2930347
  8. Choi, S.C., Park, J.S. and Kim, J.H. (2007), "Vibration control of pre-twisted rotating composite thin-walled beams with piezoelectric fiber composites", J. Sound Vib., 300(1), 176-196. https://doi.org/10.1016/j.jsv.2006.07.051
  9. Kar, R.C. and Ray, K. (1995), "Dynamic stability of a pre-twisted, three layered, symmetric sandwich beam", J. Sound Vib., 183(4), 591-606. https://doi.org/10.1006/jsvi.1995.0274
  10. Lee, H.P. (1995), "Dynamic stability of spinning pre-twisted beams subject to axial pulsating loads", Comput. Meth. Appl. Mech. Eng., 127(1), 115-126. https://doi.org/10.1016/0045-7825(95)00855-3
  11. Long, X., Tan, K.H. K. Lee, C.K. (2013), "A 3D co-rotational beam element for steel and RC framed structures", Struct. Eng. Mech., 48(5), 587-613. https://doi.org/10.12989/sem.2013.48.5.587
  12. Long, X., Yuan, W., Tan, K.H. and Lee, C.K. (2013), "A superelement formulation for efficient structural analysis in progressive collapse", Struct. Eng. Mech., 48(3), 309-331. https://doi.org/10.12989/sem.2013.48.3.309
  13. Nabi, S.M. and Ganesan, N. (1996), "Comparison of beam and plate theories for free vibrations of metal matrix composite pretwisted blades", J. Sound Vib., 189(2), 149-160. https://doi.org/10.1006/jsvi.1996.0012
  14. Petrov, E. and Geradin, M. (1998), "Finite element theory for curved and twisted beams based on exact solutions for threedimensional solids Part 1: Beam concept and geometrically exact nonlinear formulation", Comput. Meth. Appl. Mech. Eng., 165(1), 43-92. https://doi.org/10.1016/S0045-7825(98)00061-9
  15. Polyakov, N.A. and Ustinov, Y.A. (1996), "Homogeneous solutions and Saint-Venant problems for a naturally twisted rod", J. Appl. Math. Mech., 60(4), 657-664. https://doi.org/10.1016/S0021-8928(96)00082-2
  16. Sabuncu, M. and Evran, K. (2006), "Dynamic stability of a rotating pre-twisted asymmetric cross-section Timoshenko beam subjected to an axial periodic force", Int. J. Mech. Sci., 48(6), 579-590. https://doi.org/10.1016/j.ijmecsci.2006.01.010
  17. Sinha, S.K. and Turner, K.E. (2011), "Natural frequencies of a pre-twisted blade in a centrifugal force field", J. Sound Vib., 330(11), 2655-2681. https://doi.org/10.1016/j.jsv.2010.12.017
  18. Subrahmanyam, K.B., Kulkarni, S.V. and Rao, J.S. (1981), "Coupled bending-bending vibrations of pre-twisted cantilever blading allowing for shear deflection and rotary inertia by the Reissner method", Int. J. Mech. Sci., 23(9), 517-530. https://doi.org/10.1016/0020-7403(81)90058-8
  19. Yardimoglu, B. and Yildirim, T. (2004), "Finite element model for vibration analysis of pre-twisted Timoshenko beam", J. Sound Vib., 273(4), 741-754. https://doi.org/10.1016/j.jsv.2003.05.003
  20. Yoo, H.H., Kwak, J.Y. and Chung, J. (2001), "Vibration analysis of rotating pre-twisted blades with a concentrated mass", J. Sound Vib., 240(5), 891-908. https://doi.org/10.1006/jsvi.2000.3258
  21. Young, T.H. and Gau, C.Y. (2003), "Dynamic stability of pretwisted beams with non-constant spin rates under axial random forces", Int. J. Solid. Struct., 40(18), 4675-4698. https://doi.org/10.1016/S0020-7683(03)00197-5
  22. Yu, A., Fang, M. and Ma, X. (2002), "Theoretical research on naturally curved and twisted beams under complicated loads", Comput. Struct., 80(32), 2529-2536. https://doi.org/10.1016/S0045-7949(02)00329-2
  23. Zubov, L. M (2006), "The non-linear Saint-Venant problem of the torsion, stretching and bending of a naturally twisted rod", J. Appl. Math. Mech., 70(2), 300-310. https://doi.org/10.1016/j.jappmathmech.2006.06.016
  24. Zupan, D. and Saje, M. (2004), "On "A proposed standard set of problems to test finite element accuracy": the twisted beam", Finite Elem. Anal. Des., 40(11), 1445-1451. https://doi.org/10.1016/j.finel.2003.10.001