Structural Engineering and Mechanics

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The finite element model research of the pre-twisted thin-walled beam

  • Chen, Chang Hong (School of Mechanics and Civil Engineering, Northwestern Polytechnical University) ;
  • Zhu, Yan Fei (School of Mechanics and Civil Engineering, Northwestern Polytechnical University) ;
  • Yao, Yao (School of Mechanics and Civil Engineering, Northwestern Polytechnical University) ;
  • Huang, Ying (School of Civil Engineering, Xi’an University of Architecture and Technology)
  • Received : 2015.04.02
  • Accepted : 2015.12.25
  • Published : 2016.02.10
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Abstract

Based on the traditional mechanical model of thin-walled straight beam, the paper makes analysis and research on the pre-twisted thin-walled beam finite element numerical model. Firstly, based on the geometric deformation differential relationship, the Saint-Venant warping strain of pre-twisted thin-walled beam is deduced. According to the traditional thin-walled straight beam finite element mechanical model, the finite element stiffness matrix considering the Saint-Venant warping deformations is established. At the same time, the paper establishes the element stiffness matrix of the pre-twisted thin-walled beam based on the classic Vlasov Theory. Finally, by calculating the pre-twisted beam with elliptical section and I cross section and contrasting three-dimensional solid finite element using ANSYS, the comparison analysis results show that pre-twisted thin-walled beam element stiffness matrix has good accuracy.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China, Shanxi National Science Foundation of China, Central Universities

References

  1. ANSYS Inc. (2007), ANSYS APDL Programmer's Guide Release 11.0, 3th Edition, America
  2. Banerjee, J.R. (2001), "Free vibration analysis of a twisted beam using the dynamic stiffness method", Int. J. Solid. Struct., 38, 6703-6722. https://doi.org/10.1016/S0020-7683(01)00119-6
  3. Carnegie, W. and Thomas, J. (1972), "The effects of shear deformation and rotary inertia on the lateral frequencies of cantileverbeams in bending", J. Eng. Indus. Tran. Am. Soc. Mech. Eng., 94, 267-278.
  4. Chen, C.K. and Ho, S.H. (1999), "Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform", Int. J. Mech. Sci., 41, 1339-1356. https://doi.org/10.1016/S0020-7403(98)00095-2
  5. Chen, W.R. and Keer, L.M. (1993), "Transverse vibrations of a rotating twisted Timoshenko beam under axial loading", J. Vib. Acoust., 115, 285-294. https://doi.org/10.1115/1.2930347
  6. Dawe, D.J. (1978), "A finite element for the vibration analysis of Timoshenko beams", J. Sound Vib., 60, 11-20. https://doi.org/10.1016/0022-460X(78)90397-8
  7. Dawson, B., Ghosh, N.G. and Carnegie, W. (1971), "Effect of slenderness ratio on the natural frequencies of pre-twisted cantilever beams of uniform rectangular cross-section", J. Mech. Eng. Sci., 13, 51-59. https://doi.org/10.1243/JMES_JOUR_1971_013_008_02
  8. Gupta, R.S. and Rao, S.S. (1978), "Finite element eigenvalue analysis of tapered and twisted Timoshenko beams", J. Sound Vib., 56, 187-200. https://doi.org/10.1016/S0022-460X(78)80014-5
  9. Leung, A.Y.T. (2010), "Dynamics and buckling of thin pre-twisted beams under axial load and torque", Int. J. Struct. Stab. Dyn., 32(10), 957-981.
  10. Lin, S.M., Wang, W.R. and Lee, S.Y. (2001), "The dynamic analysis of nonuniformly pre-twisted Timoshenko beams with elastic boundary conditions", Int. J. Mech. Sci., 43, 2385-2405. https://doi.org/10.1016/S0020-7403(01)00018-2
  11. Petrov, E. and Geradin, M. (1998), "Finite element theory for curved and twisted beams based on exact solutions for three dimensional solids. Part 1: beam concept and geometrically exact nonlinear fomulation, Part 2: anisotropic and advanced beam models", Comput. Meth. Appl. Mech. Eng., 165(6), 43-127. https://doi.org/10.1016/S0045-7825(98)00061-9
  12. Rao, S.S. and Gupta, R.S. (2001), "Finite element vibration analysis of rotating Timoshenko beams", J. Sound Vib., 242, 103-124. https://doi.org/10.1006/jsvi.2000.3362
  13. Rosen, A. (1991), "Structural and dynamic behavior of pre-twisted rods and beams", Appl. Mech. Rev., 44, 483-515. https://doi.org/10.1115/1.3119490
  14. Shadnam, M.R. and Abbasnia, R. (2002), "Stability of pre-twisted beams in crosses bracings", Appl. Mech. Tech. Phys., 43(2), 328-335. https://doi.org/10.1023/A:1014726314758
  15. Subrahmanyam, K.B., Kulkarni, S.V. and Rao, J.S. (1981), "Coupled bending-bending vibration of pre-twisted cantilever blading allowing for shear deflection and rotary inertia by the Reissner method", Int. J. Mech. Sci., 23, 517-530. https://doi.org/10.1016/0020-7403(81)90058-8
  16. Yu, A., Yang, R.Q. and Hao, Y. (2009), "Theory and application of naturally curved and twisted beams with closed thin-walled cross sections", J. Mech. Eng., 55(12), 733-741.
  17. Zelenina, A.A. and Zubov, L.M. (2006), "Saint venant problem for a naturally twisted rod in nonlinear moment elasticity theory", Doklady Phys., 51(3), 136-139. https://doi.org/10.1134/S1028335806030104
  18. 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(5), 1445-1451. https://doi.org/10.1016/j.finel.2003.10.001

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