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



Chen, Chang Hong;Zhu, Yan Fei;Yao, Yao;Huang, Ying

  • 투고 : 2015.04.02
  • 심사 : 2015.12.25
  • 발행 : 2016.02.10


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.


pre-twisted;thin-walled;coupling;warping;finite element model


  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.
  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.
  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.
  6. Dawe, D.J. (1978), "A finite element for the vibration analysis of Timoshenko beams", J. Sound Vib., 60, 11-20.
  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.
  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.
  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.
  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.
  12. Rao, S.S. and Gupta, R.S. (2001), "Finite element vibration analysis of rotating Timoshenko beams", J. Sound Vib., 242, 103-124.
  13. Rosen, A. (1991), "Structural and dynamic behavior of pre-twisted rods and beams", Appl. Mech. Rev., 44, 483-515.
  14. Shadnam, M.R. and Abbasnia, R. (2002), "Stability of pre-twisted beams in crosses bracings", Appl. Mech. Tech. Phys., 43(2), 328-335.
  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.
  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.
  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.

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연구 과제 주관 기관 : National Natural Science Foundation of China, Shanxi National Science Foundation of China, Central Universities