Structural Engineering and Mechanics

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The linear-elastic stiffness matrix model analysis of pre-twisted Euler-Bernoulli beam

  • Huang, Ying (School of Civil Engineering, Xi'an University of Architecture and Technology) ;
  • Zou, Haoran (School of Mechanics and civil Engineering, Northwestern Polytechnical University) ;
  • Chen, Changhong (School of Mechanics and civil Engineering, Northwestern Polytechnical University) ;
  • Bai, Songlin (School of Mechanics and civil Engineering, Northwestern Polytechnical University) ;
  • Yao, Yao (School of Mechanics and civil Engineering, Northwestern Polytechnical University) ;
  • Keer, Leon M. (Civil and Environmental Engineering, Northwestern University)
  • Received : 2019.02.18
  • Accepted : 2019.07.30
  • Published : 2019.12.10
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Abstract

Based on the finite element method of traditional straight Euler-Bernoulli beams and the coupled relations between linear displacement and angular displacement of a pre-twisted Euler-Bernoulli beam, the shape functions and stiffness matrix are deduced. Firstly, the stiffness of pre-twisted Euler-Bernoulli beam is developed based on the traditional straight Euler-Bernoulli beam. Then, a new finite element model is proposed based on the displacement general solution of a pre-twisted Euler-Bernoulli beam. Finally, comparison analyses are made among the proposed Euler-Bernoulli model, the new numerical model based on displacement general solution and the ANSYS solution by Beam188 element based on infinite approach. The results show that developed numerical models are available for the pre-twisted Euler-Bernoulli beam, and which provide more accurate finite element model for the numerical analysis. The effects of pre-twisted angle and flexural stiffness ratio on the mechanical property are investigated.

Keywords

Acknowledgement

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

The authors would like to acknowledge the financial support by the National Natural Science Foundation of China (51408489, 51248007, 51308448 and 11572249), the China Scholarship Council (201606295016), and the Shaanxi National Science Foundation of China (2017JQ7255), and Sponsored by the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University (ZZ2019127).

References

  1. Adair, D. and Jaeger, M. (2018), "Vibration analysis of a uniform pre-twisted rotating Euler-Bernoulli beam using the modified Adomian decomposition method", Math. Mech. Solids, 23(9), 1345-1363. https://doi.org/10.1177/1081286517720843.
  2. ANSYS Inc. (2016), ANSYS Programmer's Guide Release 18.0, 7th Ed., USA.
  3. Banerjee, J. R. (2001), "Free vibration analysis of a twisted beam using the dynamic stiffness method", J. Solids Structures, 38(38), 6703-6722. https://doi.org/10.1016/S0020-7683(01)00119-6.
  4. 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.
  5. Bahaadini, R. and Saidi, A. R. (2019), "Aero-thermoelastic flutter analysis of pre-twisted thin-walled rotating blades reinforced with functionally graded carbon nanotubes", European J. Mech. A/Solids, 75, 285-306. https://doi.org/10.1016/j.euromechsol.2019.01.018.
  6. Chen, J. and Li, Q. S. (2019), "Vibration characteristics of a rotating pre-twisted composite laminated blade", Compos. Struct., 208, 78-90. https://doi.org/10.1016/j.compstruct.2018.10.005.
  7. 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.
  8. Chen, W. R. and Keer, L. M. (1993), "Transverse vibrations of a rotating twisted Timoshenko beam under axial loading", J. Vib. Acoustics, 115(3), 285-294. https://doi.org/10.1115/1.2930347.
  9. Chen, C. H., Zhu, Y. F., Yao, Y., Huang, Y. and Long, X. (2016), "An evaluation method to predict progressive collapse resistance of steel frame structures", J. Constructional Steel Res., 122, 238-250. https://doi.org/10.1016/j.jcsr.2016.03.024.
  10. Chen, C. H., Yao, Y. and Huang, Y. (2014), "Elastic flexural and torsional buckling behavior of pre-twisted bar under axial load", Struct. Eng. Mech., 49(2), 273-283. https://doi.org/10.12989/sem.2014.49.2.273.
  11. 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.
  12. Gu, X. J., Hao, Y. X., Zhang, W., Liu, L. T. and Chen, J. (2019), "Free vibration of rotating cantilever pre-twisted panel with initial exponential function type geometric imperfection", Appl. Math. Model., 68, 327-352. https://doi.org/10.1016/j.apm.2018.11.037.
  13. Huang, Y., Chen, C., Zou, H. and Yao, Y. (2019), "The finite element model of pre-twisted Euler beam based on general displacement solution", Struct. Eng. Mech., 69(5), 479-486. https://doi.org/10.12989/sem.2019.69.5.479.
  14. Huang, Y., Chen, C., Zou, H. and Yao, Y. (2019), "The finite element model of pre-twisted Euler beam based on general displacement solution", Struct. Eng. Mech., 69(5), 479-486. https://doi.org/10.12989/sem.2019.69.5.479.
  15. Lee, J. Y. (2016), "Analysis of Vibration for the Pre-twisted Beam Considering the Effect of Rotary Inertia Using the Transfer Matrix Method", Trans. Korean Soc. Noise Vib. Eng., 26(2), 217-224. https://doi.org/10.5050/KSNVE.2016.26.2.217.
  16. Mohanty, S. C., Dash, R. R. and Rout, T. (2015), "Vibration and dynamic stability of pre-twisted thick cantilever beam made of functionally graded material", J. Struct. Stability Dynam., 15(04), https://doi.org/10.1142/S0219455414500588.
  17. Nabi, S. M. and Ganesan, N. (1996), "Comparison of beam and plate theories for free vibrations of metal matrix composite pre-twisted blades", J. Sound Vib., 189(2), 149-160. https://doi.org/10.1006/jsvi.1996.0012.
  18. Oh, Y. and Yoo, H. H. (2018), "Vibration analysis of a rotating pre-twisted blade considering the coupling effects of stretching, bending, and torsion", J. Sound Vib., 431, 20-39. https://doi.org/10.1016/j.jsv.2018.05.030.
  19. Rao, S. S. and Gupta, R. S. (2001), "Finite element vibration analysis of rotating Timoshenko beams", J. Sound Vib., 242(1), 103-124. https://doi.org/10.1006/jsvi.2000.3362.
  20. Ramesh, M. N. V. and Rao, N. M. (2013), "Free vibration analysis of pre-twisted rotating FGM beams", J. Mech. Mater. Design, 9(4), 367-383. https://doi.org/10.1007/s10999-013-9226-x.
  21. 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.
  22. Shenas, A. G., Ziaee, S. and Malekzadeh, P. (2017), "Nonlinear vibration analysis of pre-twisted functionally graded microbeams in thermal environment", Thin-Walled Struct., 118, 87-104. https://doi.org/10.1016/j.tws.2017.05.003.
  23. Shenas, A. G., Ziaee, S. and Malekzadeh, P. (2019), "Post-buckling and vibration of post-buckled rotating pre-twisted FG microbeams in thermal environment", Thin-Walled Struct., 138, 335-360. https://doi.org/10.1016/j.tws.2019.02.012.
  24. Shenas, A. G., Malekzadeh, P. and Ziaee, S. (2017), "Vibration analysis of pre-twisted functionally graded carbon nanotube reinforced composite beams in thermal environment", Compos. Struct., 162, 325-340. https://doi.org/10.1016/j.compstruct.2016.12.009.
  25. Wang, X. and Yuan, Z. (2018), "Three-dimensional vibration analysis of curved and twisted beams with irregular shapes of cross-sections by sub-parametric quadrature element method", Comput. Math. Appl., 76(6), 1486-1499. https://doi.org/10.1016/j.camwa.2018.07.001.
  26. Yao, M., Niu, Y. and Hao, Y. (2019), "Nonlinear dynamic responses of rotating pre-twisted cylindrical shells", Nonlinear Dynam., 95(1), 151-174. https://doi.org/10.1007/s11071-018-4557-7.
  27. 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.
  28. 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.
  29. Zhang, B., Zhang, Y. L., Yang, X. D. and Chen, L. Q. (2019), "Saturation and stability in internal resonance of a rotating blade under thermal gradient", J. Sound Vib., 440, 34-50. https://doi.org/10.1016/j.jsv.2018.10.012.
  30. Zupan, D. and Saje, M. (2004), "On 'A proposed standard set of problems to test finite element accuracy': the twisted beam", Finite Elements Analysis and Design, 40(11), 1445-1451. https://doi.org/10.1016/j.finel.2003.10.001.