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Parametric Studies on Bending of Twisted Timoshenko Beams Under Complex Loadings

Published online by Cambridge University Press:  22 March 2012

W.-R. Chen
W.-R. Chen*
Affiliation:
Department of Mechanical Engineering, Chinese Culture University, Taipei, Taiwan 11114, R.O.C.
*
*[email protected]
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Abstract

Static bending of a twisted Timoshenko beam subjected to combined transverse and axial loadings is studied. The equilibrium equations are established in the twist coordinates by applying the principle of minimum potential energy. The governing equations are then reduced into solvable algebraic equations using a finite element approach. The effects of the twist angle, thickness-to-width ratio, length-to-thickness ratio, loading and boundary conditions on the static bending characteristics of the twisted beams are investigated. The present parametric analyses will provide engineers a good insight into the influence of various structural aspects of the twisted beam on its response to different static loads.

Keywords

Static bendingTimoshenko beamFinite elementTwist angle
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 1 , March 2012 , pp. N1 - N6
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

REFERENCE

1. Rosen, A., “Structural and Dynamic Behavior of Pre-Twisted Rods and Beams,” Applied Mechanics Reviews, 44, pp. 483–515 (1991).Google Scholar
2. Carnegie, W., “Static Bending of Pre-Twisted Cantilever Blading,” Proceedings of the Institution of Mechanical Engineers, 171, pp. 873–894 (1957).Google Scholar
3. Subrahmanyam, K. B., Kulkarni, S. V. and Rao, J. S., “Static Bending of Pretwisted Cantilever Blading,” Proceedings of the Indian Society of Theoretical and Applied Mechanics Twenty-Fourth Congress, pp. 37–54 (1980).Google Scholar
4. Chen, W. R., “Closed-Form Solutions on Bending of Cantilever Twisted Timoshenko Beams Under Various Bending Loads,” Structural Engineering & Mechanics, 35, pp. 261–264 (2010).CrossRefGoogle Scholar
5. Abid, S., Taktak, M., Dammak, F. and Haddar, M., “An Accurate Two-Node Finite Element for the Pre-Twisted Beam Modeling,” Strojnicky Casopis, 59, pp. 135–150 (2008).Google Scholar
6. Petrov, E. and Géadin, M., “Finite Element Theory for Curved and Twisted Beams Based on Exact Solutions for Three-Dimensional Solids Part 1: Beam Concept and Geometrically Exact Nonlinear Formulation,” Computer Methods in Applied Mechanics and Engineering, 165, pp. 43–92 (1998).CrossRefGoogle Scholar
7. Yu, A., Fang, M. and Ma, X., “Theoretical Research on Naturally Curved and Twisted Beams under Complicated Loads,” Computers & Structures, 80, pp. 2529–2536 (2002).Google Scholar
8. Zupan, D. and Saje, M., “The Three-Dimensional Beam Theory: Finite Element Formulation Based on Curvature,” Computers & Structures, 81, pp. 1875–1888 (2003).Google Scholar
9. Zupan, D. and Saje, M., “Finite Element Formulation of Geometrically Exact Three-Dimensional Beam Theories Based on Interpolation of Strain Measures,” Computer Methods in Applied Mechanics and Engineering, 192, pp. 5209–5248 (2003).Google Scholar
10. Tang, S. and Yu, A., “Generalized Variational Principle on Nonlinear Theory of Naturally Curved and Twisted Beams,” Applied Mathematical Computer, 153, pp. 275–288 (2004).Google Scholar
11. Yu, A. M., Yang, X. G. and Nie, G. H., “Generalized Coordinate for Warping of Naturally Curved and Twisted Beams with General Cross-Sectional Shapes,” International Journal of Solids and Structures, 43, pp. 2853–2867 (2006).CrossRefGoogle Scholar
12. Zupan, D. and Saje, M., “The Linearized Three-Dimensional Beam Theory of Naturally Curved and Twisted Beams: The Strain Vectors Formulation,” Computer Methods in Applied Mechanics and Engineering, 195, pp. 4557–4578 (2006).CrossRefGoogle Scholar
13. Reddy, J. N., Applied Functional Analysis and Variational Methods in Engineering, McGraw-Hill Book Co., Singapore (1986).Google Scholar
14. Chen, W. R. and Keer, L. M., “Transverse Vibrations of a Rotating Twisted Timoshenko Beam Under Axial Loading,” Journal of Vibration and Acoustics, 115, pp. 285–294 (1993).CrossRefGoogle Scholar
15. Chen, W. R., “On the Vibration and Stability of Spinning Axially Loaded Pre-Twisted Timoshenko Beams,” Finite Elements in Analysis and Design, 46, pp. 1037–1047 (2010).Google Scholar
16. Bathe, K. J., Finite Element Procedures, Prentice-Hall, NJ, (1996).Google Scholar
17. Hughes, T. J. R, Taylor, R. L. and Kanoknukulchai, W., “A Simple and Efficient Finite Element for Plate Bending,” International Journal for Numerical Methods in Engineering, 11, pp. 1529–1543 (1977).Google Scholar