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Warping stresses of a rectangular single leaf flexure under torsion
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 Title & Authors
Warping stresses of a rectangular single leaf flexure under torsion
Nguyen, Nghia Huu; Kim, Ji-Soo; Lee, Dong-Yeon;
 Abstract
We describe a stress analysis of a single leaf flexure under torsion in which the warping effect is considered. The theoretical equations for the warping normal stress () and shear stresses ( and ) are derived by applying the warping function of a rectangular cross-sectional beam and the twist angle equation that includes the warping torsion. The results are compared with those of the non-warping case and are verified using finite element analysis (FEA). A sensitivity analysis over the length, width, and thickness is performed and verified via FEA. The results show that the errors between the theory of warping stress results and the FEA results are lower than 4%. This indicates that the proposed theoretical stress analysis with warping is accurate in the torsion analysis of a single leaf flexure.
 Keywords
torsion;warping;warping normal stress;leaf flexure;warping shear stress;
 Language
English
 Cited by
1.
Analytical investigation on effective elastic stiffness of eccentric steel beam–column joints, Advances in Structural Engineering, 2018, 21, 1, 125  crossref(new windwow)
 References
1.
Bhagat, U., Shirinzadeh, B., Clark, L., Chea, P., Qin, Y., Tian, Y. and Zhang, D. (2014), "Design and analysis of a novel flexure-based 3-DOF mechanism", Mech. Mach. Theor., 74, 173-187. crossref(new window)

2.
Brouwer, D.M., Meijaard, J.P. and Jonker, J.B. (2013), "Large deflection stiffness analysis of parallel prismatic leaf-spring flexures", J. Precis. Eng., 37, 505-521. crossref(new window)

3.
Erkmen, R.E. and Mohareb, M. (2006), "Torsion analysis of thin-walled beams including shear deformation effects", Thin Wall Struct., 44, 1096-1108. crossref(new window)

4.
Hayashi, M. and Fukuda, M. (2012), "Generation of nanometer displacement using reduction mechanism consisting of torsional leaf spring hinges", Int. J. Precis. Eng. Man., 13(5), 679-684. crossref(new window)

5.
Kim, J.S., Lim, B.D. and Lee, D.Y. (2015), "Compliance matrix of a single leaf flexure", submitted to Acta Mechanica.

6.
Koseki, T.T.Y., Arai, T. and Koyachi, N. (2002), "Kinematic analysis of translational 3-DOF micro parallel mechanism using matrix method", Adv. Robotics., 16(3), 251-264. crossref(new window)

7.
Kujawa, M. (2011), "Torsion of restrained thin-walled bars of open constraint bisymmetric cross-section", Tast quarterly, 16(1), 5-15.

8.
Lee, M.Y., Park, E.J., Yeom, J.K., Hong, D.P. and Lee, D.Y. (2012), "Pure nano-rotation scanner", Adv. Mech. Eng., 2012, Article ID 962439, 1-11.

9.
Nguyen, N.H. and Lee, D.Y. (2015), "Bending analysis of a single leaf flexure using higher-order beam theory", Struct. Eng. Mech., 53(4), 781-790. crossref(new window)

10.
Nguyen, N.H., Lim, B.D. and Lee, D.Y. (2015), "Displacement analysis of a sngle-bent leaf flexure under transverse load", Int. J. Precis. Eng. Man., 16(4), 749-754. crossref(new window)

11.
Nguyen, N.H., Lim, B.D. and Lee, D.Y. (2015), "Torsional analysis of a single-bent leaf flexure", Struct. Eng. Mech., 54(1), 189-198. crossref(new window)

12.
Pilkey, W.D. (2002), Analysis and design of elastic beams: computational methods, John Wiley & Sons Inc. New York, USA

13.
Sapountzakis, E.J. (2012), "Bars under torsional loading: a generalized beam theory approach", ISRN Civil Eng., 2013, 1-39.

14.
Sapountzakis, E.J. and Dourakopoulos, J.A. (2010), "Shear deformation effect in flexural-torsional buckling analysis of beams of arbitrary cross section by BEM", Struct. Eng. Mech., 35(2), 141-173. crossref(new window)

15.
Sapountzakis, E.J. and Mokos, V.G. (2003), "Warping shear stresses in nonuniform torsion of composite bars by BEM", Comput. Meth. Appl. Mech. Eng., 192, 4337-4353. crossref(new window)

16.
Sapountzakis, E.J. and Tsipiras, V.J. (2010), "Warping shear stresses in nonlinear nonuniform torsional vibrations of bars by BEM", Eng. Struct., 32, 741-752. crossref(new window)

17.
Sapountzakis, E.J., Tsipiras, V.J. and Argyridi, A.K. (2015), "Torsional vibration analysis of bars including secondary torsional shear deformation effect by the boundary element method", J. Sound Vib., 355, 208-231. crossref(new window)

18.
Schitter, G., Thurner, P.J. and Hansma, P.K. (2008), "Design and input-shaping control of a novel scanner for high-speed atomic force microscopy", Mechatronics, 18(2008), 282-288. crossref(new window)

19.
Sun, Z., Yang, L. and Yang, G. (2015), "The displacement boundary conditions for Reddy higher-order shear cantilever beam theory", Acta Mech., 226, 1359-1367. crossref(new window)

20.
Timoshenko, S.P. and Goodier, J.N. (1951), Theory of Elasticity, McGraw-Hill Book Company, New York, USA.

21.
Wang X.F., Yang Q.S. and Zhang Q.L. (2010), "A new beam element for analyzing geometrical and physical nonlinearity", Acta Mech., 26, 605-615. crossref(new window)

22.
Yang, Y.B. and McGuire, W. (1984), "A procedure for analysing space frames with partial warping restraint", Int. J. Numer. Meth. Eng., 20, 1377-1398. crossref(new window)

23.
Yong, Y.K., Aphale, S.S. and Moheimani, S.O.R. (2009), "Design, identification, and control of a flexure-based XY stage for fast nanoscale positioning", IEEE T. Nanotechnol., 8(1), 46-54. crossref(new window)