Warping stresses of a rectangular single leaf flexure under torsion

- Journal title : Structural Engineering and Mechanics
- Volume 59, Issue 3, 2016, pp.527-537
- Publisher : Techno-Press
- DOI : 10.12989/sem.2016.59.3.527

Title & Authors

Warping stresses of a rectangular single leaf flexure under torsion

Nguyen, Nghia Huu; Kim, Ji-Soo; Lee, Dong-Yeon;

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

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.

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.

3.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.