Structural Engineering and Mechanics

  • 제53권4호
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  • Pages.781-790
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  • 2015
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Bending analysis of a single leaf flexure using higher-order beam theory

  • 투고 : 2014.10.29
  • 심사 : 2015.01.07
  • 발행 : 2015.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

We apply higher-order beam theory to analyze the deflections and stresses of a cantilevered single leaf flexure in bending. Our equations include shear deformation and the warping effect in bending. The results are compared with Euler-Bernoulli and Timoshenko beam theory, and are verified by finite element analysis (FEA). The results show that the higher-order beam theory is in a good agreement with the FEA results, with errors of less than 10%. These results indicate that the analysis of the deflections and stresses of a single leaf flexure should consider the shear and warping effects in bending to ensure high precision mechanism design.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea (NRF)

참고문헌

  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. Theo., 74, 173-187. https://doi.org/10.1016/j.mechmachtheory.2013.12.006
  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. https://doi.org/10.1016/j.precisioneng.2012.11.008
  3. Crandall, S.H. and Dahl, N.C. (1978), Introduction to the Mechanics of Solids, McGraw-Hill, New York, USA.
  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. https://doi.org/10.1007/s12541-012-0088-1
  5. Hutchinson, J.R. (2001), "Shear coefficients for Timoshenko beam theory", J. Appl. Mech.-T., ASME, 68(1), 87-92. https://doi.org/10.1115/1.1349417
  6. Kim, J.H., Kim, S.H. and Kwak, Y.K. (2004), "Development and optimization of 3-D bridge-type hinge mechanisms", Sens. Actuat., 116, 530-538. https://doi.org/10.1016/j.sna.2004.05.027
  7. Kim, J.J., Choi., Y.M., Ahn, D., Hwang, B., Gweon, D.G. and Jeong, J. (2012), "A millimeter-range flexurebased nano-positioning stage using a self-guided displacement amplification mechanism", Mech. Mach. Theo., 50, 109-120. https://doi.org/10.1016/j.mechmachtheory.2011.11.012
  8. Koseki, Y.T.A. and Koyachim N. (2002), "Kinematic analysis of translational 3-Dof micro parallel mechanism using matrix method", Adv. Robot., 16(3), 251-264. https://doi.org/10.1163/156855302760121927
  9. Lee, M.Y., Park, E.J., Yeom, J.K., Hong, D.P. and Lee, D.Y. (2012), "Pure nano-rotation scanner", Adv. Mech. Eng., Article ID 962439, 1-11.
  10. Levinson, M. (1981), " A New Rectangular Beam Theory", J. Sound. Vib., 74(1), 81-87. https://doi.org/10.1016/0022-460X(81)90493-4
  11. Reddy J.N., Wang, C.M. and Lee, K.H. (1997), "Relationships between bending solutions of classical and shear deformation beam theories", Int. J. Solid. Struct., 34(26), 3373-3384. https://doi.org/10.1016/S0020-7683(96)00211-9
  12. Reddy, J.N., Wang, C.M., Lim, G.T. and Ng, K.H. (2001), "Bending Solutions of Levinson Beams and Plates in Terms of the Classical Theories", Int. J. Solid. Struct., 38, 4701-4720. https://doi.org/10.1016/S0020-7683(00)00298-5
  13. 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, 282-288. https://doi.org/10.1016/j.mechatronics.2008.02.007
  14. Wang, C.M., Reddy, J.N. and Lee, K.H. (2000), Shear Deformable Beams and Plates: Relationships with Classical Solutions, Bending of beams, Elsevier Science, UK.
  15. Yong, Y.K., Aphale, S.S. and Moheimani, S.O.R. (2009), "Design, identification, and control of a flexurebased XY stage for fast nanoscale positioning", IEEE T. Nanotech., 8(1), 46-54. https://doi.org/10.1109/TNANO.2008.2005829

피인용 문헌

  1. Effect of higher order terms of Maclaurin expansion in nonlinear analysis of the Bernoulli beam by single finite element vol.58, pp.6, 2016, https://doi.org/10.12989/sem.2016.58.6.949
  2. Warping stresses of a rectangular single leaf flexure under torsion vol.59, pp.3, 2016, https://doi.org/10.12989/sem.2016.59.3.527