DOI QR코드

DOI QR Code

In-Plane Buckling Analysis of Curved Beams Using DQM

미분구적법(DQM)을 이용한 곡선보의 내평면 좌굴해석

  • Kang, Ki-Jun (Department of Automative Engineering, Hoseo University) ;
  • Kim, Young-Woo (Department of Automative Engineering, Hoseo University)
  • 강기준 (호서대학교 공과대학 자동차공학과) ;
  • 김영우 (호서대학교 공과대학 자동차공학과)
  • Received : 2012.04.19
  • Accepted : 2012.07.12
  • Published : 2012.07.31

Abstract

The differential quadrature method (DQM) is applied to computation of the eigenvalues of in-plane buckling of the curved beams. Critical moments and loads are calculated for the beam subjected to equal and opposite bending moments and uniformly distributed radial loads with various end conditions and opening angles. Results are compared with existing exact solutions where available. The DQM gives good accuracy even when only a limited number of grid points is used. More results are given for two sets of boundary conditions not considered by previous investigators for in-plane buckling: clamped-clamped and simply supported-clamped ends.

Keywords

Critical Load;Critical Moment;Curved Beam;DQM;Exact Solution;In-Plane Buckling

Acknowledgement

Supported by : Hoseo University

References

  1. M. Ojalvo, E. Demuts and F. Tokarz, "Out-of-Plane Buckling of Curved Members", J. Struct. Dvi., ASCE, Vol. 95, pp. 2305-2316, 1969.
  2. V. Z. Vlasov, Thin Walled Elastic Beams, 2nd edn, English Translation, National Science Foundation, Washington, D.C., 1961.
  3. J. P. Papangelis and N. S. Trahair, "Flexural-Torsional Buckling of Arches", J. Struct. Engng, ASCE, Vol. 113, pp. 889-906, 1987. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:4(889)
  4. S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, 2nd edn, McGraw-Hill, New York, 1961.
  5. Y. B. Yang and S. R. Kuo, "Static Stability of Curved Thin-Walled Beams", J. Struct. Engng, ASCE, Vol. 112, pp. 821-841, 1986.
  6. S. R. Kuo and Y. B. Yang, "New Theory on Buckling of Curved Beams", J. Engng Mech., ASCE, Vol. 117, pp. 1698-1717, 1991. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:8(1698)
  7. Y. J. Kang and C. H. Yoo, "Thin-Walled Curved Beams, II: Analytical Solutions for Buckling of Arches", J. Struct. Engng, ASCE, Vol. 120, pp. 2102-2125, 1994.
  8. K. Kang and Y. Kim, "In-Plane Vibration Analysis of Asymmetric Curved Beams Using DQM", J. KAIS., Vol. 11, pp. 2734-2740, 2010.
  9. R. E. Bellman and J. Casti, "Differential Quadrature and Long-Term Integration", J. Math. Anal. Applic., Vol. 34, pp. 235-238, 1971. https://doi.org/10.1016/0022-247X(71)90110-7
  10. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th edn, Dover, New York, 1944.
  11. S. K. Jang, C. W. Bert and A. G. Striz, "Application of Differential Quadrature to Static Analysis of Structural Components", Int. J. Numer. Mech. Engng, Vol. 28, pp. 561-577, 1989. https://doi.org/10.1002/nme.1620280306
  12. K. Kang and J. Han, "Analysis of a Curved beam Using Classical and Shear Deformable Beam Theories", Int. J. KSME., Vol. 12, pp. 244-256, 1998. https://doi.org/10.1007/BF02947169
  13. K. Kang, "Vibration Analysis of Curved Beams Using Differential Quadrature", J. KIIS., Vol. 14, pp. 199-207, 1999.

Cited by

  1. In-Plane Buckling Analysis of Asymmetric Curved Beam Using DQM vol.14, pp.10, 2013, https://doi.org/10.5762/KAIS.2013.14.10.4706