- Volume 13 Issue 7
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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)
- Received : 2012.04.19
- Accepted : 2012.07.12
- Published : 2012.07.31
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.
Critical Load;Critical Moment;Curved Beam;DQM;Exact Solution;In-Plane Buckling
Supported by : Hoseo University
- M. Ojalvo, E. Demuts and F. Tokarz, "Out-of-Plane Buckling of Curved Members", J. Struct. Dvi., ASCE, Vol. 95, pp. 2305-2316, 1969.
- V. Z. Vlasov, Thin Walled Elastic Beams, 2nd edn, English Translation, National Science Foundation, Washington, D.C., 1961.
- 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)
- S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, 2nd edn, McGraw-Hill, New York, 1961.
- Y. B. Yang and S. R. Kuo, "Static Stability of Curved Thin-Walled Beams", J. Struct. Engng, ASCE, Vol. 112, pp. 821-841, 1986.
- 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)
- 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.
- K. Kang and Y. Kim, "In-Plane Vibration Analysis of Asymmetric Curved Beams Using DQM", J. KAIS., Vol. 11, pp. 2734-2740, 2010.
- 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
- A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th edn, Dover, New York, 1944.
- 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
- 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
- K. Kang, "Vibration Analysis of Curved Beams Using Differential Quadrature", J. KIIS., Vol. 14, pp. 199-207, 1999.
- 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