Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
권호 표지
DOI QR코드

DOI QR Code

In-Plane Buckling Analysis of Asymmetric Curved Beam Using DQM

미분구적법(DQM)을 이용한 비대칭 곡선보의 내평면 좌굴해석

  • Kang, Ki-Jun (School of Mechanical Engineering, Hoseo University) ;
  • Park, Cha-Sik (School of Mechanical Engineering, Hoseo University)
  • 강기준 (호서대학교 공과대학 기계공학부) ;
  • 박차식 (호서대학교 공과대학 기계공학부)
  • Received : 2013.07.04
  • Accepted : 2013.10.10
  • Published : 2013.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. This method has been applied to a large number of cases to circumvent the difficulties of programming complex algorithms for the computer, as well as excessive use of storage due to conditions of complex geometry and loading. Under in-plane uniform distributed load, the buckling of asymmetric curved beam with varying cross section is analyzed by using differential quadrature method (DQM). Critical load due to diverse cross section variation and opening angle is calculated. Analysis result of DQM is compared with the result of exact analytic solution. As DQM is used with small grid points, exact analysis result is shown. New result according to diverse cross section variation is also suggested.

편미분방정식해법을 위한 효일적인 방법 중의 하나는 미분구적법이다. 이방법은 복잡한 구조 및 하중에 따른 컴퓨터 용량의 과도한 사용뿐만 아니라, 복합알고리즘의 어려움 피하기 위해 많은 분야에 적용되어 왔다. 본 연구에서는 내평면 등분포하중 하에서 단면적이 변하는 비대칭 곡선보의 좌굴 (buckling)을 미분구적법(DQM)으로 해석하였다. 다양한 단면적 변화와 열림각 (opening angle)에 따른 임계하중을 계산하였다. DQM의 해석결과는 정확한 수학적해법 (exact analytic solution)과 비교하였으며, DQM은 적은 격자점 (grid point)을 사용하여 정확한 해석결과를 보여주었다. 또한, 다양한 단면적 변화에 따른 새로운 결과를 제시하였다.

Keywords

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. DOI: http://dx.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. DOI: http://dx.doi.org/10.1061/(ASCE)0733-9399(1986)112:8(821)
  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. DOI: http://dx.doi.org/10.1061/(ASCE)0733-9399(1994)120:10(2102)
  8. K. Kang and Y. Kim, "In-Plane Vibration Analysis of Asymmetric Curved Beams Using DQM", J. KAIS., Vol. 11, pp. 2734-2740, 2010. https://doi.org/10.5762/KAIS.2010.11.8.2734
  9. R. E. Bellman and J. Casti, "Differential Quadrature and Long-Term Integration", J. Math. Anal. Applic., Vol. 34, pp. 235-238, 1971. DOI: http://dx.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. DOI: http://dx.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.
  14. K. Kang and Y. Kim, "In-Plane Buckling Analysis of Curved Beams Using DQM", J. KAIS., Vol. 13, pp. 2858-2864, 2012. DOI: http://dx.doi.org/10.5762/KAIS.2012.13.7.2858
  15. K. Kang and C. Park, "In-Plane Buckling Analysis of Curved Beams with Varying Cross-Section", RITE., Hoseo University, Vol. 31, pp. 21-29, 2012.
  16. A. R. Kukreti, et al., "Differential Quadrature and Rayleigh-Ritz Methods to Determine the Fundamental Frequency of Simply Supported Rectangular Plate with Linearly Varying Thickness ", J. Sound Vibr., Vol. 189, No. 1, pp. 103-122. 1996. DOI: http://dx.doi.org/10.1006/jsvi.1996.0008