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 Extensional Buckling Analysis of Curved Beams under Uniformly Distributed Radial Loads Using DQM

등분포하중 하에서 미분구적법(DQM)을 이용한 곡선 보의 내평면 신장 좌굴해석

  • Kang, Ki-Jun (Department of Mechanical Engineering, Hoseo University)
  • 강기준 (호서대학교 공과대학 기계공학부)
  • Received : 2018.04.06
  • Accepted : 2018.07.06
  • Published : 2018.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

The increasing use of curved beams in buildings, vehicles, ships, and aircraft has prompted studies directed toward the development of an accurate method for analyzing the dynamic behavior of such structures. The stability behavior of elastic curved beams has been the subject of a large number of investigations. Solutions of the relevant differential equations have been obtained traditionally using standard finite difference or finite element methods. These techniques require a great deal of computer time as the number of discrete nodes becomes relatively large under the conditions of complex geometry and loading. One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. The differential quadrature method (DQM) has been applied to a large number of cases to overcome the difficulties of the complex algorithms of programming for the computer, as well as the excessive use of storage due to the conditions of complex geometry and loading. The in-plane buckling of curved beams considering the extensibility of the arch axis was analyzed under uniformly distributed radial loads using the DQM. The critical loads were calculated for the member with various parameter ratios, boundary conditions, and opening angles. The results were compared with the precise results by other methods for cases, in which they were available. The DQM, using only a limited number of grid points, provided results that agreed very well (less than 0.3%) with the exact ones. New results according to diverse variations were obtained, showing the important roles in the buckling behavior of curved beams, and can be used in comparisons with other numerical solutions or with experimental test data.

빌딩, 자동차, 선박, 항공기 등에서의 곡선보 사용 증가가 이러한 구조물의 동적거동해석에 필요한 정확한 해법 발전에 괄목할 만한 기여를 해왔다. 탄성곡선 보의 안정성거동은 많은 연구자들의 한 과제분야였다. 전통적으로 미분방정식의 해법은 유한치분법이나 유한요소법으로 해결해왔다. 이러한 방법들은 복잡한 기하학적 구조 및 하중에 따른 격자점의 증가로 많은 컴퓨팅시간을 요구한다. 편미분방정식의 해를 구하기 위한 효율적인 방법 중의 하나는 미분구적법이다. 복잡한 기하학적 구조 및 하중 은 컴퓨터 용량을 과도하게 사용할 뿐만 아니라, 복합알고리즘 프로그램의 어려움을 극복하기위하여 미분구적법(DQM)이 많은 분야에 적용되어왔다. DQM을 이용하여 곡선 보의 아크 축 신장을 고려한 내 평면 좌굴을 등분포 하중 하에서 해석하였다. 다양한 매개변수 비, 경계조건, 그리고 열림 각에 따른 임계하중을 계산하였다. DQM 결과는 활용 가능한 다른 엄밀해와 비교하였다. DQM은 적은 격자점을 사용하고도 엄밀해 결과와 일치함을 보여주었다 (0.3% 미만). 다양한 변경에 따른 새로운 결과가 또한 제시 되였고, 그 결과는 곡선 보의 좌굴거동에 중요한 역할을 보여주었고, 다른 수치해석결과 혹은 실험결과비교에 사용될 수 있다.

Keywords

References

  1. M. Ojalvo, E. Demuts, 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. S. P. Timoshenko, J. M. Gere, Theory of elastic stability, 2nd edn, McGraw-Hill, New York, 1961.
  4. Y. B. Yang, S. R. Kuo, "Static stability of curved thin-walled beams", J. Struct. Engng, ASCE, Vol. 112, pp. 821-841, 1986.
  5. S. R. Kuo, 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)
  6. Y. J. Kang, C. H. Yoo, "Thin-walled curved beams II: Analytical solutions for buckling of arches", J. Struct. Engng, ASCE, Vol. 120, pp. 2102-2125, 1994.
  7. J. Han, K. Kang, "Buckling analysis of arches using DQM", J. KIIS., Vol. 12, pp. 220-229, 1997.
  8. R. E. Bellman, 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
  9. T. Wah, "Buckling of Thin Circular Rings under Uniform Pressure", Int. J. Solids Struct., Vol. 3, pp. 967-974, 1967. https://doi.org/10.1016/0020-7683(67)90022-4
  10. S. K. Jang, C. W. Bert, 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
  11. K. Kang, Y. Kim, "In-plane vibration analysis of asymmetric curved beams using DQM", JKAIS., Vol. 11, pp. 2734-274, 2010.
  12. K. Kang, C. Park, "In-plane buckling analysis of asymmetric curved beams using DQM", JKAIS., Vol. 141, pp. 4706-4712, 2013.
  13. K. Kang, C. Park, "Extensional vibration analysis of curved beams including rotatory inertia and shear deformation using DQM", JKAIS., Vol. 17, pp. 284-293, 2016.