Spatial Post-buckling Analysis of Thin-walled Space Frames based on the Corotational Formulation

대회전을 고려한 공간 박벽 뼈대구조물의 기하 비선형 후좌굴 거동 해석

  • 이경찬 (서울대학교 교량설계핵심기술연구단) ;
  • 박정일 (서울대학교 건설환경종합연구소) ;
  • 김성보 (충북대학교 토목공학과) ;
  • 장승필 (서울대학교 지구환경시스템공학부)
  • Received : 2007.08.10
  • Accepted : 2007.11.12
  • Published : 2007.12.27

Abstract

In this paper, we described a co-rotational formulation for the geometrical nonlinear analysis of three-dimensional frames. We suggested a new concept called the Zero-Twist-Section Condition (ZTSC) to decide the element coordinate system consistently. According to the ZTSC procedure, it is possible to obtain an element coordinate system and natural deformations consistently when finite displacements and rotations are induced in an element. Based on the developed procedure, numerical examples are investigated to calculate natural rotations while finite displacements are imposed on an element. Also, the developed co-rotational procedure gives accurate results in the analysis of post-buckling problems with finite rotations.

이 연구에서는 박벽 뼈대 구조물의 3차원 기하 비선형 해석을 위한 Corotational 정식화를 유도하였으며, 특히 변형 후 부재좌표계 결정에서 모호했던 기존의 이론을 단면의 물리적 적합 조건을 이용하여 해결하였다. 부재 양단의 순수 비틀림 회전값이 서로 크기는 같고 방향은 반대가 되는 상태를 적합조건으로 적용하고, 이를 특별히 ZTSC(Zero Twisted Section Condition)이라고 명명하였다. 개발된 방법의 타당성을 검증하기 위하여 기존의 다른 연구자가 사용한 방법과 비교하여 대회전변위가 발생한 경우에 대한 순수회전변위 결과를 검토하였으며, 개발된 Corotational 정식화를 이용하여 3차원 대변위가 발생하는 세장한 구조물의 후좌굴 해석을 성공적으로 수행하였다.

Keywords

References

  1. 김문영, 최명수, 장영, 김남일(2002) 박벽보의 응력해석을 위한 단면상수의 자동산정, 한국강구조학회 논문집, 한국강구조 학회, 제14권, 제1호, pp. 41-49
  2. 김성보, 김문영, 장승필(2002) 비대칭 단면을 갖는 공간뼈대구 조의 후좌굴해석을 위한 개선이론, 대한토목학회 논문집, 대한토목학회, 제22권, 제2-A호, pp. 189-200
  3. 박효기, 김성보, 김문영, 장승필(1999) 비대칭단면을 갖는 공간 뼈대구조의 횡-비틂 후좌굴 유한요소해석, 한국강구조학회논문집, 한국강구조학회, 제11권, 제2호, pp. 153-165
  4. Argyris, J. et al. (1979) Finite element method - the natural approach. Computer methods in applied mechanics and engineering, Vol. 17/18, pp. 1-106 https://doi.org/10.1016/0045-7825(79)90083-5
  5. Argyris, J. (1982) An excursion into large rotations. Computer methods in applied mechanics and engineering, Vol. 32, pp. 85-155 https://doi.org/10.1016/0045-7825(82)90069-X
  6. Bathe, K-J. and Bolourchi, S. (1979) Large displacement analysis of three-dimensional beam structures. International Journal of numerical methods and engineering, Vol. 14, pp. 961-986 https://doi.org/10.1002/nme.1620140703
  7. Battini, J-M. and Pacoste, C. (2002) Co-rotational beam elements with warping effects in instability problems, Computer methods in applied mechanics and engineering, Vol. 191, pp. 1755-1789 https://doi.org/10.1016/S0045-7825(01)00352-8
  8. Cardona, A. and Geradin, M. (1988) A beam finite element non-linear theory with finite rotations. International Journal of numerical methods and engineering, Vol. 26, pp. 2403-2438 https://doi.org/10.1002/nme.1620261105
  9. Chen, H. H., Lin, W. Y. and Hsiao, K. M. (2006) Co-rotational finite element formulation for thinwalled beams with generic open section. Computer methods in applied mechanics and engineering, Vol. 195, pp. 2334-2370 https://doi.org/10.1016/j.cma.2005.05.011
  10. Crisfield, M. A. (1990) A consistent co-rotational formulation for nonlinear, three-dimensional, beamelements. Computer methods in applied mechanics and engineering, Vol. 81, pp. 131-150 https://doi.org/10.1016/0045-7825(90)90106-V
  11. Crisfield, M. A. (1997) Non-linear finite element analysis of solids and structures volume 2: advanced topics, John Wiley & Sons, UK
  12. Gruttmann, F., Sauer, R. and Wagner, W. (1998) A geometrical nonlinear eccentric 3D-beam element with arbitrary cross-sections, Computer methods in applied mechanics and engineering, Vol. 160, pp. 383-400 https://doi.org/10.1016/S0045-7825(97)00305-8
  13. Hsiao, K. M. (1992) Corotational total Lagrangian formulation for three-dimensional beam element, AIAA Journal Vol. 30, No. 3, pp. 797-804 https://doi.org/10.2514/3.10987
  14. Hsiao, K. M., Lin, J. Y. and Lin, W. Y. (1999) A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams, Computer methods in applied mechanics and engineering, Vol. 169, pp. 1-18 https://doi.org/10.1016/S0045-7825(98)00152-2
  15. Kim, M. Y., Chang, S. P. and Kim, S. B. (2001) Spatial postbuckling analysis of nonsymmetric thin-walled frames. II: geometrically nonlinear FE procedures. ASCE Journal of engineering mechanics, Vol. 127, No. 8, pp. 779-790 https://doi.org/10.1061/(ASCE)0733-9399(2001)127:8(779)
  16. Kuo, S. R., Yang, Y. B. and Chou, J. H. (1993) Nonlinear analysis of space frames with finite rotations. ASCE Journal of structural engineering, Vol. 119, No. 1, pp. 1-15 https://doi.org/10.1061/(ASCE)0733-9445(1993)119:1(1)
  17. Li, Z. X. (2007) A mixed co-rotational formulation of 2D beam element using vectorial rotational variables, Communications in numerical methods in engineering, Vol. 23, No. 1, pp. 45-69 https://doi.org/10.1002/cnm.882
  18. Rankin, C. C. and Brogan, F. A. (1984) An element independent corotational procedure for the treatment of large rotations. Collapse analysis of structures, ed. L. H. Sobel & K. Thomas, ASME, New York, pp. 85-100
  19. Simo, J. C. and Vu-Quoc, L. (1986) A three-dimensional finite strain rod model. Part II: Computational aspects. Computer methods in applied mechanics and engineering, Vol. 58, pp. 79-116 https://doi.org/10.1016/0045-7825(86)90079-4
  20. Urthaler, Y. and Reddy, J. N. (2005) A corotational finite element formulation for the analysis of planar beams. Communications in numerical methods in engineering, Vol. 21, pp. 553-570 https://doi.org/10.1002/cnm.773
  21. Yazdchi, M. and Crisfield, M. A. (2002) Buoyancy forces and the 2D finite element analysis of flexible offshore pipes and risers. International journal for numerical methods in engineering, Vol. 54, pp. 61-88 https://doi.org/10.1002/nme.415
  22. Yang, Y. B. and Kuo, S. R. (1994) Theory of nonlinear framed structures, Prentice Hall, Singapore