DOI QR코드

DOI QR Code

아치구조의 최적형상 탐색

Optimal Shape Finding of Arch Structures

  • 이상진 (경상국립대학교 건축공학과)
  • Lee, Sang-Jin (Dept. of Architectural Engineering, Gyeongsang National University)
  • 투고 : 2022.03.13
  • 심사 : 2022.05.15
  • 발행 : 2022.05.30

초록

This study proposes a shape finding method for arch structure. It aims to provide a general procedure for finding the optimal shape of arch structures using the optimization technique. All the process is utilized by using the visual programming technique. The NURBS (Non-Uniform Rational B-spline) definition is introduced to represent the geometry of the arch structure. The strain energy of the arch structure is evaluated by using the plug-in Karamba3D in Grasshopper environment. The shape optimization with the strain energy to be minimized and height constraint is then performed by using the plug-in NM-opti. Numerical examples are carried out to verify the capability of the present shape finding method and to find the optimum shape of the arch in various situations. From numerical examples, the present shape finding method can effectively produce a new optimum shape of the arch regardless of natural and essential boundary conditions.

키워드

참고문헌

  1. De Boor, C. (1978). A Practical Guide to Splines, Springer.
  2. Farshad, M. (1976). On optimal form of arches, J. of the Franklin Institute, 302(2), 87-194. https://doi.org/10.1016/0016-0032(76)90022-3
  3. Gregson, S. (2018). Nelder-Mead optimisation component in Grasshopper, Manual, Eckersley O'Callaghan.
  4. Killian, A., & Ochsendorf, J. (2005). Particle-Spring Systems for Structural Form Finding, J. of the Int. Assoc. for Shell & Spatial Structures, 46(147), 77-84.
  5. Lee, S.J. (1999). A study on the shape and thickness optimization of shells using CAGD through minimization of strain energy with volume constraint, J. Compu. Struc. Eng. Institute of Korea, 12(4), 551-561.
  6. Lee. S.J. (2014). Finite element method with MATLAB, SJ Mirae.
  7. Lee, S.J. (2021). Shape optimization of shell structures using visual programming, J. of the Architectural Institute of Korea, 37(12), 311-319.
  8. Lewis, W.J. (2016). Mathematical model of a moment-less arch, Proc. R. Soc. A, 472:20160019 https://doi.org/10.1098/rspa.2016.0019
  9. Millais, M. (2005). Building Structures: from concepts to design, 2nd Edition, Spon Press, Abingdon, UK
  10. Preisinger, C. (2019). Karamba3D: User manual
  11. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Downhill Simplex Method in Multidimensions, in Numerical Recipes: The Art of Scientific Computing (3rd ed.). New York: Cambridge University Press.
  12. Robert McNeel & Associates (2021) The Grasshopper primer, Mode Lab
  13. Serra, M. (1994). Optimal Arch: Approximate Analytical and Numerical Solutions, Int. J. Computers & Structures, 52(6), 1213-1220. https://doi.org/10.1016/0045-7949(94)90186-4
  14. Tadjbakhsh, I.G. (1981). Stability and optimum design of arch-type structures, Int. J. Solids & Structures, 17(6), 565-574. https://doi.org/10.1016/0020-7683(81)90019-6
  15. Tadjbakhsh, I. & Farshad, M. (1973). On conservatively loaded funiular arches and their optimal design, Proceedings of IUTAM Symposium on Optimization in Structural Design, Warsaw
  16. Taysi, N., Gogus, M.T., & Ozakca, M. (2008). Optimization of arches using genetic algorithm, Computational Optimization & Applications, 41(3), 377-394. https://doi.org/10.1007/s10589-007-9111-3
  17. Vanderplaats, G.N., & Han, H. (1986). A general-purpose optimization program for engineering design, Int. J. Computers & Structures, 24(1), 13-21. https://doi.org/10.1016/0045-7949(86)90331-7