Journal of the Architectural Institute of Korea Structure & Construction (대한건축학회논문집:구조계)

Architectural Institute of Korea (대한건축학회)
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A Study on Geodesic Line Search and Smooth Cutting Patterning of Membrane Structures by Using the Modified Sub-plane

수정-서브플랜을 이용한 막 구조물의 측지선 탐색과 곡선 재단도 작성에 관한 연구

  • 손수덕 (한국기술교육대학교 건축공학부) ;
  • 이승재 (한국기술교육대학교 건축공학부)
  • Received : 2012.08.03
  • Published : 2012.12.25
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Abstract

This paper investigated a simple and useful technique of smooth geodesic cutting patterning of membrane structures and a sub-plane on surface, modified sub-plane and spline interpolation are used for geodesic line search. Firstly, a partial adjustment and element redirection of sub-plane of extracted elements series and substituting alternative nodal point were proposed for the geodesic search with modification of sub-plane. Secondly various spline approximations were applied to flatten the strip for the generation of smooth cutting pattern. This search technique is very simple enough to attain the geodesic line without difficult mathematical or computational method. Additionally, seam line of smooth cutting patterning also can be generated by spline approximation by using the geometric information of discrete nodes. The geodesic line of the cable-supported pneumatic membrane model with 670 nodes and 1188 triangular elements are examined, and cutting pattern of arch-supported membrane model are generated to verify the process of smooth cutting pattern generation.

Keywords

Acknowledgement

Supported by : 국토해양부

References

  1. 권택진, 서삼열, 김재열, 이장복, 최호, 막 구조물의 최소자승법을 이용한 재단도 해석에 관한 연구, 대한건축학회논문집 구조계, 제15권, 7호, pp.29-36, 1999
  2. 배종효, 한상을, 측지선 알고리즘을 이용한 막구조물의 재단도 생성, 대한건축학회논문집 구조계, 제16권 12호, pp.33-40, 2000
  3. 손수덕, 김승덕, 정을석, 전진형, 비선형 형상 탐색 기법에 따른 막구조물의 오차와 수렴성 평가에 관한 연구, 한국공간구조학회논문집, 제7권 3호, pp.57-66, 2007
  4. 손수덕, 정을석, 김승덕, 단일공기막 구조물의 설계하중에 따른 비선형 응력-변형해석 및 설계에 관한 연구, 한국쉘.공간구조학회논문집, 제5권 2호, pp.47-55, 2005
  5. 손수덕, 정을석, 김승덕, 막 구조물의 재단도 작성과 막재의 손실률에 관한 연구, 한국공간구조학회논문집, 제6권 1호, pp.117-127, 2006
  6. 안상길, 손수덕, 김승덕, 막 구조물의 측지선을 이용한 재단도 작성에 관한 연구, 한국쉘${\cdot}$공간구조학회 학술발표회논문집, 제 2권 1호, pp.125-132, 2005
  7. 이경수, 한상을, 막구조물의 재단도를 위한 측지선 형상해석 알고리즘, 한국강구조학회논문집, 제22권 1호, pp.33-42, 2010
  8. 이장복, 김재열, 하창우, 권택진, 막 구조물의 재단도 해석 및 준공평형 형상해석에 관한 연구, 대한건축학회논문집 구조계, 제16권 7호, pp.9-17, 2000
  9. 전진형, 손수덕, 정을석, 김승덕, 막 구조물의 삼각형 Re-mesh 패턴을 적용한 재단도 작성에 관한 연구, 한국공간구조학회논문집, 제7권 3호, pp.153-165, 2007
  10. Barnes, M.R., Form Finding and Analysis of Tension Structures by Dynamic Relaxation. International Journal of Space Structures, Vol. 14, No. 2, pp.89-104, 1999 https://doi.org/10.1260/0266351991494722
  11. De Boor, C., A Practical Guide To Splines, Springer- Verlag, 1978
  12. Grundig, L., Ekert, L. and Moncrieff, E., Geodesic and Semi-geodesic line algorithms for Cutting Pattern Generation of Architectural Textile Structures, Proceedings, Asia-Pacific Conference on Shell And Spatial Structures, Beijing, pp.435-443, 1996
  13. Hegyi D., Sajtos I., Geiszter G. and Hincz K. (2006) Eight-node quadrilateral double-curved surface element for membrane analysis, Computer & Structures, Vol. 84, pp.2151-2158, 2006 https://doi.org/10.1016/j.compstruc.2006.08.046
  14. IMSL C Numerical Library (2006) C Math Library version
  15. 0 User'S Guide: Ch.3 Interpolation and Approximation, Visual Numerics, pp.163-260, 2006
  16. Ishii, K. (1999) Form finding analysis in consideration of cutting pattern of membrane structures, International Journal of Space Structures, Vol. 14, No. 2, pp.105-119, 1999 https://doi.org/10.1260/0266351991494731
  17. Kim, J.Y. and Lee, J.B., A new technique for optimum cutting pattern generation of membrane structures, Engineering Structures, Vol. 24, pp.745-756, 2002 https://doi.org/10.1016/S0141-0296(02)00003-2
  18. Moncrieff, E. and Topping, B.H.V., Computer method for the generation of membrane cutting patterns, Computer & Structures, Vol. 37, No. 4, pp.441-450, 1990 https://doi.org/10.1016/0045-7949(90)90034-Y
  19. Ohsaki M. and Uetani K., Shape-stress trade-off design of membrane structures for specified sequence of boundary shapes, Computer methods in applied mechanics and engineering, Vol. 182, pp.73-88, 2000 https://doi.org/10.1016/S0045-7825(99)00086-9
  20. Ong, C.F., Wakefield, D.S. and Barnes M.R., Interactive graphic CAD for tension structures, Computers & Structures, Vol. 41, No. 6, pp.1305-1312, 1991 https://doi.org/10.1016/0045-7949(91)90267-P
  21. Phelan, D.G. and Haber, R.B., An integrated design method for cable-reinforced membrane structures, Shells, Membranes and Spaces frames, Proceedings, IASS Symposium, Osaka, Vol. 2, pp.119-125, 1986
  22. Tabarrok, B. and Qin, Z., Form finding and cutting pattern generation for fabric tension structures, Computer-Aided Civil and Infrastructure Engineering, Vol. 8, No. 5, pp.377-384, 1993
  23. Tsubota, H. and Yoshida, A., Theoretical analysis of determining optimum cutting patterns for membrane structures, Proceedings, IASS Symposium, Madrid, Vol. 3, pp.11-15, 1989
  24. Wakefield, D.S., Engineering analysis of tension structures: theory and practice, Engineering Structures, Vol. 21, pp.680-690, 1999 https://doi.org/10.1016/S0141-0296(98)00023-6
  25. Xia, X. and Meek, J.L., Computer cutting pattern generation of membrane structures, International Journal of Space Structures, Vol.15, No. 2, pp.95-110, 2000 https://doi.org/10.1260/0266351001495008
  26. Xu, X. and Guan, F., A new method of cutting pattern, International Journal of Space Structures, Vol. 19, No. 2, pp.103-107, 2004 https://doi.org/10.1260/0266351042249600
  27. Yagi, T. and Ohmori, H., A new approach for cutting pattern analysis of membrane structures, Proceedings, IASS-LAS98 Conference, Sydney, Vol. 2 pp.895-910, 1998
  28. Zhang Q. and Luo, X., Finite element method for developing arbitrary surfaces to flattened forms, Finite elements in analysis and design, Vol. 39, pp.977-984, 2003 https://doi.org/10.1016/S0168-874X(02)00142-7