International journal of steel structures (국제강구조저널)

Korean Society of Steel Construction (한국강구조학회)
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Linear Form Finding Approach for Regular and Irregular Single Layer Prism Tensegrity

  • Received : 2017.09.10
  • Accepted : 2018.04.04
  • Published : 2018.12.31
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Abstract

In an irregular prism tensegrity, the number of force equilibrium equations is less than the number of unknown parameters of nodal coordinates and member force ratios. As a result, the form-finding process normally becomes nonlinear with additional conditions or needs to be carried out with the use of iterative procedures. For cases of irregular prism tensegrity which involves large number of members, it was found that previously proposed methods of form-finding are not practical. Moreover, there is a need for a form-finding approach which is able to cater to different requirements on final configuration. In this paper, the length relation condition is introduced to be used in combination with the force equilibrium equation. With the combined use of length relation and equilibrium conditions, a linear form-finding approach for irregular prism tensegrity was successfully formulated and developed. An easy-to-use interactive form-finding tool has been developed which can be used for form-finding of irregular prism tensegrities with large number of elements as well as under diverse specific requirements on their configurations.

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References

  1. Duffy, J., Rooney, J., Knight, B., & Crane, C., III. (2000). A review of a family of self deploying tensegrity structures with elastic ties. Shock and Vibration Digest, 32, 100-106. https://doi.org/10.1177/058310240003200202
  2. Faroughi, S., Kamran, M. A., & Lee, J. (2014). A genetic algorithm approach for 2-D tensegrity form finding. Advances in Structural Engineering, 17, 1669-1679. https://doi.org/10.1260/1369-4332.17.11.1669
  3. Feng, X., & Guo, S. (2015). A novel method of determining the sole configuration of tensegrity structures. Mechanics Research Communications, 69, 66-78. https://doi.org/10.1016/j.mechrescom.2015.06.012
  4. Fuller, R. B. (1962). Tensile - integrity structures. United States Patent 3,063,521.
  5. Fuller, R. B., & Marks, R. (1960). The dymaxion world of Buckminster Fuller. New York: Reinhold Publications.
  6. Knight, B., Zhang, Y., Duffy, J. & Crane, C. (2000). On the line geometry of a class of tensegrity structures. In Proceedings of a symposium commemorating the legacy, works and life of Sir Robert Stawell Ball upon 100 Anniversary of A Treatise on the theory of Screws, July 9 - 11, 2000 (pp. 1-29). University of Cambridge.
  7. Koohestani, K. (2015). Reshaping of tensegrities using a geometrical variation approach. International Journal of Solids and Structures, 71, 233-243. https://doi.org/10.1016/j.ijsolstr.2015.06.025
  8. Koohestani, K., & Guest, S. D. (2013). A new approach to the analytical and numerical form-finding of tensegrity structures. International Journal of Solids and Structures, 50, 2995-3007. https://doi.org/10.1016/j.ijsolstr.2013.05.014
  9. Lee, S., Gan, B. S., & Lee, J. (2016). A fully automatic group selection for form-finding process of truncated tetrahedral tensegrity structures via a double-loop genetic algorithm. Composites Part B Engineering, 106, 308-315. https://doi.org/10.1016/j.compositesb.2016.09.018
  10. Lee, S., & Lee, J. (2014a). Form-finding of tensegrity structures with arbitrary strut and cable members. International Journal of Mechanical Sciences, 85, 55-62. https://doi.org/10.1016/j.ijmecsci.2014.04.027
  11. Lee, S., & Lee, J. (2014b). Optimum self-stress design of cable-strut structures using frequency constraints. International Journal of Mechanical Sciences, 89, 462-469. https://doi.org/10.1016/j.ijmecsci.2014.10.016
  12. Lee, S., & Lee, J. (2016). A novel method for topology design of tensegrity structures. Composite Structures, 152, 11-19. https://doi.org/10.1016/j.compstruct.2016.05.009
  13. Motro, R. (2003). Tensegrity: Structural systems for the future. Netherland: Elsevier.
  14. Ohsaki, M., & Zhang, J. Y. (2015). Nonlinear programming approach to form-finding and folding analysis of tensegrity structures using fictitious material properties. International Journal of Solids and Structures, 69-70, 1-10. https://doi.org/10.1016/j.ijsolstr.2015.06.020
  15. Pugh, A. (1976). An introduction to tensegrity. Berkeley: University of California Press.
  16. Skelton, R. E., Adhikari, R., Pinaud, J.-P., Chan, W., & Helton, J. (2001). An introduction to the mechanics of tensegrity structures. In Proceedings of the 40th IEEE conference on decision and control, 2001 (pp.4254-4259). IEEE.
  17. Snelson, K. (1965). Continuous tension, discontinuous compression structures. United States Patent 3,169,611.
  18. Tibert, G., & Pellegrino, S. (2011). Review of form-finding methods for tensegrity structures. International Journal of Space Structures, 26, 241-255. https://doi.org/10.1260/0266-3511.26.3.241
  19. Zhang, P., Kawaguchi, K. I., & Feng, J. (2014a). Prismatic tensegrity structures with additional cables: Integral symmetric states of self-stress and cable-controlled reconfiguration procedure. International Journal of Solids and Structures, 51, 4294-4306. https://doi.org/10.1016/j.ijsolstr.2014.08.014
  20. Zhang, L.-Y., Li, Y., Cao, Y.-P., & Feng, X.-Q. (2014b). Stiffness matrix based form-finding method of tensegrity structures. Engineering Structures, 58, 36-48. https://doi.org/10.1016/j.engstruct.2013.10.014