DOI QR코드

DOI QR Code

Inverse analysis of erection process for prismatic tensegrity structures with redundant cables

  • Pei Zhang (College of Civil and Transportation Engineering, Hohai University) ;
  • Huiting Xiong (School of Civil Engineering, Wanjiang University of Technology) ;
  • Jingjing Yang (College of Civil and Transportation Engineering, Hohai University) ;
  • Jiayan Liu (Key Laboratory of Concrete and Pre-stressed Concrete Structures of Ministry of Education, Southeast University)
  • 투고 : 2021.12.16
  • 심사 : 2023.07.26
  • 발행 : 2023.10.25

초록

Firstly, a new kind of prismatic tensegrity structures with redundant cables is defined, the topology, geometry and forming conditions of which are introduced further. The development of its mechanical properties including self-stress states and structural stiffness with the increment of the twist angle is also investigated carefully. Combined with the topology of this kind of structures, a reasonable erection scheme is proposed, in which some temporary lifting points need to be set and two groups of vertical cables are tensioned in batches. Then, a simplified dynamic relaxation method is employed to track the erection process inversely, which aims to predict each intermediate equilibrium state during the construction, and give the key structural parameters that can effectively guide the construction. The removal of the active cables, the relaxation or tension of the passive cables are simulated by controlling their axial stiffness, so that the structural composition as well as the serial numbers of the elements always keep invariant regardless of the withdrawal of the slack cables. The whole analysis process is clear in concept, simple to implement and easy to popularize. Finally, several examples are given to verify the practicability and effectiveness of the proposed method further.

키워드

과제정보

The research described in this paper was financially supported by China Postdoctoral Science Foundation (No. 2020M671319), the Open Project Funded by Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University (No. CPCSME2022-01), Jiangsu Planned Projects for Postdoctoral Research Funds (No. 2020Z317), and the Key Scientific Research Projects by Wanjiang University of Technology (No. WG23020ZD).

참고문헌

  1. Cai, J.G., Zhang, Q., Zhang, Y.Q., Lee, D. and Feng, J. (2018), "Structural evaluation of a foldable cable-strut structure for kinematic roofs", Steel Compos. Struct., 29(5), 669-680. https://doi.org/10.12989/scs.2018.29.5.669.
  2. Connelly, R. and Whiteley, W. (1996), "Second-order rigidity and prestress stability for tensegrity frameworks", SIAM J. Discrete Math., 9(3), 453-491. https://doi.org/10.1137/s0895480192229236.
  3. Chen, Y., Yan, J.Y. and Feng, J. (2019), "Stiffness contributions of tension structures evaluated from the levels of components and symmetry subspaces", Mech. Res. Commun., 100, 103401. https://doi.org/10.1016/j.mechrescom.2019.103401.
  4. Chen, L.M., Hu, D., Deng, H., Cui, Y.H. and Zhou, Y.Y. (2016), "Optimization of the construction scheme of the cable-strut tensile structure based on error sensitivity analysis", Steel Compos. Struct., 21(5), 1031-1043. https://doi.org/10.12989/scs.2016.21.5.1031.
  5. Deng, H., Jiang, Q.F. and Kwan, A.S.K. (2005), "Shape finding of incomplete cable-strut assemblies containing slack and prestressed elements", Comput. Struct., 83(21-22), 1767-1779. https://doi.org/10.1016/j.compstruc.2005.02.022.
  6. Fu, F. (2006), "Non-linear static analysis and design of Tensegrity domes", Steel Compos. Struct., 6(5), 417-433. https://doi.org/10.12989/scs.2006.6.5.417.
  7. Gonzalez, A., Luo, A.N. and Shi, D.Y. (2019), "Reconfiguration method of tensegrity units using infinitesimal mechanisms", Eng. Comput., 36(6), 1934-1949. https://doi.org/10.1108/ec-09-2018-0430.
  8. Guest, S.D. (2011), "The stiffness of tensegrity structures", IMA J. Appl. Math., 76(1), 57-66. https://doi.org/10.1093/imamat/hxq065.
  9. Hangai, Y., Kawaguchi, K. and Oda, K. (1992), "Self-equilibrated stress system and structural behavior of truss structures stabilized by cable tension", Int. J. Space Struct., 7(2), 91-99. https://doi.org/10.1177/026635119200700203.
  10. Han, S. and Lee, K. (2003), "A study of the stabilizing process of unstable structures by dynamic relaxation method", Comput. Struct., 81(17), 1677-1688. https://doi.org/10.1016/S0045-7949(03)00187-1.
  11. Kawaguchi, K., Hangai, Y., Pellegrino, S. and Furuya, H. (1996), "Shape and stress control analysis of prestressed truss structures", J. Reinf. Plast. Comp., 15(12), 1226-1236. https://doi.org/10.1177/073168449601501204.
  12. Lee, K., Han, S. and Park, T. (2012), "Stabilization process analysis of cable dome structure", Int. J. Steel Struct., 12(4), 495-507. https://doi.org/10.1007/s13296-012-4004-4.
  13. Lee, K., Huque, Z. and Han, S. (2014), "Analysis of stabilizing process for stress-erection of Strarch frame", Eng. Struct., 59, 49-67. https://doi.org/10.1016/j.engstruct.2013.09.043.
  14. Ma, S., Chen, M.H. and Skelton, R.E. (2022), "Tensegrity system dynamics based on finite element method", Compos. Struct., 280, 114838. https://doi.org/10.1016/j.compstruct.2021.114838.
  15. Panigrahi, R., Gupta, A. and Bhalla, S. (2009), "Dismountable steel tensegrity grids as alternate roof structures", Steel Compos. Struct., 9(3), 239-253. https://doi.org/10.12989/scs.2009.9.3.239.
  16. Pellegrino, S. (1993), "Structural computations with the singular value decomposition of the equilibrium matrix", Int. J. Solids Struct., 30(21), 3025-3035. https://doi.org/10.1016/0020-7683(93)90210-x.
  17. Wang, X.Y., Cai, J.G., Lee, D., Xu, Y.X. and Feng, J. (2021), "Numerical form-finding of multi-order tensegrity structures by grouping elements", Steel Compos. Struct., 41(2), 267-277. https://doi.org/10.12989/scs.2021.41.2.267.
  18. Yuan, X.F., Li, A.L., Shen, Y.B. and Qian, R.J. (2016), "Kinematic path analysis of kinematically indeterminate systems", KSCE J. Civ. Eng., 20(2), 813-819. https://doi.org/10.1007/s12205-015-0481-2.
  19. Yuan, X.F. and Dong, S.L. (2001), "Inverse analysis of construction process of cable dome", J. Build. Struct., 22(2), 75-79. https://doi.org/10.3321/j.issn:1000-6869.2001.02.014.
  20. Yuan, X.F. and Dong, S.L. (2003), "Integral feasible prestress of cable domes", Comput. Struct., 81(21), 2111-2119. https://doi.org/10.1016/s0045-7949(03)00254-2.
  21. Zhang, T.H., Kawaguchi, K. and Wu, M.E. (2019), "Optimization of frame structures with kinematical indeterminacy for optimum folding", J. Eng. Mech., 145(9), 04019072. https://doi.org/10.1061/(asce)em.1943-7889.0001646.
  22. Zhang, J.H. and Sun, K. (2011), "Construction process simulation of cable dome", Adv. Struct. Eng., 94-96, 750-754. https://doi.org/10.4028/www.scientific.net/amm.94-96.750.
  23. Zhang, P., Fan, W.Y., Chen, Y., Feng, J. and Sareh, P. (2022), "Structural symmetry recognition in planar structures using Convolutional Neural Networks", Eng. Struct., 260, 114227. https://doi.org/10.1016/j.engstruct.2022.114227.
  24. Zhang, W.F., Liu, Y.C., Ji, J. and Teng, Z.C. (2014), "Analysis of dynamic behavior for truss cable structures", Steel Compos. Struct., 16(2), 117-133. https://doi.org/10.12989/scs.2014.16.2.117.
  25. Zhang, P., Kawaguchi, K. and Feng, J. (2014), "Prismatic tensegrity structures with additional cables: Integral symmetric states of self-stress and cable-controlled reconfiguration procedure", Int. J. Solids Struct., 51(25-26), 4294-4306. https://doi.org/10.1016/j.ijsolstr.2014.08.014.
  26. Zhang, P. and Feng, J. (2017), "Initial prestress design and optimization of tensegrity systems based on symmetry and stiffness", Int. J. Solids Struct., 106-107, 68-90. https://doi.org/10.1016/j.ijsolstr.2016.11.030.
  27. Zhu, D.X., Deng, H. and Wu, X.S. (2020), "Selecting active members to drive the mechanism displacement of tensegrities", Int. J. Solids Struct., 191-192, 278-292. https://doi.org/10.1016/j.ijsolstr.2020.01.021.
  28. Zhang, P., Zhou, J.K. and Chen, J.S. (2021), "Form-finding of complex tensegrity structures using constrained optimization method", Compos. Struct., 268, 113971. https://doi.org/10.1016/j.compstruct.2021.113971.