Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Numerical form-finding of multi-order tensegrity structures by grouping elements

  • Wang, Xinyu (Key Laboratory of C& PC Structures of Ministry of Education, Southeast University) ;
  • Cai, Jianguo (Key Laboratory of C& PC Structures of Ministry of Education, Southeast University) ;
  • Lee, Daniel Sang-hoon (The Royal Danish Academy of Fine Arts, School of Architecture, School of Architecture, Institute of Technology) ;
  • Xu, Yixiang (School of Aerospace, UNNC, University of Nottingham Ningbo China) ;
  • Feng, Jian (Key Laboratory of C& PC Structures of Ministry of Education, Southeast University)
  • Received : 2020.09.09
  • Accepted : 2021.09.15
  • Published : 2021.10.25
⟨ Previous Next ⟩

Abstract

Multi-order tensegrity structures are an attractive form of compliant deployable structures. An efficient numerical form-finding method is proposed for multi-stable tensegrity structures in this paper. The current method first analyze the force density matrix for sets of more feasible force densities that satisfy the non-degeneracy conditions. Then, based on symmetrical grouping of elements, a genetic algorithm is used to minimize the eigenvalues; as a result, multiple orders of equilibrium can be found. For the investigation, two symmetric tensegrity structures are analyzed using the currently proposed method, and the method's applicability and accuracy have been examined.

Keywords

Acknowledgement

The work presented in this article was supported by the National Natural Science Foundation of China (No.51822805, No.51878147 and U1937202), a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, and the Excellent Young Teachers Program of Southeast University.

References

  1. Bletzinger, KU. and Ramm, E. (1999), "A general finite element approach to the form finding of tensile structures by the updated reference strategy", Int. J. Space Struct., 14(2), 131-145. https://doi.org/10.1260/0266351991494759.
  2. Bishop, D.M. (1993) Group theory and chemistry. Courier Corporation.
  3. Cai, J.G. and Feng, J. (2015), "Form-finding of tensegrity structures using an optimization method", Eng. Struct., 104, 126-132. https://doi.org/10.1016/j.engstruct.2015.09.028.
  4. Cai, J.G, Zhang, Q., Zhang, Y., Lee, D.S.H. 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.
  5. Connelly, R. and Back, A. (1998), "Mathematics and Tensegrity: Group and representation theory make it possible to form a complete catalogue of 'strut-cable' constructions with prescribed symmetries", Am. Sci., 86(2), 142-151. https://doi.org/10.1511/1998.2.142.
  6. Chen, Y., Sareh, P., Feng, J. and Sun, Q. (2017), "A computational method for automated detection of engineering structures with cyclic symmetries". Comput. Struct., 191(15),153-164. https://doi.org/10.1016/j.compstruc.2017.06.013.
  7. Connelly, R. and Terrell, M. (1995), "Globally rigid Symmetric Tensegrities", Struct. Topol., 21, 59-78. https://doi.org/10.1177/026635119200700208.
  8. Chen, Y. and Feng, J. (2014), "Efficient method for moorepenrose inverse problems involving symmetric structures based on group theory", J. Comput. Civ. Eng., 28(2), 182-190. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000266.
  9. Do, D.T.T., Lee, S. and Lee, J. (2016), "A modified differential evolution algorithm for tensegrity structures", Comput. Struct., 158, 11-19. https://doi.org/10.1016/j.compstruct.2016.08.039.
  10. Estrada, G.G., Bungartz, H.J. and Mohrdieck, C. (2006), "Numerical form-finding of 2D tensegrity structures", Int. J. Solids Struct., 43(22-23), 6855-6868. https://doi.org/10.1016/j.ijsolstr.2006.02.012.
  11. 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.
  12. Gan, B.S., Zhang, J. and Nguyen, D.K. (2015), "Node-based genetic form-finding of irregular tensegrity structures", Comput. Struct., 159, 61-73. https://doi.org/10.1016/j.compstruc.2015.07.003.
  13. Ho-Huu, V., Vo-Duy, T. and Luu-Van, T. (2016), "Optimal design of truss structures with frequency constraints using improved differential evolution algorithm based on an adaptive mutation scheme", Autom. Constr., 68, 81-94. https://doi.org/10.1016/j.autcon.2016.05.004.
  14. Holland, J.H. (1975), Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, Control and Artificial Intelligence University of Michigan Press.
  15. Ikeda, K. and Murota, K. (2010), Imperfect Bifurcation in Structures and Materials: Group-Theoretic Bifurcation Theory, Applied Mathematical Sciences.
  16. Koohestani, K. (2012), "Form-finding of tensegrity structures via genetic algorithm", Int. J. Solids Struct., 49(5), 739-747. https://doi.org/10.1016/j.ijsolstr.2011.11.015.
  17. Kangwai, R.D. and Guest, S.D. (2000), "Symmetry-adapted equilibrium matrices", Int. J. Solids Struct., 37(11), 1525-1548. https://doi.org/10.1016/S0020-7683(98)00318-7.
  18. Kaveh, A. and Rahami, H. (2011), "Block circulant matrices and applications in free vibration analysis of cyclically repetitive structures", Acta Mech., 217(1), 51-62. https://doi.org/10.1007/s00707-010-0382-x.
  19. Kumar, R. (2010), "System and method for the use of an adaptive mutation operator in genetic algorithms", United States Patent Patent No US7, 660,773 B1.
  20. Kaveh, A., Nikbakht, M. and Rahami, H. (2010) "Improved group theoretic method using graphs products, for the analysis of symmetric-regular structures", Acta Mech., 210(3-4), 265-289. https://doi.org/10.1007/s00707-009-0204-1.
  21. Kaveh, A., Rahami, H., Ardalan, H.A. and Mirghaderi S.R. (2013), "Analysis of regular structures with member irregularity using the equilibrium equations and the singular value decomposition", Adv. Struct. Eng., 16(5), 823-843. https://doi.org/10.1260/1369-4332.16.5.823.
  22. Linkwitz, K. and Schek, H.J. (1971), "Einige bemerkungen zur berechnung von vorgespannten seilnetzkonstruktionen", Arch. Appl. Mech., 40(3), 145-158. https://doi.org/10.1007/BF00532146.
  23. Li, Y., Feng, X.Q., and Cao, Y.P. (2010), "A Monte Carlo form-finding method for large scale regular and irregular tensegrity structures", Int. J. Solids Struct., 47(14-15), 1888-1898. https://doi.org/10.1016/j.ijsolstr.2010.03.026.
  24. Lee, S., Gan, B.S. and Lee J. (2016), "A fully automatic group selection for form-finding process of truncated tetrahedral tensegrity structures via a double-loop genetic algorithm", Compos. B. Eng., 106, 308-315. https://doi.org/10.1016/j.compositesb.2016.09.018.
  25. Motro, R. (2003), Tensegrity: structural systems for the future, Elsevier.
  26. Murakami, H. and Nishimura, Y. (2001), "Static and dynamic characterization of regular truncated icosahedral and dodecahedral tensegrity modules", Int. J. Solids Struct., 38(50), 9359-9381. https://doi.org/10.1016/S0020-7683(01)00030-0.
  27. Masic, M., Skelton, R.E., and Gill, P.E. (2005), "Algebraic tensegrity form-finding", Int. J. Solids Struct., 42(16-17), 4833- 4858. https://doi.org/10.1016/j.ijsolstr.2005.01.014.
  28. Micheletti, A. and Williams, W.O. (2007), "A marching procedure for form-finding for tensegrity structures", J. Mech. Mater. Struct., 2(5), 857-882. https://doi.org/10.2140/jomms.2007.2.857.
  29. Pellegrino, S. (1986), "Mechanics of kinematically indeterminate structures", Ph.D. dissertation, University of Cambridge, U.K.
  30. Pagitz, M. and Tur, J.M.M. (2009), "Finite element based form-finding algorithm for tensegrity structures", Int. J. Solids Struct., 46(17), 3235-324. https://doi.org/10.1016/j.ijsolstr.2009.04.018.
  31. Richard, B.F. (1962), "Tensile-integrity structures", U.S. Patent 3,063,521, 11-13.
  32. Raj, R.P. and Guest, S.D. (2006), "Using symmetry for tensegrity form-finding", J. Int. Assoc. Shell Spatial Struct., 47(3), 245-252. https://doi.org/10.1016/j.ijsolstr.2011.11.015.
  33. Rahami. H., Kaveh, A., Ardalan, M.A. and Mirghaderi S.R. (2013), "Analysis of near-regular structures with node irregularity using SVD of equilibrium matrix", Int. J. Civ. Eng., 11(4), 226-241. http://ijce.iust.ac.ir/article-1-938-en.html.
  34. Skelton, R.E., Adhikari, R., Pinaud, J.P., Chan, W. and Helton, J.W. (2001), "An introduction to the mechanics of tensegrity structures. Decision and Control", Proceedings of the 40th IEEE Conference on. IEEE, 5, 4254-4259, Orlando, Florida USA, December.
  35. Sultan, C., Corless, M. and Skelton, R.E. (2001), "Symmetrical reconfiguration of tensegrity structures", Int. J. Solids Struct., 39(8), 2215-223. https://doi.org/10.1016/S0020-7683(02)00100-2.
  36. Tur, J.M.M. and Juan, S.H. (2009), "Tensegrity frameworks: Dynamic analysis review and open problems", Mech. Mach. Theory., 44(1), 1-18. https://doi.org/10.1016/j.mechmachtheory.2008.06.008.
  37. Veenendaal, D. and Block, P. (2012), "An overview and comparison of structural form finding methods for general networks", Int. J. Solids Struct., 49(26), 3741-3753. https://doi.org/10.1016/j.ijsolstr.2012.08.008.
  38. Vo-Duy, T., Ho-Huu, V. and Dang-Trung, H. (2016), "A two-step approach for damage detection in laminated composite structures using modal strain energy method and an improved differential evolution algorithm", Compos. Struct., 147, 42-53. https://doi.org/10.1016/j.compstruct.2016.03.027.
  39. Vassart, N. and Motro, R. (1999), "Multi-parametered Form-finding Method: Application to Tensegrity Systems", Int. J. Space Struct., 14(2), 147-154. https://doi.org/10.1260/0266351991494768.
  40. Wright, A.H. (1999), "Genetic Algorithms for Real Parameter Optimization", Foundations of Genetic Algorithms, 1, 205-218. https://doi.org/10.1016/B978-0-08-050684-5.50016-1.
  41. Xu, X. and Luo, Y. (1999), "Form-finding of non-regular tensegrities using a genetic algorithm", Mech. Res. Commun., 37(1), 85-91. https://doi.org/10.1016/j.mechrescom.2009.09.003.
  42. Xu, X. and Luo, Y. (2010), "Multi-Stable Tensegrity Structures", J. Struct. Eng., 137(1), 117-123. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000281.
  43. Yamamoto, M., Gan, B.S. and Fujita, K. (2011), "A genetic algorithm based form-finding for tensegrity structure", Procedia Eng., 14(2259), 2949-2956. https://doi.org/10.1016/j.proeng.2011.07.371.
  44. Zhang, J.Y. and Ohsaki, M. (2006), "Adaptive force density method for form-finding problem of tensegrity structures", Int J Solids Struct., 43(18-19), 5658-5673. https://doi.org/10.1016/j.ijsolstr.2005.10.011.
  45. Zhang, J.Y., Guest, S.D. and Ohsaki, M. (2009) "Symmetric prismatic tensegrity structures: Part I. Configuration and stability", Int J Solids Struct., 46(1), 1-14. https://doi.org/10.1016/j.ijsolstr.2008.08.032.
  46. Zlokovic, G.M. and Zlokovic, D. (1989), Group theory and G-vector spaces in structural analysis: vibration, stability, and statics, E. Horwood.
  47. 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.