Browse > Article
http://dx.doi.org/10.12989/scs.2021.41.2.267

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)
Publication Information
Steel and Composite Structures / v.41, no.2, 2021 , pp. 267-277 More about this Journal
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
grouping elements; force density; form-finding, multi-order; non-degeneracy condition;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 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.   DOI
2 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.   DOI
3 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.   DOI
4 Pellegrino, S. (1986), "Mechanics of kinematically indeterminate structures", Ph.D. dissertation, University of Cambridge, U.K.
5 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.   DOI
6 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.   DOI
7 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.   DOI
8 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.   DOI
9 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.   DOI
10 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.   DOI
11 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.   DOI
12 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.   DOI
13 Connelly, R. and Terrell, M. (1995), "Globally rigid Symmetric Tensegrities", Struct. Topol., 21, 59-78. https://doi.org/10.1177/026635119200700208.   DOI
14 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.   DOI
15 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.   DOI
16 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.   DOI
17 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.   DOI
18 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.   DOI
19 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.   DOI
20 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.   DOI
21 Zlokovic, G.M. and Zlokovic, D. (1989), Group theory and G-vector spaces in structural analysis: vibration, stability, and statics, E. Horwood.
22 Motro, R. (2003), Tensegrity: structural systems for the future, Elsevier.
23 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.   DOI
24 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.   DOI
25 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.   DOI
26 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.   DOI
27 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.   DOI
28 Richard, B.F. (1962), "Tensile-integrity structures", U.S. Patent 3,063,521, 11-13.
29 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.
30 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.   DOI
31 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.   DOI
32 Ikeda, K. and Murota, K. (2010), Imperfect Bifurcation in Structures and Materials: Group-Theoretic Bifurcation Theory, Applied Mathematical Sciences.
33 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.   DOI
34 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.   DOI
35 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.   DOI
36 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.
37 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.   DOI
38 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.   DOI
39 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.   DOI
40 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.   DOI
41 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.
42 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.
43 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.   DOI
44 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.   DOI
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.   DOI
46 Bishop, D.M. (1993) Group theory and chemistry. Courier Corporation.
47 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.   DOI