Multistable Tensegrity Structures
Publication: Journal of Structural Engineering
Volume 137, Issue 1
Abstract
Tensegrity structures have been intensively studied since they appeared in the 1950s. Their applications have been extended from architecture to other areas including aerospace structures, cell mechanics, and robotics. In this paper, an interesting characteristic, the so-called multistability, is reported. A detailed investigation on a multistable tensegrity structure whose basic stable configuration corresponds to the expanded octahedron tensegrity is presented. Using an evolutionary form-finding scheme, together with the dynamic relaxation method, two other self-equilibrated configurations with higher strain energies are found. The stabilities of these configurations are verified by a matrix analysis process. Then, an investigation on the actuations and the corresponding threshold energies triggering the transformations between the different configurations is carried out. A typical set of actuation loads and the corresponding threshold energies for the state transformations are identified. The existence and the stability of the multistable configurations are verified by physical models. This study provides a theoretical basis for the further applications of multistable tensegrity structures.
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Acknowledgments
This work was supported by grants from National Natural Science Foundation of China (Grant No. NNSFC50978227) and China Postdoctoral Science Foundation (Grant No. UNSPECIFIED20090461384). The writers also thank Mr. Feng Yu, Jingmeng Xu, Zhouneng Zhong, and Pengcheng Yang for their great help in making the physical models.
References
Adam, B., and Smith, I. F. C. (2007a). “Tensegrity active control: Multiobjective approach.” J. Comput. Civ. Eng., 21(1), 3–10.
Adam, B., and Smith, I. F. C. (2007b). “Self-diagnosis and self-repair of an active tensegrity structure.” J. Struct. Eng., 133(12), 1752–1761.
Barnes, M. R. (1999). “Form-finding and analysis of tension structures by dynamic relaxation.” Int. J. Space Struct., 14(2), 89–104.
De Jong, K. A. (1975). “An analysis of the behavior of a class of genetic adaptive systems.” Ph.D. thesis, Univ. of Michigan, Mich.
Defossez, M. (2003). “Shape memory effect in tensegrity structures.” Mech. Res. Commun., 30, 311–316.
Djouadi, S., Motro, R., Pons, J. C., and Crosnier, B. (1998). “Active control of tensegrity systems.” J. Aerosp. Eng., 11(2), 37–44.
Domer, B., Fest, E., Lalit, V., and Smith, I. F. C. (2003). “Combining dynamic relaxation method with artificial neural networks to enhance simulation of tensegrity structures.” J. Struct. Eng., 129(5), 672–681.
Fest, E., Shea, K., Domer, B., and Smith, I. F. C. (2003). “Adjustable tensegrity structures.” J. Struct. Eng., 129(4), 515–526.
Geiger, D. H. (1988). “Design details of an elliptical cable dome and a large span cable dome (210 m) under construction in the United States.” Proc., IASS ASCE. Int. Symp. on Innovative Applications of Shells and Spatial Forms, Oxford Univ. Press, Oxford, U.K.
Ingber, D. E. (2003). “Tensegrity I. Cell structure and hierarchical systems biology.” J. Cell. Sci., 116, 1157–1173.
Kawaguehi, M., Abe, M., and Tatemichi, I. (1999). “Design, test and realization of ‘suspend-dome’ system.” Journal of the International Association for Shell and Spatial Structures, 40(131), 179–192.
Marks, R., and Fuller, R. B. (1973). Dymaxion world of Buckminster Fuller, Anchor-Doubleday, Garden City, N.Y.
Masic, M., and Skelton, R. E. (2006). “Selection of prestress for optimal dynamic/control performance of tensegrity structures.” Int. J. Solids Struct., 43, 2110–2125.
Paul, C., Lipson, H., and Valero-Cuevas, F. J. (2005). “Evolutionary form-finding of tensegrity structures.” Proc., GECCO’05, Association for Computing Machinery, New York.
Paul, C., Lipson, H., and Valero-Cuevas, F. J. (2006). “Design and control of tensegrity robots for locomotion.” IEEE Trans. Rob. Autom., 22(5), 944–957.
Pellegrino, S. (1990). “Analysis of pre-stressed mechanisms.” Int. J. Solids Struct., 26(12), 3025–3035.
Pellegrino, S. (1994). “Structural computation with the singular value decomposition of the equilibrium.” Int. J. Solids Struct., 30(21), 3025–3035.
Pellegrino, S., and Calladine, C. R. (1986). “Matrix analysis of statistically and kinematically indeterminate frameworks.” Int. J. Solids Struct., 22, 409–428.
Pugh, A. (1976). An introduction to tensegrity, Univ. of California Press, Berkeley, Calif.
Stamenovic, D., Fredberg, J. J., Wang, N., Butler, J. P., and Ingber, D. E. (1996). “A microstructural approach to cytoskeletal mechanics based on tensegrity.” J. Theor. Biol., 181, 125–136.
Stamenovic, D., and Ingber, D. E. (2002). “Models of cytoskeletal mechanics of adherent cells.” Biomech. Model. Mechanobiol., 1, 95–108.
Tibert, A. G., and Pellegrino, S. (2003). “Review of form-finding methods for tensegrity structures.” Int. J. Space Struct., 18, 209–223.
Wang, N., Butler, J. P., and Ingber, D. E. (1993). “Mechanotransduction across the cell surface and through the cytoskeleton.” Science, 260, 1124–1127.
Xu, X., and Luo, Y. (2010). “Form-finding of nonregular tensegrities using a genetic algorithm.” Mech. Res. Commun., 37, 85–91.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 137 • Issue 1 • January 2011
Pages: 117 - 123
Copyright
© 2011 ASCE.
History
Received: Aug 24, 2008
Accepted: Jul 2, 2010
Published online: Jul 15, 2010
Published in print: Jan 2011
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