Skip to main content

Advertisement

Log in

Snapping instability in prismatic tensegrities under torsion

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Tensegrities are a class of lightweight and reticulated structures consisting of stressed strings and bars. It is shown that each prismatic tensegrity can have two self-equilibrated and stable states, leading to a snapping instability behavior under an applied torque. The predicted mechanism is experimentally validated, and can be used in areas such as advanced sensors and actuators, energy storage/adsorption equipments, and folding/unfolding devices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Skelton, R. E. and de Oliveira, M. C. Tensegrity Systems, Springer, Dordrecht (2009)

    MATH  Google Scholar 

  2. Sultan, C. Tensegrity: 60 years of art, science, and engineering. Advances in Applied Mechanics, 43, 69–145 (2009)

    Article  Google Scholar 

  3. Rhode-Barbarigos, L., Ali, N. B. H., Motro, R., and Smith, I. F. C. Designing tensegrity modules for pedestrian bridges. Engineering Structures, 32, 1158–1167 (2010)

    Article  Google Scholar 

  4. Sunny, M. R., Sultan, C., and Kapania, R. K. Optimal energy harvesting from a membrane attached to a tensegrity structure. AIAA Journal, 52, 307–319 (2014)

    Article  Google Scholar 

  5. Fraternali, F., Senatore, L., and Daraio, C. Solitary waves on tensegrity lattices. Journal of the Mechanics and Physics of Solids, 60, 1137–1144 (2012)

    Article  Google Scholar 

  6. Stamenović, D. and Ingber, D. E. Tensegrity-guided self assembly: from molecules to living cells. Soft Matter, 5, 1137–1145 (2009)

    Article  Google Scholar 

  7. Veenendaal, D. and Block, P. An overview and comparison of structural form finding methods for general networks. International Journal of Solids and Structures, 49, 3741–3753 (2012)

    Article  Google Scholar 

  8. Zhang, L. Y., Li, Y., Cao, Y. P., Feng, X. Q., and Gao, H. J. Self-equilibrium and super-stability of truncated regular polyhedral tensegrity structures: a unified analytical solution. Proceedings of the Royal Society, A: Mathematical Physical and Engineering Sciences, 468, 3323–3347 (2012)

    Article  MathSciNet  Google Scholar 

  9. Koohestani, K. and Guest, S. D. A new approach to the analytical and numerical form-finding of tensegrity structures. International Journal of Solids and Structures, 50, 2995–3007 (2013)

    Article  Google Scholar 

  10. Feng, X. Q., Li, Y., Cao, Y. P., Yu, S. W., and Gu, Y. T. Design methods of rhombic tensegrity structures. Acta Mechanica Sinica, 26, 559–565 (2010)

    Article  MATH  Google Scholar 

  11. Li, Y., Feng, X. Q., Cao, Y. P., and Gao, H. J. Constructing tensegrity structures from one-bar elementary cells. Proceedings of the Royal Society, A: Mathematical Physical and Engineering Sciences, 466, 45–61 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhang, L. Y., Zhao, H. P., and Feng, X. Q. Constructing large-scale tensegrity structures with bar-bar connection using prismatic elementary cells. Archive of Applied Mechanics, 85, 383–394 (2015)

    Article  Google Scholar 

  13. Defossez, M. Shape memory effect in tensegrity structures. Mechanics Research Communications, 30, 311–316 (2003)

    Article  MATH  Google Scholar 

  14. Li, Y., Feng, X. Q., Cao, Y. P., and Gao, H. J. A Monte Carlo form-finding method for large scale regular and irregular tensegrity structures. International Journal of Solids and Structures, 47, 1888–1898 (2010)

    Article  MATH  Google Scholar 

  15. Xu, X. and Luo, Y. Z. Multistable tensegrity structures. Journal of Structural Engineering-ASCE, 137, 117–123 (2011)

    Article  Google Scholar 

  16. Micheletti, A. Bistable regimes in an elastic tensegrity system. Proceedings of the Royal Society, A: Mathematical Physical and Engineering Sciences, 469, 20130052 (2013)

    Article  Google Scholar 

  17. Zhang, L. Y., Li, Y., Cao, Y. P., and Feng, X. Q. Stiffness matrix based form-finding method of tensegrity structures. Engineering Structures, 58, 36–48 (2014)

    Article  Google Scholar 

  18. Guest, S. D. The stiffness of tensegrity structures. IMA Journal of Applied Mathematics, 76, 57–66 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Fraternali, F., Carpentieri, G., and Amendola, A. On the mechanical modeling of the extreme softening/stiffening response of axially loaded tensegrity prisms. Journal of the Mechanics and Physics of Solids, 74, 136–157 (2015)

    Article  Google Scholar 

  20. Moored, K. W. and Bart-Smith, H. Investigation of clustered actuation in tensegrity structures. International Journal of Solids and Structures, 46, 3272–3281 (2009)

    Article  MATH  Google Scholar 

  21. Ali, N. B. H., Rhode-Barbarigos, L., and Smith, I. F. C. Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm. International Journal of Solids and Structures, 48, 637–647 (2011)

    Article  MATH  Google Scholar 

  22. Zhang, L., Lu, M. K., Zhang, H. W., and Yan, B. Geometrically non-linear elasto-plastic analysis of clustered tensegrity based on the co-rotational approach. International Journal of Mechanical Sciences, 93, 154–165 (2015)

    Article  Google Scholar 

  23. Zhang, L., Gao, Q., Liu, Y., and Zhang, H.W. An efficient finite element formulation for non-linear analysis of clustered tensegrity. Engineering Computations, 33 (2016) DOI 10.1108/EC-08-2014-0168

  24. Kebiche, K., Kazi-Aoual, M. N., and Motro, R. Geometrical non-linear analysis of tensegrity systems. Engineering Structures, 21, 864–876 (1999)

    Article  Google Scholar 

  25. Tran, H. C. and Lee, J. Geometric and material non-linear analysis of tensegrity structures. Acta Mechanica Sinica, 27, 938–949 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. Zhang, L., Gao, Q., and Zhang, H. W. An efficient algorithm for mechanical analysis of bimodular truss and tensegrity structures. International Journal of Mechanical Sciences, 70, 57–68 (2013)

    Article  Google Scholar 

  27. Zhang, L. Y., Li, Y., Cao, Y. P., Feng, X. Q., and Gao, H. J. A numerical method for simulating non-linear mechanical responses of tensegrity structures under large deformations. Journal of Applied Mechanics-Transactions of the ASME, 80, 061018 (2013)

    Article  Google Scholar 

  28. Stamenović, D., Fredberg, J. J., Wang, N., Butler, J. P., and Ingber, D. E. A microstructural approach to cytoskeletal mechanics based on tensegrity. Journal of Theoretical Biology, 181, 125–136 (1996)

    Article  Google Scholar 

  29. Oppenheim, I. J. and Williams, W. O. Geometric effects in an elastic tensegrity structure. Journal of Elasticity, 59, 51–65 (2000)

    Article  MATH  Google Scholar 

  30. Crane, C. D., Duffy, J., and Correa, J. C. Static analysis of tensegrity structures. Journal of Mechanical Design, 127, 257–268 (2005)

    Article  Google Scholar 

  31. Plaut, R. H. and Virgin, L. N. Vibration and snap-through of bent elastica strips subjected to end rotations. Journal of Applied Mechanics-Transactions of the ASME, 76, 041011 (2009)

    Article  Google Scholar 

  32. Fargette, A., Neukirch, S., and Antkowiak, A. Elastocapillary snapping: capillarity induces snap-through instabilities in small elastic beams. Physical Review Letters, 112, 137802 (2014)

    Article  Google Scholar 

  33. Mao, G. Y., Li, T. F., Zou, Z. N., Qu, S. X., and Shi, M. X. Prestretch effect on snap-through instability of short-length tubular elastomeric balloons under inflation. International Journal of Solids and Structures, 51, 2109–2115 (2014)

    Article  Google Scholar 

  34. Shekastehband, B., Abedi, K., Dianat, N., and Chenaghlou, M. R. Experimental and numerical studies on the collapse behavior of tensegrity systems considering cable rupture and strut collapse with snap-through. International Journal of Non-Linear Mechanics, 47, 751–768 (2012)

    Article  Google Scholar 

  35. Li, T. F., Keplinger, C., Baumgartner, R., Bauer, S., Yang, W., and Suo, Z. G. Giant voltage-induced deformation in dielectric elastomers near the verge of snap-through instability. Journal of the Mechanics and Physics of Solids, 61, 611–628 (2013)

    Article  Google Scholar 

  36. Dai, F. H., Li, H., and Du, S. Y. Cured shape and snap-through of bistable twisting hybrid [0/90/metal]T laminates. Composites Science and Technology, 86, 76–81 (2013)

    Article  Google Scholar 

  37. Avramov, K. V. and Mikhlin, Y. V. Snap-through truss as an absorber of forced oscillations. Journal of Sound and Vibration, 290, 705–722 (2006)

    Article  Google Scholar 

  38. Connelly, R. and Terrell, M. Globally rigid symmetric tensegrities. Structural Topology, 21, 59–79 (1995)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiqiao Feng.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11432008 and 11502016), the China Postdoctoral Science Foundation (No. 2015M570035), the Tsinghua University Initiative Scientific Research Program (No. 20121087991), and the Fundamental Research Funds for the Central Universities of China (No. FRF-TP-15-029A1)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, L., Zhang, C., Feng, X. et al. Snapping instability in prismatic tensegrities under torsion. Appl. Math. Mech.-Engl. Ed. 37, 275–288 (2016). https://doi.org/10.1007/s10483-016-2040-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-016-2040-6

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

Navigation