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Determination of a unique configuration of free-form tensegrity structures

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Abstract

A numerical method is presented for form-finding of free-form tensegrity structures. The topology and an initial randomly generated force density vector are the required information in the present form-finding process. An approach of defining a unique configuration of free-form tensegrity structures by specifying an independent set of nodal coordinates is rigorously provided, which means that the geometrical and mechanical properties of the structure can be at least partly controlled by the proposed method. Several numerical examples are presented to demonstrate the efficiency and robustness in searching new self-equilibrium stable free-form configurations of tensegrity structures.

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References

  1. Fuller R.B.: Synergetics-Explorations in the Geometry of Thinking. Macmillan Publishing Co. Inc., London, UK (1975)

    Google Scholar 

  2. Tibert A.G., Pellegrino S.: Deployable tensegrity reflectors for small satellites. J. Spacecr. Rocket. 39, 701–709 (2002)

    Article  MATH  Google Scholar 

  3. Fu F.: Structural behavior and design methods of tensegrity domes. J. Constr. Steel Res. 61, 23–35 (2005)

    Article  Google Scholar 

  4. Tran H.C., Lee J.: Initial self-stress design of tensegrity grid structures. Comput. Struct. 88, 558–566 (2010)

    Article  Google Scholar 

  5. Kebiche K., Kazi-Aoual M.N., Motro R.: Geometrical non-linear analysis of tensegrity systems. Eng. Struct. 21, 864–876 (1999)

    Article  Google Scholar 

  6. Rhode-Barbarigos L., Ali N.B.H., Motro R., Smith I.F.C.: Designing tensegrity modules for pedestrian bridges. Eng. Struct. 32, 1158–1167 (2010)

    Article  Google Scholar 

  7. Tran H.C., Lee J.: Self-stress design of tensegrity grid structures with exostresses. Int. J. Solids Struct. 47, 2660–2671 (2010)

    Article  MATH  Google Scholar 

  8. Ingber D.E.: The architecture of life. Sci. Am. 278, 48–57 (1998)

    Article  Google Scholar 

  9. Ingber D.E., Tensegrity I.: Cell structure and hierarchical systems biology. J. Cell Sci. 116, 1157–1173 (2003)

    Article  Google Scholar 

  10. Stamenovic D.: Effects of cytoskeletal prestress on cell rheological behavior. Acta Biomater. 1, 255–262 (2005)

    Article  Google Scholar 

  11. Connelly R., Whiteley W.: Second-order rigidity and prestress stability for tensegrity frameworks. SIAM J. Discret. Math. 9, 453–491 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Jórdan T., Recski A., Szabadka Z.: Rigid tensegrity labelings of graphs. Eur. J. Comb. 30, 1887–1895 (2009)

    Article  MATH  Google Scholar 

  13. Paul C., Lipson H., Valero-Cuevas F.: Design and control of tensegrity robots for locomotion. IEEE T. Robot. 22, 944–957 (2006)

    Article  Google Scholar 

  14. Rovira A.G., Tur J.M.M.: Control and simulation of a tensegrity-based mobile robot. Robot. Auton. Syst. 57, 526–535 (2009)

    Article  Google Scholar 

  15. Wang B.B.: Free-Standing Tension Structures: From Tensegrity Systems to Cable Strut Systems. Spon Press, London and New York (2004)

    Google Scholar 

  16. Pinaud, J.P., Solari, S., Skelton, R.E.: Deployment of a class 2 tensegrity boom. In: Proceedings of SPIE Smart Structures and Materials, pp. 155–162. (2004)

  17. Lazopoulos K.A.: Stability of an elastic tensegrity structure. Acta Mech. 179, 1–10 (2005)

    Article  MATH  Google Scholar 

  18. Lazopoulos K.A., Lazopoulou N.K.: On the elastica solution of a tensegrity structure: application to cell mechanics. Acta Mech. 182, 253–263 (2006)

    Article  MATH  Google Scholar 

  19. Pirentis A.P., Lazopoulos K.A.: On the singularities of a constrained (incompressible-like) tensegrity-cytoskeleton model under equitriaxial loading. Int. J. Solids Struct. 47, 759–767 (2010)

    Article  MATH  Google Scholar 

  20. Connelly R., Terrell M.: Globally rigid symmetric tensegrities. Topol. Struct. 21, 59–78 (1995)

    MATH  MathSciNet  Google Scholar 

  21. Murakami H., Nishimura Y.: Initial shape finding and modal analyses of cyclic right-cylindrical tensegrity modules. Comput. Struct. 79, 891–917 (2001)

    Article  Google Scholar 

  22. Sultan C., Corless M., Skelton R.E.: The prestressability problem of tensegrity structures: some analytical solutions. Int. J. Solids Struct. 38, 5223–5252 (2001)

    Article  MATH  Google Scholar 

  23. Vassart N., Motro R.: Multiparametered formfinding method: application to tensegrity systems. Int. J. Space Struct. 14, 147–154 (1999)

    Article  Google Scholar 

  24. Schek H.J.: The force density method for form finding and computation of general networks. Comput. Methods Appl. Mech. Eng. 3, 115–134 (1974)

    Article  MathSciNet  Google Scholar 

  25. Motro, R., Najari, S., Jouanna, P.: Static and dynamic analysis of tensegrity systems. In: Proceedings of the International Symposium on Shell and Spatial Structures, Computational Aspects, pp. 270–279. Springer, Berlin (1986)

  26. Barnes M.R.: Form finding and analysis of tension structures by dynamic relaxation. Int. J. Space Struct. 14, 89–104 (1999)

    Article  Google Scholar 

  27. Masic M., Skelton R., Gill P.: Algebraic tensegrity form-finding. Int. J. Solids Struct. 42, 4833–4858 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  28. Zhang J.Y., Ohsaki M.: Adaptive force density method for form-finding problem of tensegrity structures. Int. J. Solids Struct. 43, 5658–5673 (2006)

    Article  MATH  Google Scholar 

  29. Estrada G., Bungartz H., Mohrdieck C.: Numerical form-finding of tensegrity structures. Int. J. Solids Struct. 43, 6855–6868 (2006)

    Article  MATH  Google Scholar 

  30. Pagitz M., Tur J.M.M.: Finite element based form-finding algorithm for tensegrity structures. Int. J. Solids Struct. 46, 3235–3240 (2009)

    Article  MATH  Google Scholar 

  31. Tran H.C., Lee J.: Advanced form-finding of tensegrity structures. Comput. Struct. 88, 237–246 (2010)

    Article  Google Scholar 

  32. Juan S.H., Tur J.M.M.: Tensegrity frameworks: static analysis review. Mech. Mach. Theory 43, 859–881 (2008)

    Article  MATH  Google Scholar 

  33. Sultan C.: Tensegrity: 60 years of art, science and engineering. Adv. Appl. Mech. 43, 69–145 (2009)

    Article  Google Scholar 

  34. Tibert A.G., Pellegrino S.: Review of form-finding methods for tensegrity structures. Int. J. Space Struct. 18, 209–223 (2003)

    Article  Google Scholar 

  35. Zhang L., Maurin B., Motro R.: Form-finding of nonregular tensegrity systems. J. Struct. Eng. ASCE 132, 1435–1440 (2006)

    Article  Google Scholar 

  36. Baudriller H., Maurin B., Cañadas P., Montcourrier P., Parmeggiani A., Bettache N.: Form-finding of complex tensegrity structures: application to cell cytoskeleton modelling. C. R. Mécanique 334, 662–668 (2006)

    Article  MATH  Google Scholar 

  37. Micheletti A., Williams W.O.: A marching procedure for form-finding for tensegrity structures. J. Mech. Mater. Struct. 2, 101–126 (2007)

    Article  Google Scholar 

  38. Rieffel J., Valero-Cuevas F., Lipson H.: Automated discovery and optimization of large irregular tensegrity structures. Comput. Struct. 87, 368–379 (2009)

    Article  Google Scholar 

  39. Xu X., Luo Y.: Form-finding of nonregular tensegrities using a genetic algorithm. Mech. Res. Commun. 37, 85–91 (2010)

    Article  Google Scholar 

  40. Motro R.: Tensegrity: Structural Systems for the Future. Kogan Page Science, London (2003)

    Google Scholar 

  41. Connelly R.: Rigidity and energy. Invent. Math. 66, 11–33 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  42. Connelly R.: Tensegrity structures: why are they stable?. In: Thorpe, M.F., Duxbury, P.M. (eds) Rigidity Theory and Applications, pp. 47–54. Kluwer Academic Publishers, Dordrecht (1999)

    Google Scholar 

  43. Calladine C.R.: Buckminster Fuller’s “tensegrity” structures and Clerk Maxwell’s rules for the construction of stiff frames. Int. J. Solids Struct. 14, 161–172 (1978)

    Article  MATH  Google Scholar 

  44. Pellegrino S., Calladine C.R.: Matrix analysis of statically and kinematically indeterminate frameworks. Int. J. Solids Struct. 22, 409–428 (1986)

    Article  Google Scholar 

  45. Meyer C.D.: Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia (2000)

    Book  MATH  Google Scholar 

  46. Connelly R., Back A.: Mathematics and tensegrities. Am. Sci. 86, 142–151 (1998)

    Article  Google Scholar 

  47. Guest S.: The stiffness of prestressed frameworks: a unifying approach. Int. J. Solids Struct. 43, 842–854 (2006)

    Article  MATH  Google Scholar 

  48. Murakami H.: Static and dynamic analyses of tensegrity structures. Part II. Quasi-static analysis. Int. J. Solids Struct. 38, 3615–3629 (2001)

    Article  Google Scholar 

  49. Ohsaki M., Zhang J.Y.: Stability conditions of prestressed pin-jointed structures. Int. J. Nonlinear Mech. 41, 1109–1117 (2006)

    Article  Google Scholar 

  50. Pellegrino S.: Structural computations with the singular value decomposition of the equilibrium matrix. Int. J. Solids Struct. 30, 3025–3035 (1993)

    Article  MATH  Google Scholar 

  51. Yang W.Y., Cao W., Chung T.S.: Applied Numerical Methods Using Matlabs. Wiley InterScience, United States of America (2005)

    Book  Google Scholar 

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  1. Department of Architectural Engineering, Sejong University, 98 Kunja Dong, Kwangjin Ku, Seoul, 143-747, Korea

    Hoang Chi Tran & Jaehong Lee

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  1. Hoang Chi Tran
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  2. Jaehong Lee
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Correspondence to Jaehong Lee.

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Tran, H.C., Lee, J. Determination of a unique configuration of free-form tensegrity structures. Acta Mech 220, 331–348 (2011). https://doi.org/10.1007/s00707-011-0479-x

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