Abstract
A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities. The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations, while the material nonlinearity is treated through elastoplastic stress-strain relationship. The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method. A computer program is developed to predict the mechanical responses of tensegrity systems under tensile, compressive and flexural loadings. Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program. The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications. On the other hand, its bending strength capacity is not sensitive to the self-stress level.
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References
Fuller, R.B.: Synergetics-Explorations in the Geometry of Thinking. Macmillan Publishing Co. Inc., London, UK (1975)
Tibert, A.G., Pellegrino, S.: Deployable tensegrity reflectors for small satellites. J. Spacecraft Rockets 39(5), 701–709 (2002)
Fu, F.: Structural behavior and design methods of tensegrity domes. J. Constr. Steel Res. 61(1), 23–35 (2005)
Tran, H.C., Lee, J.: Initial self-stress design of tensegrity grid structures. Comput. Struct. 88(9–10), 558–566 (2010)
Kebiche, K., Kazi-Aoual, M.N., Motro, R.: Geometrical nonlinear analysis of tensegrity systems. Eng. Struct. 21(9), 864–876 (1999)
Rhode-Barbarigos, L., Ali, N.B.H., Motro, R., et al.: Designing tensegrity modules for pedestrian bridges. Eng. Struct. 32(4), 1158–1167 (2010)
Tran, H.C., Lee, J.: Self-stress design of tensegrity grid structures with exostresses. Int. J. Solids Struct. 47(20), 2660–2671 (2010)
Ingber, D.E.: The architecture of life. Sci. Am. 278(1), 48–57 (1998)
Ingber, D.E.: Tensegrity I. Cell structure and hierarchical systems biology. J. Cell Sci. 116(7), 1157–1173 (2003)
Stamenovic, D.: Effects of cytoskeletal prestress on cell rheological behavior. Acta Biomater. 1(3), 255–262 (2005)
Feng, X.Q., Li, Y., Cao, Y.P., et al.: Design methods of rhombic tensegrity structures. Acta Mech. Sinica 26(4), 559–565 (2010)
Connelly, R., Whiteley, W.: Second-order rigidity and prestress stability for tensegrity frameworks. SIAM J. Discrete Math. 9(3), 453–491 (1996)
Jórdan, T., Recski, A., Szabadka, Z.: Rigid tensegrity labelings of graphs. Eur. J. Combin. 30(8), 1887–1895 (2009)
Paul, C., Lipson, H., Valero-Cuevas, F.: Design and control of tensegrity robots for locomotion. IEEE T. Robot. 22(5), 944–957 (2006)
Rovira, A.G., Tur, J.M.M.: Control and simulation of a tensegrity-based mobile robot. Robot. Auton. Syst. 57(5), 526–535 (2009)
Wang, B.B.: Free-standing Tension Structures: From Tensegrity Systems to Cable Strut Systems. Spon Press, London and New York (2004)
Pinaud, J.P., Solari, S., Skelton, R.E.: Deployment of a class 2 tensegrity boom. In: Proceedings of SPIE Smart Structures and Materials, SPIE Press 155–162 (2004)
Motro, R.: Tensegrity: Structural Systems for the Future. (1st edn.) Kogan Page Science, London (2003)
Tibert, A.G., Pellegrino, S.: Review of form-finding methods for tensegrity structures. Int. J. Space Struct. 18(4), 209–223 (2003)
Kahla, N.B., Kebiche, K.: Nonlinear elastoplastic analysis of tensegrity systems. Eng. Struct. 22(11), 1552–1566 (2000)
Murakami, H.: Static and dynamic analyses of tensegrity structures. Part II. Quasi-static analysis. Int. J. Solids Struct. 38(20), 3615–3629 (2001)
Crane III, C.D., Duffy, J., Correa, J.: Static analysis of tensegrity structures. J. Mech. Design 127(2), 257–268 (2005)
Bathe, K.J., Ramm, E., Wilson, E.: Finite element formulations for large deformation dynamic analysis. Int. J. Numer. Meth. Eng. 9(2), 353–386 (1975)
Bathe, K.J., Ozdemir, H.: Elastic-plastic large deformation static and dynamic analysis. Comput. Struct. 6(2), 81–92 (1976)
Bathe, K.J.: Finite Element Procedures. Englewood Cliffs, New Jersey: Prentice-Hall (1996)
Murakami, H.: Static and dynamic analyses of tensegrity structures. Part 1. Nonlinear equations of motion. Int. J. Solids Struct. 38(20), 3599–3613 (2001)
Masic, M., Skelton, R., Gill, P.: Algebraic tensegrity form-finding. Int. J. Solids Struct. 42(16–17), 4833–4858 (2005)
Deng, H., Kwan, A.S.K.: Unified classification of stability of pin-jointed bar assemblies. Int. J. Solids Struct. 42(15), 4393–4413 (2005)
Zhang, J.Y., Ohsaki, M.: Adaptive force density method for form-finding problem of tensegrity structures. Int. J. Solids Struct. 43(18–19), 5658–5673 (2006)
Ohsaki, M., Zhang, J.Y.: Stability conditions of prestressed pin-jointed structures. Int. J. Nonlinear Mech. 41(10), 1109–1117 (2006)
Pellegrino, S., Calladine, C.R.: Matrix analysis of statically and kinematically indeterminate frameworks. Int. J. Solids Struct. 22(4), 409–428 (1986)
Tran, H.C., Lee, J.: Advanced form-finding for cable-strut structures. Int. J. Solids Struct. 47(14–15), 1785–1794 (2010)
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Tran, H.C., Lee, J. Geometric and material nonlinear analysis of tensegrity structures. Acta Mech Sin 27, 938–949 (2011). https://doi.org/10.1007/s10409-011-0520-2
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DOI: https://doi.org/10.1007/s10409-011-0520-2