Adaptive Tensegrity Module. I: Closed-Form and Finite-Element Analyses
Publication: Journal of Structural Engineering
Volume 140, Issue 9
Abstract
This paper describes the closed-form and discrete computational models for a geometrically nonlinear and linear static analysis of the adaptive tensegrity module presented in the companion paper. Due to the symmetry of the spatial tensegrity system, a simplified closed-form analysis is based on a two-dimensional (2D) solution of an equivalent prestressed triangular cable truss acting under a vertical point load. Novel concrete forms of the cable and deflection equations are derived. The analytical models serve to determine the response, i.e., horizontal components of cable forces and deflections as the basis for control commands. A three-dimensional (3D) discrete geometrically nonlinear analysis of the adaptive tensegrity module is based on the application of a nonlinear finite-element method. The results obtained by the nonlinear finite-element analysis are compared with those obtained by using both the simplified linear and nonlinear closed-form solutions. Physical relevance and mathematical correctness of the applied theoretical approaches were confirmed by the results. Finally, the numerical model is applied to assess the response of the prestressed tensegrity module considering the effects of large deformations and slackening of cables.
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Acknowledgments
This work is part of Research Project No. 1/0321/12, partially founded by the Scientific Grant Agency of the Ministry of Education of Slovak Republic and the Slovak Academy of Sciences. The present research has been carried out within the project Centre of excellent integrated research for progressive building structures, materials and technologies, supported by European Union Structural funds.
References
Adam, B., and Smith, I. F. C. (2008). “Reinforcement learning for structural control.” J. Comput. Civil Eng., 133–139.
Ansys 12 [Computer software]. Canonsburg, PA, Ansys.
Bel Hadj Ali, N., Rhode-Barbarigos, L., Albi, A. A. P., and Smith, I. F. C. (2010). “Design optimization and dynamic analysis of a tensegrity-based footbridge.” Eng. Struct., 32(11), 3650–3659.
Bel Hadj Ali, N., Rhode-Barbarigos, L., and Smith, I. F. C. (2011). “Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm.” Int. J. Solids Struct., 48(5), 637–647.
Buchholdt, H. A. (1998). Introduction to cable roof structures, 2nd Ed., Cambridge University Press, Cambridge.
Djouadi, S., Motro, R., Pons, J. C., and Crosnier, B. (1998). “Active control of tensegrity systems.” J. Aerosp. Eng., 37–43.
Domer, B., and Smith, I. F. C. (2005). “An active structure that learns.” J. Comput. Civ. Eng., 16–24.
European Committee for Standardization (CEN). (2006). “Design of steel structures. Part 1.11 design of structures with tension components.” Eurocode 3, Brussels.
Fest, E., Shea, K., and Smith, I. F. C. (2004). “Active tensegrity structure.” J. Struct. Eng., 1454–1465.
Gasparini, D., and Gautam, V. (2002). “Geometrically nonlinear static behaviour of cable structures.” J. Struct. Eng., 1317–1329.
Gul, M., and Catbas, F. N. (2011). “Damage assessment with ambient vibration data using a novel time series analysis methodology.” J. Struct. Eng., 1518–1526.
Hernandes Juan, S., and Mirats Tur, J. M. (2008). “Tensegrity frameworks: Static analysis review.” Mech. Mach. Theor., 43(7), 859–881.
Ingber, D. E. (1998). “The architecture of life.” Sci. Am., 278(1), 48–57.
Ingber, D. E. (2003). “Tensegrity I. Cell structure and hierarchical systems biology.” J. Cell Sci., 116(7), 1157–1173.
Irvine, H. M. (1981). Cable structures, MIT Press, Cambridge, U.K.
Jayaraman, H. B., and Knudson, W. C. (1981). “A curved element for the analysis of cable structures.” Comput. Struct., 14(3–4), 325–333.
Kadkhodayan, M., Alamatian, J., and Turvey, G. J. (2008). “A new fictitious time for the dynamic relaxation (DXDR) method.” Int. J. Numer. Methods Eng., 74(6), 996–1018.
Kanno, Y., Ohsaki, M., and Ito, J. (2002). “Large-deformation and friction analysis of non-linear elastic cable networks by second-order cone programming.” Int. J. Numer. Methods Eng., 55(9), 1079–1114.
Kassimali, A., and Parsi-Feraidoonian, H. (1987). “Strength of cable trusses under combined loads.” J. Struct. Eng., 907–924.
Kmet, S. (1994). “Rheology of pre-stressed cable structures.” Adv. Finite Elem. Tech., M. Papadrakakis and B. H. V. Topping, eds., Civil-Comp Press, Edinburgh, Scotland, 185–200.
Kmet, S., and Kokorudova, Z. (2006). “Non-linear analytical solution for cable truss.” J. Eng. Mech., 119–123.
Kmet, S., and Platko, P. (2014). “Adaptive tensegrity module. II: Tests and comparison of results.” J. Struct. Eng., 04014056.
Mirats Tur, J. M., and Hernandes, J. S. (2009). “Tensegrity frameworks: Dynamic analysis review and open problems.” Mech. Mach. Theor., 44(1), 1–18.
Motro, R. (2003). Tensegrity: Structural systems for the future, Hermes Science Publishing, Penton Science, London, U.K.
Murakami, H., and Nishimura, Y. (2001). “Initial shape finding and modal analyses of cyclic right-cylindrical tensegrity modules.” Comput. Struct., 79(9), 891–917.
Pargana, J. B., Lloyd-Smith, D., and Izzuddin, B. A. (2010). “Fully integrated design and analysis of tensioned fabric structures: Finite elements and case studies.” Eng. Struct., 32(4), 1054–1068.
Paul, C., Valero-Cuevas, F. J., and Lipson, H. (2006). “Design and control of tensegrity robots for locomotion.” IEEE Transactions on Robotics and Automation, 22(5), 944–957.
Rakowski, J. (1983). “Contribution on nonlinear solution of cable systems.” Bauingenieur, 58(2), 57–65 (in German).
Raoof, M., and Davies, T. J. (2004). “Influence of variations in the axial stiffness of steel cables on vertical deflections of cable trusses.” J. Constr. Steel Res., 60(3–5), 411–420.
Skelton, R. E., and Sultan, C. (1997). “Controllable tensegrity, a new class of smart structures.” Proc., Conf. on Mathematics and Control in Smart Structures—Smart Structures and Materials 1997, Vol. 3039, SPIE—International Society Optical Engineering, Bellingham, 166–177.
Sultan, C., Corless, M., and Skelton, E. R. (2001). “The prestressability problem of tensegrity structures: some analytical solutions.” Int. J. Solids Struct., 38(30–31), 5223–5252.
Sultan, C., and Skelton, R. (2003). “Deployment of tensegrity structures.” Int. J. Solids Struct., 40(18), 4637–4657.
Tibert, A. G., and Pellegrino, S. (2003). “Review of form-finding methods for tensegrity structures.” Int. J. Space Struct., 18(4), 209–223.
Topping, B. H. V., and Ivanyi, P. (2007). Computer aided design of cable membrane structures, Saxe-Coburg Publications, Kippen, Stirlingshire, Scotland.
Van De Wijdeven, J., and De Jager, B. (2005). “Shape change of tensegrity structures: Design and control.” Proc., American Control Conf., Vol. 4, IEEE, New York, 2522–2527.
Xu, X., and Luo, Y. (2010). “Force finding of tensegrity systems using simulated annealing algorithm.” J. Struct. Eng., 1027–1031.
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Published In
Journal of Structural Engineering
Volume 140 • Issue 9 • September 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Oct 30, 2012
Accepted: Sep 26, 2013
Published online: Apr 23, 2014
Published in print: Sep 1, 2014
Discussion open until: Sep 23, 2014
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