Abstract
A great attraction of prestressed cable-strut structures is that the initial prestresses can guarantee the structural stability. However, increasing the prestress level of these structures does not necessarily improve the structural stiffness. Here, we investigate the influence of prestress on the stiffness of prestressed cable-strut structures, whereas potential buckling of compression struts is taken into consideration. Symmetry representation of internal mechanism modes and group theory is introduced for parallel and efficient computations on the lower frequencies, which are associated with the internal mechanisms. Nonlinear static equilibrium and improved group-theoretic analysis on these cable-strut structures are iteratively performed. Numerical results show that there is a nonlinear correlation between the prestress level and stiffness. Importantly, continuous increase in prestress for a structure with compression struts can decrease the lower frequencies, and thus weaken the structural stiffness. The first natural frequency tends to be zero when the prestress is close to the critical buckling force of certain compression struts. The presented method can be used as a reasonable choice for force-finding and health-monitoring of prestressed cable-strut structures.
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References
Ali, N., Smith, I.: Dynamic behavior and vibration control of a tensegrity structure. Int. J. Solids Struct. 47, 1285–1296 (2010)
Zhang, L.Y., Li, Y., Cao, Y.P., Feng, X.Q.: Stiffness matrix based form-finding method of tensegrity structures. Eng. Struct. 58, 36–48 (2014)
Guest, S.: The stiffness of prestressed frameworks: a unifying approach. Int. J. Solids Struct. 43, 842–854 (2006)
Skelton, R.E., de Oliveira, M.C.: Tensegrity Systems. Springer, New York (2009)
Koohestani, K., Guest, S.D.: A new approach to the analytical and numerical form-finding of tensegrity structures. Int. J. Solids Struct. 50, 2995–3007 (2013)
Koohestani, K.: A computational framework for the form-finding and design of tensegrity structures. Mech. Res. Commun. 54, 41–49 (2013)
Lee, S., Woo, B., Lee, J.: Self-stress design of tensegrity grid structures using genetic algorithm. Int. J. Mech. Sci. 79, 38–46 (2014)
Zhang, P., Kawaguchi, K., Feng, J.: Prismatic tensegrity structures with additional cables: integral symmetric states of self-stress and cable-controlled reconfiguration procedure. Int. J. Solids Struct. 51, 4294–4306 (2014)
Furuya, H.: Concept of deployable tensegrity structures in space application. Int. J. Space Struct. 7, 143–151 (1992)
Ashwear, N., Tamadapu, G., Eriksson, A.: Optimization of modular tensegrity structures for high stiffness and frequency separation requirements. Int. J. Solids Struct. 80, 297–309 (2016)
Masic, M., Skelton, R.E.: Selection of prestress for optimal dynamic/control performance of tensegrity structures. Int. J. Solids Struct. 43, 2110–2125 (2006)
Moussa, B., Ben, K.N., Pons, J.C.: Evolution of natural frequencies in tensegrity systems: a case study. Int. J. Space Struct. 16, 57–73 (2001)
Wu, M.G., Sasaki, M.: Structural behaviors of an arch stiffened by cables. Eng. Struct. 29, 529–541 (2007)
Ali, N.B.H., Rhode-Barbarigos, L., Albi, A.A.P., Smith, I.F.C.: Design optimization and dynamic analysis of a tensegrity-based footbridge. Eng. Struct. 32, 3650–3659 (2010)
Greschik, G.: Truss beam with tendon diagonals: mechanics and designs. AIAA J. 46, 557–567 (2008)
Hanaor, A.: Double-layer tensegrity grids: static load response. Part II: experimental study. J. Struct. Eng. 117, 1675–1684 (1991)
Ashwear, N., Eriksson, A.: Natural frequencies describe the pre-stress in tensegrity structures. Comput. Struct. 138, 162–171 (2014)
Murtha-Smith, E.: Alternate path analysis of space trusses for progressive collapse. J. Struct. Eng. 114, 1978–1999 (1988)
Kaveh, A., Nikbakht, M.: Buckling load of symmetric plane frames using canonical forms and group theory. Acta Mech. 185, 89–128 (2006)
Kaveh, A.: Optimal Analysis of Structures by Concepts of Symmetry and Regularity. Springer, New York (2013)
Kaveh, A., Rahami, H., Nikbakht, M.: Vibration analysis of regular structures by graph products: cable networks. Comput. Struct. 88, 588–601 (2010)
Kaveh, A., Nikbakht, M.: Analysis of space truss towers using combined symmetry groups and product graphs. Acta Mech. 218, 133–160 (2011)
Chen, Y., Sareh, P., Feng, J., Sun, Q.: A computational method for automated detection of engineering structures with cyclic symmetries. Comput. Struct. 191, 153–164 (2017)
Chen, Y., Fan, L., Feng, J.: Kinematic of symmetric deployable scissor-hinge structures with integral mechanism mode. Comput. Struct. 191, 140–152 (2017)
Chen, Y., Feng, J.: Generalized eigenvalue analysis of symmetric prestressed structures using group theory. J. Comput. Civ. Eng. ASCE 26, 488–497 (2012)
Beatini, V., Royer-Carfagni, G.: Cable-stiffened foldable elastica for movable structures. Eng. Struct. 56, 126–136 (2013)
Shekastehband, B., Abedi, K.: Collapse behavior of tensegrity systems due to cable rupture. Int. J. Struct. Stabil. Dyn. 13, 496–506 (2013)
Vassilopoulou, I., Gantes, C.J.: Vibration modes and natural frequencies of saddle form cable nets. Comput. Struct. 88, 105–119 (2010)
Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method for Solid and Structural Mechanics. Butterworth-Heinemann, Oxford (2005)
Sultan, C.: Stiffness formulations and necessary and sufficient conditions for exponential stability of prestressable structures. Int. J. Solids Struct. 50, 2180–2195 (2013)
Chen, Y., Feng, J.: Group-theoretic method for efficient buckling analysis of prestressed space structures. Acta Mech. 226, 957–973 (2015)
Kaveh, A., Nikbakht, M.: Stability analysis of hyper symmetric skeletal structures using group theory. Acta Mech. 200, 177–197 (2008)
Kaveh, A., Nikbakht, M.: Improved group-theoretical method for eigenvalue problems of special symmetric structures, using graph theory. Adv. Eng. Softw. 41, 22–31 (2010)
Calladine, C.R., Pellegrino, S.: First-order infinitesimal mechanisms. Int. J. Solids Struct. 27, 505–515 (1991)
Chen, Y., Feng, J., Liu, Y.: A group-theoretic approach to the mobility and kinematic of symmetric over-constrained structures. Mech. Mach. Theory 105, 91–107 (2016)
Guest, S.D., Fowler, P.W.: A symmetry-extended mobility rule. Mech. Mach. Theory 40, 1002–1014 (2005)
Pellegrino, S., Calladine, C.R.: Matrix analysis of statically and kinematically indeterminate frameworks. Int. J. Solids Struct. 22, 409–428 (1986)
Connelly, R., Fowler, P.W., Guest, S.D., Schulze, B., Whiteley, W.J.: When is a symmetric pin-jointed framework isostatic? Int. J. Solids Struct. 46, 762–773 (2009)
Chen, Y., Feng, J., Ma, R., Zhang, Y.: Efficient symmetry method for calculating integral prestress modes of statically indeterminate cable-strut structures. J. Struct. Eng. ASCE 141, 04014240 (2015)
Chen, Y., Feng, J., Zhang, Y.T.: A necessary condition for stability of kinematically indeterminate pin-jointed structures with symmetry. Mech. Res. Commun. 60, 64–73 (2014)
Chen, Y., Feng, J.: Improved symmetry method for the mobility of regular structures using graph products. J. Struct. Eng. ASCE 142, 04016051 (2016)
Zhang, J.Y., Guest, S.D., Ohsaki, M.: Symmetric prismatic tensegrity structures. Part I: configuration and stability. Int. J. Solids Struct. 46, 1–14 (2009)
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Chen, Y., Sun, Q. & Feng, J. Stiffness degradation of prestressed cable-strut structures observed from variations of lower frequencies. Acta Mech 229, 3319–3332 (2018). https://doi.org/10.1007/s00707-018-2167-6
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DOI: https://doi.org/10.1007/s00707-018-2167-6