A novel method for determining the feasible integral self-stress states for tensegrity structures

References

[1] Fu F. Structural behavior and design methods of Tensegrity domes. J Construct Steel Res. 2005;61(1):23–5.10.1016/j.jcsr.2004.06.004Search in Google Scholar

[2] Gómez-Jáuregui V, Arias R, Otero C, Manchado C. Novel Technique for Obtaining Double-Layer Tensegrity Grids. Int J Space Structures. 2012;27(2-3):155–66.10.1260/0266-3511.27.2-3.155Search in Google Scholar

[3] Skelton RE, Fraternali F, Carpentieri G, Micheletti A. Minimum mass design of tensegrity bridges with parametric architecture and multiscale complexity. Mech Res Commun. 2014;58:124–32.10.1016/j.mechrescom.2013.10.017Search in Google Scholar

[4] Liapi K, Kim J. A Parametric Approach to the Design of Vaulted Tensegrity Networks. Int J Archit Comput. 2004;2(2):245–62.10.1260/1478077041518737Search in Google Scholar

[5] Cimmino MC, Miranda R, Sicignano E, Ferreira AJ, Skelton RE, Fraternali F. Composite solar façades and wind generators with tensegrity architecture. Compos, Part B Eng. 2017;115:275–81.10.1016/j.compositesb.2016.09.077Search in Google Scholar

[6] Zolesi VS, Ganga PL, Scolamiero L, Micheletti A, Podio-Guidugli P, Tibert G, et al. On an innovative deployment concept for large space structures, In: 42nd Int. Conf. Environ. Syst., San Diego; 2012:1–14.10.2514/6.2012-3601Search in Google Scholar

[7] Wendling S, Oddou C, Isabey D. Stiffening response of a cellular tensegrity model. J Theor Biol. 1999 Feb;196(3):309–25.10.1006/jtbi.1998.0841Search in Google Scholar

[8] Stamenović D, Fredberg JJ, Wang N, Butler JP, Ingber DE. A microstructural approach to cytoskeletal mechanics based on tensegrity. J Theor Biol. 1996 Jul;181(2):125–36.10.1006/jtbi.1996.0120Search in Google Scholar

[9] Djouadi S, Motro R, Pons JC, Crosnier B. Active Control of Tensegrity Systems. J Aerosp Eng. 1998;11(2):37–44.10.1061/(ASCE)0893-1321(1998)11:2(37)Search in Google Scholar

[10] Liu K, Wu J, Paulino GH, Qi HJ. Programmable Deployment of Tensegrity Structures by Stimulus-Responsive Polymers. Sci Rep. 2017 Jun;7(1):3511.10.1038/s41598-017-03412-6Search in Google Scholar PubMed PubMed Central

[11] Yang S, Sultan C. Modeling of tensegrity-membrane systems. Int J Solids Struct. 2015;82:125–43.10.1016/j.ijsolstr.2015.09.012Search in Google Scholar

[12] Nouri Rahmat Abadi B, Mehdi Shekarforoush SM, Mahzoon M, Farid M. Kinematic, Stiffness, and Dynamic Analyses of a Compliant Tensegrity Mechanism. J Mech Robot. 2014;6(4):041001.10.1115/1.4027699Search in Google Scholar

[13] Paul C, Valero-Cuevas FJ, Lipson H. Design and control of tensegrity robots for locomotion. IEEE Trans Robot. 2006;22(5):944–57.10.1109/TRO.2006.878980Search in Google Scholar

[14] Sabelhaus A, Friesen J. SunSpiral V., Ji H., Hylton P., Madaan Y., et al., Mechanism Design and Simulation of the Ultra Spine, A Tensegrity Robot, In: Proceedings of ASME 2015 Int. Des. Eng. Tech. Conf. Comput. Inf. Eng. Conf. Boston; 2015:1–11.10.1115/DETC2015-47583Search in Google Scholar

[15] Chen LH, Kim K, Tang E, Li K, House R, Zhu EL, et al. Soft Spherical Tensegrity Robot Design Using Rod-Centered Actuation and Control. J Mech Robot. 2017;9(2):025001.10.1115/1.4036014Search in Google Scholar

[16] Salahshoor H, Pal RK, Rimoli JJ. Material symmetry phase transitions in three-dimensional tensegrity metamaterials. J Mech Phys Solids. 2018;119:382–99.10.1016/j.jmps.2018.07.011Search in Google Scholar

[17] Rimoli JJ, Pal RK. Mechanical response of 3-dimensional tensegrity lattices. Compos, Part B Eng. 2017;115:30–42.10.1016/j.compositesb.2016.10.046Search in Google Scholar

[18] Amendola A, Krushynska A, Daraio C, Pugno NM, Fraternali F. Tuning frequency band gaps of tensegrity metamaterials with local and global prestress. Int J Solids Struct. 2018;155:47–56.10.1016/j.ijsolstr.2018.07.002Search in Google Scholar

[19] Fraddosio A, Pavone G, Piccioni MD. Minimal mass and self-stress analysis for innovative V-Expander tensegrity cells. Compos Struct. 2019;209:754–74.10.1016/j.compstruct.2018.10.108Search in Google Scholar

[20] Fraddosio A, Marzano S, Pavone G, Piccioni MD. Morphology and self-stress design of V-Expander tensegrity cells. Compos, Part B Eng. 2017;115:102–16.10.1016/j.compositesb.2016.10.028Search in Google Scholar

[21] Ferkiss V, Fuller RB, Applewhite EJ. Synergetics: Explorations in the Geometry of Thinking, Macmillan Pub Co. Technol Cult. 1976;17(1):104.10.2307/3103256Search in Google Scholar

[22] Ashwear N, Eriksson A. Natural frequencies describe the pre-stress in tensegrity structures. Comput Struc. 2014;138:162–71.10.1016/j.compstruc.2014.01.020Search in Google Scholar

[23] Oppenheim IJ, Williams WO. Geometric effects in an elastic tensegrity structure. J Elast. 2000;59(1/3):51–65.10.1007/978-94-010-0728-3_6Search in Google Scholar

[24] Tran HC, Lee J. Geometric and material nonlinear analysis of tensegrity structures. Acta Mech. Sin. Xuebao. 2011;27(6):938–49.Search in Google Scholar

[25] Zhang LY, Li Y, Cao YP, Feng XQ. Stiffness matrix based form-finding method of tensegrity structures. Eng Struct. 2014;58:36–48.10.1016/j.engstruct.2013.10.014Search in Google Scholar

[26] Gilewski W, Kłosowska J, Obara P. Form finding of tensegrity structures via Singular Value Decomposition of compatibility matrix, In: Proceedings of Adv. Mech. Theor. Comput. Interdiscip. Issues - 3rd Polish Congr. Mech. PCM 2015 21st Int. Conf. Comput. Methods Mech. C. Poland; 2015:191–96.10.1201/b20057-43Search in Google Scholar

[27] Koohestani K. Automated element grouping and self-stress identification of tensegrities. Eng Comput. 2015;32(6):1643–60.10.1108/EC-08-2014-0165Search in Google Scholar

[28] 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. 2015;141(10):04014240.10.1061/(ASCE)ST.1943-541X.0001228Search in Google Scholar

[29] Tran HC, Lee J. Form-finding of tensegrity structures with multiple states of self-stress. Acta Mech. 2011;222(1-2):131–47.10.1007/s00707-011-0524-9Search in Google Scholar

[30] Sánchez R, Maurin B, Kazi-Aoual MN, Motro R. Selfstress States Identification and Localization in Modular Tensegrity Grids. Int J Space Structures. 2007;22(4):215–24.10.1260/026635107783133780Search in Google Scholar

[31] Quirant J, Kazi-Aoual MN, Motro R. Designing tensegrity systems: the case of a double layer grid. Eng Struct. 2003;25(9):1121–30.10.1016/S0141-0296(03)00021-XSearch in Google Scholar

[32] Tran HC, Lee J. Initial self-stress design of tensegrity grid structures. Comput Struc. 2010;88(9-10):558–66.10.1016/j.compstruc.2010.01.011Search in Google Scholar

[33] Tibert AG, Pellegrino S. Review of Form-Finding Methods for Tensegrity Structures. Int J Space Structures. 2011;26(3):241–55.10.1260/0266-3511.26.3.241Search in Google Scholar

[34] Zhang JY, Ohsaki M. Adaptive force density method for form-finding problem of tensegrity structures. Int J Solids Struct. 2006;43(18-19):5658–73.10.1016/j.ijsolstr.2005.10.011Search in Google Scholar

[35] Lee S, Lee J. A novel method for topology design of tensegrity structures. Compos Struct. 2016;152:11–9.10.1016/j.compstruct.2016.05.009Search in Google Scholar

[36] Schek HJ. The force density method for form finding and computation of general networks. Comput Methods Appl Mech Eng. 1974;3(1):115–34.10.1016/0045-7825(74)90045-0Search in Google Scholar

[37] Xu X, Wang Y, Luo Y. An improved multi-objective topology optimization approach for tensegrity structures. Adv Struct Eng. 2018;21(1):59–70.10.1177/1369433217706780Search in Google Scholar

[38] Ehara S, Kanno Y. Topology design of tensegrity structures via mixed integer programming. Int J Solids Struct. 2010;47(5):571–9.10.1016/j.ijsolstr.2009.10.020Search in Google Scholar

[39] Zhang JY, Taguchi T. Form-Finding and Stability Analysis of Tensegrity Structures using Nonlinear Programming and Fictitious Material Properties. Int J Solids Struct. 2015;69-70:1–10.10.1016/j.ijsolstr.2015.06.020Search in Google Scholar

[40] So AM, Ye Y. A semidefinite programming approach to tensegrity theory and realizability of graphs, In: Proceedings of seventeenth Annu. ACMSIAM Symp. Discret. algorithm SODA. Miami; 2006:766–75. https://doi.org/10.1145/1109557.1109641.10.1145/1109557.1109641Search in Google Scholar

[41] Bel Hadj Ali N, Rhode-Barbarigos L, Smith IF. Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm. Int J Solids Struct. 2011;48(5):637–47.10.1016/j.ijsolstr.2010.10.029Search in Google Scholar

[42] Fagerström G. Dynamic Relaxation of Tensegrity Structures, In: Proceedings of Between Man Mach. Proc. 14th Int. Conf. Comput. Archit. Des. Res. Asia, (22-25 April 2009, Yunlin, Taiwan) Taiwan; 2009:553–62.Search in Google Scholar

[43] Pagitz M, Mirats Tur JM. Finite element based form-finding algorithm for tensegrity structures. Int J Solids Struct. 2009;46(17):3235–40.10.1016/j.ijsolstr.2009.04.018Search in Google Scholar

[44] Klinka K, Arcaro V, Gasparini D. Form finding of tensegrity structures using finite elements and mathematical programming. J Mech Mater Struct. 2012;7(10):899–907.10.2140/jomms.2012.7.899Search in Google Scholar

[45] Chen Y, Feng J, Wu Y. Prestress stability of pin-jointed assemblies using ant colony systems. Mech Res Commun. 2012;41:30–6.10.1016/j.mechrescom.2012.02.004Search in Google Scholar

[46] Xu X, Luo Y. Form-finding of nonregular tensegrities using a genetic algorithm. Mech Res Commun. 2010;37(1):85–91.10.1016/j.mechrescom.2009.09.003Search in Google Scholar

[47] Feng X. The optimal initial self-stress design for tensegrity grid structures. Comput Struc. 2017;193:21–30.10.1016/j.compstruc.2017.07.029Search in Google Scholar

[48] Linkwitz K, Schek HJ. Density Methods Applied to Form Finding of Initially Stressed Systems. Novel Approaches in Civil Engineering; 1971. pp. 341–50.Search in Google Scholar

[49] Connelly R., Tensegrity structures. Why are they stable?, Rigidity theory Appl., 1998, 47–54.10.1007/0-306-47089-6_3Search in Google Scholar

[50] Xu X, Wang Y, Luo Y. Finding member connectivities and nodal positions of tensegrity structures based on force density method and mixed integer nonlinear programming. Eng Struct. 2018;166:240–50.10.1016/j.engstruct.2018.03.063Search in Google Scholar

[51] Cai J, Wang X, Deng X, Feng J. Form-finding method for multi-mode tensegrity structures using extended force density method by grouping elements. Compos Struct. 2018;187:1–9.10.1016/j.compstruct.2017.12.010Search in Google Scholar

[52] Cai J, Feng J. Form-finding of tensegrity structures using an optimization method. Eng Struct. 2015;104:126–32.10.1016/j.engstruct.2015.09.028Search in Google Scholar

[53] Lee S, Lee J, Kang JW. Results of generalized equilibrium path from form-finding of tensegrity structure. Int J Steel Struct. 2017;17(3):1225–31.10.1007/s13296-017-9028-3Search in Google Scholar

[54] Gan BS, Zhang J, Nguyen DK, Nouchi E. Node-based genetic form-finding of irregular tensegrity structures. Comput Struc. 2015;159:61–73.10.1016/j.compstruc.2015.07.003Search in Google Scholar

[55] Yuan XF, Ma S, Jiang SH. Form-finding of tensegrity structures based on the Levenberg–Marquardt method. Comput Struc. 2017;192:171–80.10.1016/j.compstruc.2017.07.005Search in Google Scholar

[56] Koohestani K. On the analytical form-finding of tensegrities. Compos Struct. 2017;166:114–9.10.1016/j.compstruct.2017.01.059Search in Google Scholar

[57] Estrada GG, Bungartz HJ, Mohrdieck C. Numerical form-finding of tensegrity structures. Int J Solids Struct. 2006;43(22-23):6855–68.10.1016/j.ijsolstr.2006.02.012Search in Google Scholar

[58] Calladine CR. Buckminster Fuller’s “Tensegrity” structures and Clerk Maxwell’s rules for the construction of stiff frames. Int J Solids Struct. 1978;14(2):161–72.10.1016/0020-7683(78)90052-5Search in Google Scholar

[59] Pellegrino S, Calladine CR. Matrix analysis of statically and kinematically indeterminate frameworks. Int J Solids Struct. 1986;22(4):409–28.10.1016/0020-7683(86)90014-4Search in Google Scholar

[60] Calladine CR, Pellegrino S. First-order infinitesimal mechanisms. Int J Solids Struct. 1991;27(4):505–15.10.1016/0020-7683(91)90137-5Search in Google Scholar

[61] Zhou J, Chen W, Zhao B, Qiu Z, Dong S. Distributed indeterminacy evaluation of cable-strut structures: formulations and applications. J. Zhejiang Univ. A. 2015;16(9):737–48.Search in Google Scholar

[62] Yuan X, Chen L, Dong S. Prestress design of cable domes with new forms. Int J Solids Struct. 2007;44(9):2773–82.10.1016/j.ijsolstr.2006.08.026Search in Google Scholar

[63] Zhou J, Chen W, Zhao B, Dong S. A feasible symmetric state of initial force design for cable-strut structures. Arch Appl Mech. 2017;87(8):1385–97.10.1007/s00419-017-1257-6Search in Google Scholar

[64] Zhang JY, Ohsaki M. Tensegrity Structures. Springer; 2015. https://doi.org/10.1007/978-4-431-54813-3.10.1007/978-4-431-54813-3Search in Google Scholar

[65] Chen Y, Sun Q, Feng J. Improved Form-Finding of Tensegrity Structures Using Blocks of Symmetry-Adapted Force Density Matrix. J Struct Eng. 2018;144(10):04018174.10.1061/(ASCE)ST.1943-541X.0002172Search in Google Scholar

[66] Zhang LY, Zhu SX, Li SX, Xu GK. Analytical form-finding of tensegrities using determinant of force-density matrix. Compos Struct. 2018;189:87–98.10.1016/j.compstruct.2018.01.054Search in Google Scholar

[67] Tran HC, Lee J. Advanced form-finding of tensegrity structures. Comput Struc. 2010;88(3-4):237–46.10.1016/j.compstruc.2009.10.006Search in Google Scholar

[68] Zhang JY, Ohsaki M. Stability conditions for tensegrity structures. Int J Solids Struct. 2007;44(11-12):3875–86.10.1016/j.ijsolstr.2006.10.027Search in Google Scholar

[69] Lee S, Gan BS, Lee J. A fully automatic group selection for form-finding process of truncated tetrahedral tensegrity structures via a double-loop genetic algorithm. Compos, Part B Eng. 2016;106:308–15.10.1016/j.compositesb.2016.09.018Search in Google Scholar

[70] Lee S, Lee J. Advanced automatic grouping for form-finding of tensegrity structures. Struct Multidiscipl Optim. 2017;55(3):959–68.10.1007/s00158-016-1549-4Search in Google Scholar

[71] Kaveh A. Computational Structural Analysis and Finite Element Methods. Springer; 2014. https://doi.org/10.1007/978-3-319-02964-1.10.1007/978-3-319-02964-1Search in Google Scholar

[72] Lee S, Lee J, Kang J. A Genetic Algorithm Based Form-finding of Tensegrity Structures with Multiple Self-stress States. J Asian Arch Build Eng. 2017;16:155-162.10.3130/jaabe.16.155Search in Google Scholar