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The application of the immanent tensegrity properties to control the behavior of double-layered grids
DOI:
https://doi.org/10.24425/ace.2023.144164Abstract
The paper focuses on the static behavior of double-layered tensegrity grids. Due to the specific characteristics, like the self-stress states and infinitesimal mechanisms, tensegrities can be used as deployable structures. For such structures, the possibility of the control of the behavior is very important. The main purpose of the work is to prove that the control of tensegrity structures with mechanisms is possible. The stiffness of such structures is found to depend not only on the geometry and material properties, but also on the initial prestress level and external load. In the case, when mechanisms do not exist, structures are insensitive to the initial prestress. It is possible to control the occurrence of mechanisms by changing the support conditions of the structure. Grids built with modified Simplex modules are considered. Two-stage analysis is performed. Firstly, the presence of the characteristic tensegrity features is examined and then, on that basis, the structures are classified into one of two classes. Next, the influence of the level of initial prestress on the behavior of structures under static load is analyzed. To evaluate this behavior, a geometrically non-linear model is used.References
[1] L. Rhode-Barbarigos, N. Bel Hadj Ali, R. Motro, and I.F.C. Smith, “Tensegrity modules for pedestrian bridges”, in Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2009, Valencia, 2009.
[2] L. Rhode-Barbarigos, N. Bel Hadj Ali, R. Motro, and I.F.C. Smith, “Designing tensegrity modules for pedestrian bridges”, Engineering Structures, vol. 32, no. 4, pp. 1158-1167, 2010, DOI: 10.1016/j.engstruct.2009.12.042.
[3] L. Rhode-Barbarigos, N. Bel Hadj Ali, R. Motro, and I.F.C. Smith, “Design aspects of a deployable tensegrity-hollow-rope footbridge”, International Journal of Space Structures, vol. 27, no. 2-3, pp. 81-95, 2012, DOI: 10.1260/0266-3511.27.2-3.81.
[4] F. Jamin, J. Averseng, J. Quirant, and S. Vigan-Amouri, “La mer accessible à tous: Les systèmes de tenségrité déployables au service de l’autonomie”, in Proceedings of the Conference Handicap 2016, Paris, France. 2016.
[5] J. Averseng, F. Jamin, and J. Quirant, “Système de tenségrité déployable et modulaire pour le développement de l’accessibilité”, in Proceedings of the Conference RUGC 2017, Nantes, France. 2017.
[6] A. Micheletti, “Modular Tensegrity Structures: The “Tor Vergata” Footbridge”, in Models and Methods in Civil Engineering, M. Frémond, F. Maceri, Eds. Springer, 2012, pp. 375-384.
[7] W. Gilewski and A. Al Sabouni-Zawadzka, “On possible applications of smart structures controlled by self-stress”, Archives of Civil and Mechanical Engineering, vol. 15, no. 2, pp. 469-478, 2014, DOI: 10.1016/j.acme.2014.08.006.
[8] K.-J. Bathe, Finite Element Procedures in Engineering Analysis. Prentice-Hall, 1982.
[9] W. Gilewski and A. Kasprzak, “Introduction to mechanics of tensegrity modules”, in Theoretical Fundamentals of Building Engineering, vol. 1, Mechanics of Materials and Structures. Warsaw: OWPW, 2012, pp. 83-94.
[10] O.C. Zienkiewicz, R.L. Taylor, and J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals. Oxford: Butterworth-Heinemann, 2013. [Online]. Available: https://www.sciencedirect.com/science/article/pii/B9781856176330000198.
[11] P. Obara and J. Tomasik, “Parametric analysis of tensegrity plate-like structures: Part 1 - Qualitative analysis”, Applied Sciences, vol. 10, no. 20, 2020, DOI: 10.3390/app10207042.
[12] P. Obara and J. Tomasik, “Parametric analysis of tensegrity plate-like structures: Part 2 - Quantitative analysis”, Applied Sciences, vol. 11, no. 2, 2021, DOI: 10.3390/app11020602.
[13] P. Obara and J. Tomasik, “Active control of stiffness of tensegrity plate-like structures built with simplex modules”, Materials, vol. 14, no. 24, 2021, DOI: 10.3390/ma14247888.
[14] C.R. Calladine, “Buckminster Fuller’s “Tensegrity” structures and Clerk Maxwell’s rules for the construction of stiff frames”, International Journal of Solids and Structures, vol. 14, no. 2, pp. 161-172, 1978, DOI: 10.1016/0020-7683(78)90052-5.
[15] C.R. Calladine, “Modal stiffnesses of a pretensioned cable net”, International Journal of Solids and Structures, vol. 18, no. 10, pp. 829-846, 1982, DOI: 10.1016/0020-7683(82)90068-3.
[16] S. Pellegrino and C.R. Calladine, “Matrix analysis of statically and kinematically indeterminate frameworks”, International Journal of Solids and Structures, vol. 22, no. 4, pp. 409-428, 1986, DOI: 10.1016/0020-7683(86)90014-4.
[17] S. Pellegrino, “Analysis of prestressed mechanisms”, International Journal of Solids and Structures, vol. 26, no. 12, pp. 1329-1350, 1990, DOI: 10.1016/0020-7683(90)90082-7.
[18] C.R. Calladine and S. Pellegrino, “First-order infinitesimal mechanisms”, International Journal of Solids and Structures, vol. 27, no. 4, pp. 505-515, 1991, DOI: 10.1016/0020-7683(91)90137-5.
[19] W. Gilewski, J. Kłosowska, and P. Obara, “Form finding of tensegrity structures via Singular Value Decomposition of compatibility matrix”, in Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues. CRC Press, 2016, pp. 191-195.
[20] P. Obara, J. Kłosowska, and W. Gilewski, “Truth and myths about 2D tensegrity trusses”, Applied Sciences, vol. 9, no. 1, art. no. 179, 2019, DOI: 10.3390/app9010179.
[21] S. Pellegrino, “Structural computations with the singular value decomposition of the equilibrium matrix”, International Journal of Solids and Structures, vol. 30, no. 21, pp. 3025-3035, 1993, DOI: 10.1016/0020-7683(93)90210-X.
[22] H. Rahami, A. Kaveh, M. Ardalan Asl, and S.R. Mirghaderi, “Analysis of near-regular structures with node irregularity using SVD of equilibrium matrix”, International Journal of Civil Engineering, vol. 11, no. 4, pp. 226-241, 2013.
[23] W. Gilewski, J. Kłosowska, and P. Obara, “Verification of Tensegrity Properties of Kono Structure and Blur Building”, Procedia Engineering", vol. 153, pp. 173-179, 2016, DOI: 10.1016/j.proeng.2016.08.099.
[24] W. Gilewski, J. Kłosowska, and P. Obara, “The influence of self-stress on the behavior of tensegrity-like real structure”, MATEC Web of Conferences, vol. 117, 2017, DOI: 10.1051/matecconf/201711700079.
[25] W. Gilewski, J. Kłosowska, and P. Obara, “Parametric analysis of some tensegrity structures”, MATEC Web Conferences, vol. 262, art. no. 10003, 2019, DOI: 10.1051/matecconf/201926210003.
[26] P. Obara, “Analysis of orthotropic tensegrity plate strips using a continuum two-dimensional model”, MATEC Web of Conferences, vol. 262, art. no. 10010, 2019, DOI: 10.1051/matecconf/201926210010.
[27] P. Obara, “Application of linear six-parameter shell theory to the analysis of orthotropic tensegrity platelike structures”, Journal of Theoretical and Applied Mechanics, vol. 57, no. 1, pp. 167-178, 2019, DOI: 10.15632/jtam-pl.57.1.167.
[28] P. Obara, Dynamic and dynamic stability of tensegrity structures. Kielce: Wydawnictwo Politechniki Swietokrzyskiej, 2019.
[29] J. Tomasik and P. Obara, “Impact of the self-stress state on the static properties of double-layered tensegrity grids”, in Modern Trends in Research on Steel, Aluminium and Composite Structures: Proceedings of the XIV International Conference On Metal Structures (ICMS2021), Poznań, Poland, 16-18 Jun. 2021. Routledge, 2021, pp. 127-133, DOI: 10.1201/9781003132134.
[30] A. Al Sabouni-Zawadzka and A. Zawadzki, “Simulation of a Deployable Tensegrity Column Based on the Finite Element Modeling and Multibody Dynamics Simulations”, Archives of Civil Engineering, vol. 66, no. 4, pp. 543-560, 2020, DOI: 10.24425/ace.2020.135236.
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