A theoretical framework based on convex analysis is formulated and developed to study tensegrity structures under steady-state loads. Many classical results for ideal tensegrities are rationally deduced from subdifferentiable models in a novel mechanical perspective. Novel energy-based criteria for rigidity and pre-stressability are provided, allowing to formulate numerical algorithms for computations.
Accepted:
Published online:
Franco Maceri 1; Michele Marino 1; Giuseppe Vairo 1
@article{CRMECA_2011__339_11_683_0, author = {Franco Maceri and Michele Marino and Giuseppe Vairo}, title = {Convex analysis and ideal tensegrities}, journal = {Comptes Rendus. M\'ecanique}, pages = {683--691}, publisher = {Elsevier}, volume = {339}, number = {11}, year = {2011}, doi = {10.1016/j.crme.2011.07.009}, language = {en}, }
Franco Maceri; Michele Marino; Giuseppe Vairo. Convex analysis and ideal tensegrities. Comptes Rendus. Mécanique, Volume 339 (2011) no. 11, pp. 683-691. doi : 10.1016/j.crme.2011.07.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.07.009/
[1] R.B. Fuller, Tensile-integrity structures, U.S. Patent No. 3 063 521, November 13, 1962.
[2] Deployable Structures (S. Pellegrino, ed.), CISM Courses and Lectures, vol. 412, Springer, Wien, New York, 2001
[3] Tensegrity frameworks, Transactions of the American Mathematical Society, Volume 265 (1981), pp. 419-446
[4] Rigidity and energy, Inventiones Mathematichae, Volume 66 (1982), pp. 11-33
[5] Second-order rigidity and prestress stability for tensegrity frameworks, Journal on Discrete Mathematics, Volume 9 (1996), pp. 453-491
[6] Mathematics and tensegrity, American Scientists, Volume 86 (1998), pp. 142-151
[7] Buckminster Fullerʼs “tensegrity” structures and Clerk Maxwellʼs rules for the construction of stiff frames, International Journal of Solids and Structures, Volume 14 (1978), pp. 161-172
[8] Matrix analysis of statically and kinematically indeterminate frameworks, International Journal of Solids and Structures, Volume 22 (1986), pp. 409-428
[9] Analysis of prestressed mechanisms, International Journal of Solids and Structures, Volume 26 (1990), pp. 1329-1350
[10] First-order infinitesimal mechanisms, International Journal of Solids and Structures, Volume 27 (1991), pp. 505-515
[11] The prestressability problem of tensegrity structures: some analytical solutions, International Journal of Solids and Structures, Volume 38 (2001), pp. 5223-5252
[12] Tensegrity: Structural Systems for the Future, Kogan Page Science, 2003
[13] W.O. Williams, A primer on the mechanics of tensegrity structures, preprint 2007.
[14] Tensegrity frameworks: Static analysis review, Mechanism and Machine Theory, Volume 43 (2008), pp. 859-881
[15] Tensegrity Systems, Springer, New York, 2009
[16] Tenségrité – Analyse et projets, Lavoisier, Paris, 2001
[17] Tensegrity-based mechanosensing from macro to micro, Progress in Biophysics and Molecular Biology, Volume 97 (2008), pp. 163-179
[18] A closed-form refined model of the cablesʼ nonlinear response in cable-stayed structures, Mechanics of Advanced Materials and Structures, Volume 16 (2009), pp. 456-466
[19] Non-Smooth Thermomechanics, Springer-Verlag, Berlin, 2001
[20] Convex analysis and unilateral static problems, Archive of Applied Mechanics, Volume 45 (1976), pp. 55-68
[21] J.J. Moreau, Fonctionnelles convexes. Editions of Department of Civil Engineering, University of Rome Tor Vergata, ISBN 9788862960014, Roma, 2003.
[22] Convex Analysis and Nonlinear Optimization, Canadian Mathematical Society, Springer, New York, 2006
Cited by Sources:
Comments - Policy