It is almost a decade since an elegant three-strut tensegrity with a delicate internal membrane graced the MFF2 exhibition at the lobby of the Faculty of Architecture and Urban Planning of the University of São Paulo in 2004.
It is worth revisiting on its 10th anniversary: I like how the stretched nylon makes visible to the naked eye the least energy surface that exists between the tensegrity's vertices. If the atom has a tensegrity structure, such a membrane may correlate with energy potentials and quantum probabilistic states.
The sculpture “Monument to the Futile Form II” (“Monumento à Forma Fútil II”, MFF2) is composed of a textile membrane, anchored to a tensegrity simplex module. A stressed membrane was added to fill the irregular space generated by the disposition of the bars of the tensegrity module. The membrane insinuates through the bars without touching them and adds another strong, primary color to the sculpture.The authors point out, they used panyhose for the membrane.
The geometrical configurations of the tensegrity module and of the membrane composing the sculpture were determined both empirically and numerically, with the aid of adequate structural analysis programs (although the geometry of the tensegrity module was already well known, since the original studies of Snelson and Füller).
The simulation of the assembling process of the tensegrity module was simulated with the aid of the PEFSYS finite element program by Delmo Deifeld, a PhD researcher in Structural Engineering of the Polytechnic School – University of São Paulo. Adjusting the length of only one cable, depicted in red in the figure, the whole structure can be erected. Several steps of the assembling sequence are show in the figure.
The tensegrity module was built from PVC hydraulic pipes, as well as steel cables, caps and fasteners, according to dimensions numerically determined by the PEFSYS program. Feasibility of stretching a membrane in-between the bars of the tensegrity module, without touching them, was initially guessed through sketches, then physically tested on the real module, with a piece of white Elanca fabric. It was concluded that the idea was feasible, but a more flexible and isotropic material should be used.
The final form of the membrane was then determined both in a 1:4 scale mock-up, using pantyhose fabric, and numerically, by means of nonlinear static analysis, using the Ansys finite element code.
In the 1:4 mock-up, some cables were substituted by rigid bars in order to enable easy manipulation. Once a satisfactory form was obtained for the membrane, size measurements made on the 1:4 pantyhose pattern were transferred to a 1:1 pattern, made of red Suplex fabric.
It's also nice to see pantyhose used in a tensegrity--a first, I think.
REFERENCES
(Deifeld, 2002) Deifeld, T.E.C.; Pauletti, R.M.O. “Um Breve Estudo Sobre as Estruturas Tensegrity”. I Simpósio Nacional sobre Tensoestruturas, 2002, São Paulo.
(Emmerich, 1999) Emmerich D. G., “Structures tendues et autotendantes”. Monographies de geometrie constructive. La Villette: Editions de l’Ecole d’Architecture de Paris, 1999.
(Fuller, 1975) Fuller, R. B. Synergetics, Explorations in the Geometry of Thinking. Macmillan Publishing Co. Inc., Vol. 1, 1975.
(Ingber, 1993) Ingber D. E., “Cellular tensegrity: defining new rules of biological design that govern the cytoskeleton”. J. Cell Sci. vol 104, p. 613-627, 1993.
(Pauletti, 2002) Pauletti, R.M.O. “Análise de Estruturas Retesadas (Tensoestruturas),
empregando Programas Generalistas”. I Simpósio Nacional sobre Tensoestruturas, 2002, São Paulo.
(Pugh, 1976) Pugh, A. An Introduction To Tensegrity. Berkeley, U.S.A, Ed. University of California Press, 1976.
(Snelson, 1996) Snelson, K. “Snelson on the tensegrity invention”. International Journal of Space Structures. vol.11, p.43–48, 1996.
(Titotto, 2004) Titotto, S.L.M.C.; Pauletti, R.M.O. “Spatiality in Membrane Structures”. IASS 2004 Symposium – Shell and Spatial Structures: from Models to Realization, 2004, Montpellier.
(Titotto, 2003) Titotto, S.L.M.C.; Pauletti, R.M.O.; Brasil, R.M.L.R.F. “Tensile Structures: Form and Function Relationships”. International Conference of Textile Composites and Inflatable Structures, 2003, Barcelona.
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