Designing an Irregular Tensegrity as a Monumental Object
A novel and versatile numerical technique to solve a self-stress equilibrium state is adopted herein as a form-finding procedure for an irregular tensegrity structure. The numerical form-finding scheme of a tensegrity structure uses only the connectivity matrix and prototype tension coefficient vector as the initial guess solution. Any information on the symmetrical geometry or other predefined initial structural conditions is not necessary to get the solution in the form-finding process. An eight-node initial condition example is presented to demonstrate the efficiency and robustness of the proposed method in the form-finding of an irregular tensegrity structure. Based on the conception from the form-finding of an eight-node irregular tensegrity structure, a monumental object is designed by considering the real world situation such as self-weight, wind and earthquake loadings.
[1] Motro R. Tensegrity: Structural Systems for the Future. London and
Sterling: An imprint of Kogan Page Science; 2003.
[2] Geiger DH, Stefaniuk A, Chen D. The design and construction of two
cable domes for the Korean Olympics, shells, membranes and space
frames. Osaka: Proceedings of IASS Symposium; 1986, p. 265-272.
[3] Geiger DH. Design details of an elliptical cable dome and a large span
cable dome (210m) under construction in the United States. Bangalore:
Proceedings of the IASS ASCE International Symposium on Innovative
Applications of Shells and Spatial Forms; 1988.
[4] Furuya H. Concept of deployable tensegrity structures in space
application. International Journal of Space Structures 1992;7:143-151.
[5] Hanaor A. Double-layer tensegrity grids as deployable structures.
International Journal of Space Structures 1993;8:135-145.
[6] Ingber DE. Cellular tensegrity: defining new rules of biological design
that govern the cytoskeleton. Journal of Cell Science 1993;104:613-627.
[7] Ingber DE. Tensegrity: the architectural basis of cellular
mechanotransduction. Annual Review of Physiology 1997;59:575-599.
[8] Ingber DE. Tensegrity I. Cell structure and hierarchical systems biology.
Journal of Cell Science 2003;116:1157-1173.
[9] Paul C, Lipson H, Valero-Cuevas F. Design and control of tensegrity
robots for locomotion. IEEE Transaction on Robotics 2006;22:944-957.
[10] Juan SH, Tur JMM. Tensegrity frameworks: static analysis review.
Mechanism and Machine Theory 2008;43:859-881.
[11] Tibert AG, Pellegrino S. Review of form-finding methods for tensegrity
structures. International Journal of Space Structures 2003;18(4):209-223.
[12] Schek HJ. The force density method for form finding and computation of
general networks. Computer Methods in Applied Mechanics and
Engineering 1974;3:115-134.
[13] Estrada GG, Bungartz HJ, Morhdieck C. Numerical form-finding of
tensegrity structures. International Journal of Solids and Structures
2006;43:6855-6868.
[14] Southwell RV. Primary stress-determination in space frames.
Engineering 1920;CIX:165-8.
[15] Calladine CR. Pellegrino S. First-order infinitesimal mechanisms.
International Journal of Solids and Structures 1991;27(4):505-515.
[16] Calladine CR. Buckminster Fuller-s ÔÇÿtensegrity- structures and Clerk
Maxwell-s rules for the construction of stiff frames. International Journal
of Solids and Structures 1978;14(2):161-172.
[17] Pellegrino S. Analysis of prestressed mechanisms. International Journal
of Solids and Structures 1990;26:1329-1350.
[18] Pellegrino S. Structural Computations with the singular value
decomposition of the equilibrium matrix. International Journal of Solids
and Structures 1993;30(21):3025-3035.
[19] Graver J, Servatius B, Servatius H. Combinatorial rigidity. Graduate
Studies in Mathematics. Americal Mathematical Society 1993;2.
[20] Connelly R. Rigidity. In P.M. Gruber and J.M. Wills, editors, Handbook
of convex geometry, pages 223-271. Elsevier Science Publishers, 1993.
[21] Connelly R. Tensegrity structures: why are they stable? Rigidity Theory
and Applications. Kluwer Academic/Plenum Publishers; 1999.
[22] Meyer CD. Matrix Analysis and Applied Linear Algebra. SIAM; 2000.
[23] Tarnai T. Duality between plane trusses and grillages. International
Journal of Solids and Structures 1989;25(12):1395-1409.
[1] Motro R. Tensegrity: Structural Systems for the Future. London and
Sterling: An imprint of Kogan Page Science; 2003.
[2] Geiger DH, Stefaniuk A, Chen D. The design and construction of two
cable domes for the Korean Olympics, shells, membranes and space
frames. Osaka: Proceedings of IASS Symposium; 1986, p. 265-272.
[3] Geiger DH. Design details of an elliptical cable dome and a large span
cable dome (210m) under construction in the United States. Bangalore:
Proceedings of the IASS ASCE International Symposium on Innovative
Applications of Shells and Spatial Forms; 1988.
[4] Furuya H. Concept of deployable tensegrity structures in space
application. International Journal of Space Structures 1992;7:143-151.
[5] Hanaor A. Double-layer tensegrity grids as deployable structures.
International Journal of Space Structures 1993;8:135-145.
[6] Ingber DE. Cellular tensegrity: defining new rules of biological design
that govern the cytoskeleton. Journal of Cell Science 1993;104:613-627.
[7] Ingber DE. Tensegrity: the architectural basis of cellular
mechanotransduction. Annual Review of Physiology 1997;59:575-599.
[8] Ingber DE. Tensegrity I. Cell structure and hierarchical systems biology.
Journal of Cell Science 2003;116:1157-1173.
[9] Paul C, Lipson H, Valero-Cuevas F. Design and control of tensegrity
robots for locomotion. IEEE Transaction on Robotics 2006;22:944-957.
[10] Juan SH, Tur JMM. Tensegrity frameworks: static analysis review.
Mechanism and Machine Theory 2008;43:859-881.
[11] Tibert AG, Pellegrino S. Review of form-finding methods for tensegrity
structures. International Journal of Space Structures 2003;18(4):209-223.
[12] Schek HJ. The force density method for form finding and computation of
general networks. Computer Methods in Applied Mechanics and
Engineering 1974;3:115-134.
[13] Estrada GG, Bungartz HJ, Morhdieck C. Numerical form-finding of
tensegrity structures. International Journal of Solids and Structures
2006;43:6855-6868.
[14] Southwell RV. Primary stress-determination in space frames.
Engineering 1920;CIX:165-8.
[15] Calladine CR. Pellegrino S. First-order infinitesimal mechanisms.
International Journal of Solids and Structures 1991;27(4):505-515.
[16] Calladine CR. Buckminster Fuller-s ÔÇÿtensegrity- structures and Clerk
Maxwell-s rules for the construction of stiff frames. International Journal
of Solids and Structures 1978;14(2):161-172.
[17] Pellegrino S. Analysis of prestressed mechanisms. International Journal
of Solids and Structures 1990;26:1329-1350.
[18] Pellegrino S. Structural Computations with the singular value
decomposition of the equilibrium matrix. International Journal of Solids
and Structures 1993;30(21):3025-3035.
[19] Graver J, Servatius B, Servatius H. Combinatorial rigidity. Graduate
Studies in Mathematics. Americal Mathematical Society 1993;2.
[20] Connelly R. Rigidity. In P.M. Gruber and J.M. Wills, editors, Handbook
of convex geometry, pages 223-271. Elsevier Science Publishers, 1993.
[21] Connelly R. Tensegrity structures: why are they stable? Rigidity Theory
and Applications. Kluwer Academic/Plenum Publishers; 1999.
[22] Meyer CD. Matrix Analysis and Applied Linear Algebra. SIAM; 2000.
[23] Tarnai T. Duality between plane trusses and grillages. International
Journal of Solids and Structures 1989;25(12):1395-1409.
@article{"International Journal of Architectural, Civil and Construction Sciences:62249", author = "Buntara Sthenly Gan", title = "Designing an Irregular Tensegrity as a Monumental Object", abstract = "A novel and versatile numerical technique to solve a self-stress equilibrium state is adopted herein as a form-finding procedure for an irregular tensegrity structure. The numerical form-finding scheme of a tensegrity structure uses only the connectivity matrix and prototype tension coefficient vector as the initial guess solution. Any information on the symmetrical geometry or other predefined initial structural conditions is not necessary to get the solution in the form-finding process. An eight-node initial condition example is presented to demonstrate the efficiency and robustness of the proposed method in the form-finding of an irregular tensegrity structure. Based on the conception from the form-finding of an eight-node irregular tensegrity structure, a monumental object is designed by considering the real world situation such as self-weight, wind and earthquake loadings.
", keywords = "Tensegrity, Form-finding, Design, Irregular,
Self-stress, Force density method.", volume = "6", number = "10", pages = "862-7", }
