Advanced Steel Construction

Vol. 11, No. 4, pp. 507-516 (2015)



JinYu Lu1,2,*, Na Li3 and GanPing Shu1,2

1Key Lab of Concrete and Prestressed Concrete Structures ofMinistry of Education, Nanjing 210096, China

2School of Civil Engineering, Southeast University, Nanjing 210096, China

3College of Electronic and Mechanical Engineering, Nanjing Forestry University, Nanjing 210037, China




View Article   Export Citation: Plain Text | RIS | Endnote


This paper proposed a novel form-finding method for irregular tensegrity structures base on matrix iteration. On the basis of two different forms of structural equilibrium equations, the estimated elemental self-stresses and nodal coordinates were constructed via the singular value decomposition of equilibrium matrix and eigenvalue decomposition of force density matrix, respectively. The configuration of tensegrity that satisfies the specified coordinates was determined through the iterative computation of self-stresses and nodal coordinates, and the constraint condition was introduced in the construction of the estimated nodal coordinates simultaneously. The detailed algorithm procedure was listed and the convergent criterion was also defined. In the end, several illustrated examples were given to prove the validity of the algorithm. Numerical examples and physical models showed that the proposed form-finding method was correct and efficient. The form-finding algorithm could be applied to find tensegrity structures that satisfied the given geometrical forms, and the creation of novel irregular tensegrity, as long as the topological relation and several known coordinate of nodes were given



Irregular tensegrity, Form-finding, Equilibrium matrix, Force density matrix, Numerical method


[1] Motro, R., “Tensegrity Structural Systems for the Future”, UK. Herms Science Publishing Limited, Kogan Page Limited, 2003.

[2] Skelton, R.E., Oliveira, M.C., “Tensegrity Systems”, Springer Dordrecht Heidelberg London New York, 2009.

[3] Juan, S.H., Tur, J.M.M., “Tensegrity frameworks: static analysis review”, Mechanism and Machine Theory, 2008, Vol. 43, No. 7, pp.859-881.

[4] Tibert, G. and Pellegrino, S., “Review of Form-finding Methods for Tensegrity Structures”, International Journal of Space Structures, 2003, Vol. 18, No. 4, pp. 209-223.

[5] Zhang, L., Maurin, B. and Motro, R., “Form-finding of Nonregular Tensegrity Systems”, Journal of Structural Engineering, ASCE, 2006, Vol. 132, No. 9, pp. 1435-1440.

[6] Zhang, J.Y., Ohsaki, M. and Kanno, Y., “A Direct Approach to the Design of Geometry and Forces of Tensegrity Systems”, International Journal of Solids and Structures, 2006, Vol. 43, pp. 2260-2278.

[7] Estrada, G.G., Bungartz, H.J. and Mohrdieck, C., “Numerical form Finding of Tensegrity Structure”, International Journal of Solids and Structures, 2006, Vol. 43, pp. 6855-6868.

[8] Tran, H.C. and Lee, J., “Advanced form Finding of Tensegrity”, Computers and Structures, 2009, Vol. 88, pp.236-247.

[9] Zhang, L.Y., Li, Y., Cao, Y.P. and Feng, X.Q., “Stiffness matrix based form-finding method of tensegrity structures”, Engineering Structures, 2014, Vol. 58, pp.36-48.

[10] Paul, C., Lipson, H. and Cuevas, F.V., “Evolutionary Form-forming of Tensegrity Structures”, Proceedings of the 2005 Genetic and Evolutionary Computation, Washington, USA, 2005, pp. 3-10.

[11] Rieffel, J., Cuevas, F.V. and Lipson, H., “Automated Discovery and Optimization of Large Irregular Tensegrity Structures”, Computers and Structures, 2009, Vol. 87, pp. 368-379.

[12] Xu, X. and Luo, Y., “Form-finding of nonregular tensegrities using a genetic algorithm”, Mechanics Research Communications, 2010, Vol. 37, pp. 85-91.

[13] Koohestani, K., “Form-finding of tensegrity structures via genetic algorithm”, International Journal of Solids and Structures, 2012, Vol. 49, No. 5, pp. 739-747.

[14] Xu, X. and Luo, Y., “Force Finding of Tensegrity System using Simulated Annealing Algorithm”, Journal of Structural Engineering, ASCE, 2010, Vol. 136, No. 8, pp. 1027-1031.

[15] Li, Y., Feng, X.Q., Cao, Y.P. and Gao, H., “A Monte Carlo Form-finding Method for Large Scale Regular and Irregular Tensegrity Structures”, International Journal of Solids and Structures, 2010, Vol. 47, pp. 1888-1898.

[16] Koohestani, K., “A computational framework for the form-finding and design of tensegrity structures”, Mechanics Research Communications, 2013, Vol. 54, pp.41-49.

[17] Lu, J.Y., Luo, Y.Z. and Li, N., “An Incremental Algorithm to Trace the Non-linear Equilibrium Paths of Pin-jointed Structures using the Singular Value Decomposition of the Equilibrium Matrix”, Proc. IMechE Part G: J. Aerospace Engineering, 2009, Vol. 223, pp. 881-890.

[18] Lu, J.Y., Li, N. and Luo, Y.Z., “Kinematic Analysis of Planar Deployable Structures with Angulated Beams based on Equilibrium Matrix”, Advances in Structural Engineering, 2011, Vol. 14, No. 6, pp. 1005-1015.

[19] Pellegrino, S. and Calliadine, C.R., “Matrix Analysis of Statically and Kinematically Indeterminate Frameworks”, International Journal of Solids and Structures, 1986, Vol. 22, No. 4, pp. 409-428.

[20] Pellegrino, S., “Analysis of Pre-stressed Mechanisms”, International Journal of Solids and Structures, 1990, Vol. 26, No. 12, pp. 1329-1350.