0
Research Papers

A Numerical Method for Simulating Nonlinear Mechanical Responses of Tensegrity Structures Under Large Deformations

[+] Author and Article Information
Li-Yuan Zhang

AML & CMM,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Yue Li

Institute of Nuclear and
New Energy Technology,
Tsinghua University,
Beijing 100084, China

Xi-Qiao Feng

e-mail: fengxq@tsinghua.edu.cn
AML & CMM,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Huajian Gao

School of Engineering,
Brown University,
Providence, RI 02912

1Corresponding author.

Manuscript received December 26, 2012; final manuscript received January 23, 2013; accepted manuscript posted March 7, 2013; published online August 21, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(6), 061018 (Aug 21, 2013) (10 pages) Paper No: JAM-12-1575; doi: 10.1115/1.4023977 History: Received December 26, 2012; Revised January 23, 2013; Accepted March 07, 2013

An efficient numerical method is developed to analyze the mechanical responses of tensegrity structures subjected to various actuations that lead to large and highly nonlinear (e.g., hardening or softening) deformations. The proposed method, whose accuracy and efficacy are demonstrated through a number of representative examples, holds promise for applications in design, analysis, and safety evaluations of large-scale tensegrity structures.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Juan, S. H., and Tur, J. M. M., 2008, “Tensegrity Frameworks: Static Analysis Review,” Mech. Mach. Theory, 43(7), pp. 859–881. [CrossRef]
Li, Y., Feng, X. Q., Cao, Y. P., and Gao, H. J., 2010, “Constructing Tensegrity Structures From One-Bar Elementary Cells,” Proc. R. Soc. London, Ser. A, 466(2113), pp. 45–61. [CrossRef]
Skelton, R. E., and de Oliveira, M. C., 2009, Tensegrity Systems, Springer, New York.
Sultan, C., 2009, “Tensegrity: 60 Years of Art, Science, and Engineering,” Advances in Applied Mechanics, H.Aref, and E.van der Giessen, eds., Elsevier, New York, pp. 69–145.
Feng, X. Q., Li, Y., Cao, Y. P., Yu, S. W., and Gu, Y. T., 2010, “Design Methods of Rhombic Tensegrity Structures,” Acta Mech. Sin., 26(4), pp. 559–565. [CrossRef]
Pellegrino, S., and Calladine, C. R., 1986, “Matrix Analysis of Statically and Kinematically Indeterminate Frameworks,” Int. J. Solids Struct., 22(4), pp. 409–428. [CrossRef]
Li, Y., Feng, X. Q., Cao, Y. P., and Gao, H. J., 2010, “A Monte Carlo Form-Finding Method for Large Scale Regular and Irregular Tensegrity Structures,” Int. J. Solids Struct., 47(14–15), pp. 1888–1898. [CrossRef]
Guest, S. D., 2011, “The Stiffness of Tensegrity Structures,” IMA J. Appl. Math., 76(1), pp. 57–66. [CrossRef]
Motro, R., 2003, Tensegrity: Structural Systems for the Future, Butterworth-Heinemann, London.
Oliveto, N. D., and Sivaselvan, M.V., 2011, “Dynamic Analysis of Tensegrity Structures Using a Complementarity Framework,” Comput. Struct., 89(23–24), pp. 2471–2483. [CrossRef]
Tran, H. C., and Lee, J., 2011, “Geometric and Material Nonlinear Analysis of Tensegrity Structures,” Acta Mech. Sin., 27(6), pp. 938–949. [CrossRef]
Schenk, M., Guest, S. D., and Herder, J. L., 2007, “Zero Stiffness Tensegrity Structures,” Int. J. Solids Struct., 44(20), pp. 6569–6583. [CrossRef]
Tran, H. C., and Lee, J., 2010, “Initial Self-Stress Design of Tensegrity Grid Structures,” Comput. Struct., 88(9–10), pp. 558–566. [CrossRef]
Zhang, L. Y., Li, Y., Cao, Y. P., Feng, X. Q., and Gao, H. J., 2012, “Self-Equilibrium and Super-Stability of Truncated Regular Polyhedral Tensegrity Structures: A Unified Analytical Solution,” Proc. R. Soc. London, Ser. A, 468(2147), pp. 3323–3347. [CrossRef]
Motro, R., Najari, S., and Jouanna, P., 1986, “Static and Dynamic Analysis of Tensegrity Systems,” Shell and Spatial Structures: Computational Aspects, G. D.Roeck, A. S.Quiroga, M. V.Laethem, and E.Backx, eds., Springer-Verlag, New York, pp. 270–279.
Hanaor, A., and Liao, M. K., 1991, “Double-Layer Tensegrity Grids: Static Load Response. Part I: Analytical Study,” ASCE J. Struct. Eng., 117(6), pp. 1660–1674. [CrossRef]
Hanaor, A., 1991, “Double-Layer Tensegrity Grids: Static Load Response—Part II: Experimental Study,” ASCE J. Struct. Eng., 117(6), pp. 1675–1684. [CrossRef]
Stamenović, D., Fredberg, J. J., Wang, N., Butler, J. P., and Ingber, D. E., 1996, “A Microstructural Approach to Cytoskeletal Mechanics Based on Tensegrity,” J. Theor. Biol., 181(2), pp. 125–136. [CrossRef] [PubMed]
Kebiche, K., Kazi-Aoual, M. N., and Motro, R., 1999, “Geometrical Non-Linear Analysis of Tensegrity Systems,” Eng. Struct., 21(9), pp. 864–876. [CrossRef]
Ben Kahla, N., and Kebiche, K., 2000, “Nonlinear Elastoplastic Analysis of Tensegrity Systems,” Eng. Struct., 22(11), pp. 1552–1566. [CrossRef]
Oppenheim, I. J., and Williams, W. O., 2000, “Geometric Effects in an Elastic Tensegrity Structure,” J. Elast., 59(1–3), pp. 51–65. [CrossRef]
Murakami, H., 2001, “Static and Dynamic Analyses of Tensegrity Structures—Part II: Quasi-Static Analysis,” Int. J. Solids Struct., 38(20), pp. 3615–3629. [CrossRef]
Crane, C. D., Duffy, J., and Correa, J. C., 2005, “Static Analysis of Tensegrity Structures,” ASME J. Mech. Des., 127(2), pp. 257–268. [CrossRef]
Nuhoglu, A., and Korkmaz, K. A., 2011, “A Practical Approach for Nonlinear Analysis of Tensegrity Systems,” Eng. Comput., 27(4), pp. 337–345. [CrossRef]
Moored, K. W., and Bart-Smith, H., 2009, “Investigation of Clustered Actuation in Tensegrity Structures,” Int. J. Solids Struct., 46(17), pp. 3272–3281. [CrossRef]
Ali, N. B. H., Rhode-Barbarigos, L., and Smith, I. F. C., 2011, “Analysis of Clustered Tensegrity Structures Using a Modified Dynamic Relaxation Algorithm,” Int. J. Solids Struct., 48(5), pp. 637–647. [CrossRef]
Estrada, G. G., Bungartz, H. J., and Mohrdieck, C., 2006, “Numerical Form-Finding of Tensegrity Structures,” Int. J. Solids Struct., 43(22–23), pp. 6855–6868. [CrossRef]
Eriksson, A., and Tibert, A. G., 2006, “Redundant and Force-Differentiated Systems in Engineering and Nature,” Comput. Meth. Appl. Mech. Eng., 195(41–43), pp. 5437–5453. [CrossRef]
Guest, S. D., 2006, “The Stiffness of Prestressed Frameworks: A Unifying Approach,” Int. J. Solids Struct., 43(3–4), pp. 842–854. [CrossRef]
Masic, M., Skelton, R. E., and Gill, P. E., 2005, “Algebraic Tensegrity Form-Finding,” Int. J. Solids Struct., 42(16–17), pp. 4833–4858. [CrossRef]
Tibert, A. G., and Pellegrino, S., 2003, “Review of Form-Finding Methods for Tensegrity Structures,” Int. J. Space Struct., 18(4), pp. 209–223. [CrossRef]
Zhang, L. Y., Li, Y., Cao, Y. P., and Feng, X. Q., 2013, “A Unified Solution for Self-Equilibrium and Super-Stability of Rhombic Truncated Regular Polyhedral Tensegrities,” Int. J. Solids Struct., 50(1), pp. 234–245. [CrossRef]
Kangwai, R. D., and Guest, S. D., 2000, “Symmetry-Adapted Equilibrium Matrices,” Int. J. Solids Struct., 37(11), pp. 1525–1548. [CrossRef]
Argyris, J. H., and Scharpf, D. W., 1972, “Large Deflection Analysis of Prestressed Networks,” ASCE J. Struct. Div., 98(ST3), pp. 633–654.
Bathe, K. J., Ramm, E., and Wilson, E. L., 1975, “Finite Element Formulations for Large Deformation Dynamic Analysis,” Int. J. Numer. Methods Eng., 9(2), pp. 353–386. [CrossRef]
Zhang, J. Y., and Ohsaki, M., 2006, “Adaptive Force Density Method for Form-Finding Problem of Tensegrity Structures,” Int. J. Solids Struct., 43(18–19), pp. 5658–5673. [CrossRef]
Nishimura, Y., and Murakami, H., 2001, “Initial Shape-Finding and Modal Analyses of Cyclic Frustum Tensegrity Modules,” Comput. Methods Appl. Mech. Eng., 190(43–44), pp. 5795–5818. [CrossRef]
Liu, B., and Huang, Y., 2008, “The Stable Finite Element Method for Minimization Problems,” J. Comput. Theor. Nanosci., 5(7), pp. 1251–1254. [CrossRef]
Bathe, K. J., and Cimento, A. P., 1980, “Some Practical Procedures for the Solution of Nonlinear Finite Element Equations,” Comput. Methods Appl. Mech. Eng., 22(1), pp. 59–85. [CrossRef]
Ingber, D. E., 2010, “From Cellular Mechanotransduction to Biologically Inspired Engineering,” Ann. Biomed. Eng., 38(3), pp. 1148–1161. [CrossRef] [PubMed]
Connelly, R., and Terrell, M., 1995, “Globally Rigid Symmetric Tensegrities,” Struct. Topol., 21, pp. 59–79.

Figures

Grahic Jump Location
Fig. 1

Flow chart of the structural stiffness matrix based numerical method established in the present paper

Grahic Jump Location
Fig. 2

Expandable octahedron tensegrity under tension

Grahic Jump Location
Fig. 3

Mechanical responses of pinned and looped expandable octahedron tensegrities under tension or compression along the x axis. The numerical results (symbols) obtained from the present method are compared with the analytical solutions (lines) of Stamenović et al. [18].

Grahic Jump Location
Fig. 4

A five-bar cylindrical tensegrity under internal actuation: (a) initial configuration and (b) final configuration

Grahic Jump Location
Fig. 5

Elements meeting at the node 1 in a v-bar cylindrical tensegrity

Grahic Jump Location
Fig. 6

A three-bar cylindrical tensegrity subjected to (a) axial tension and (b) torsion

Grahic Jump Location
Fig. 7

Mechanical responses of cylindrical tensegrities subjected to (a) and (b) axial tension/compression or (c) and (d) torsion. The numerical results (symbols) obtained from the present method are compared with the analytical solutions (lines) in Eqs. (43) and (44).

Grahic Jump Location
Fig. 8

Carbon nanotube-like tensegrity structures: (a) armchair (5,5) and (6,6) capped carbon nanotubes and (b) the corresponding tensegrities

Grahic Jump Location
Fig. 9

Mechanical responses of carbon nanotube-like tensegrity structures subjected to (a) axial tension and (b) torsion. The solid and dashed lines correspond to the (5,5) and (6,6) tensegrities, respectively.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In