Snapping instability in prismatic tensegrities under torsion

doi:10.1007/s10483-016-2040-6

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (3): 275-288.doi: https://doi.org/10.1007/s10483-016-2040-6

• 论文 • 下一篇

Snapping instability in prismatic tensegrities under torsion

Liyuan ZHANG^1,2, Cheng ZHANG², Xiqiao FENG², Huajian GAO³

1. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
2. AML & CNMM, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;
3. School of Engineering, Brown University, Providence, Rhode Island 02912, U.S.A.

收稿日期:2015-06-25 修回日期:2015-08-30 出版日期:2016-03-01 发布日期:2016-03-01
通讯作者: Xiqiao FENG E-mail:fengxq@tsinghua.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11432008 and 11502016), the China Postdoctoral Science Foundation (No. 2015M570035), the Tsinghua Univer-sity Initiative Scientific Research Program (No. 20121087991), and the Fundamental Research Funds for the Central Universities of China (No. FRF-TP-15-029A1)

Snapping instability in prismatic tensegrities under torsion

Liyuan ZHANG^1,2, Cheng ZHANG², Xiqiao FENG², Huajian GAO³

1. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
2. AML & CNMM, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;
3. School of Engineering, Brown University, Providence, Rhode Island 02912, U.S.A.

Received:2015-06-25 Revised:2015-08-30 Online:2016-03-01 Published:2016-03-01
Contact: Xiqiao FENG E-mail:fengxq@tsinghua.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11432008 and 11502016), the China Postdoctoral Science Foundation (No. 2015M570035), the Tsinghua Univer-sity Initiative Scientific Research Program (No. 20121087991), and the Fundamental Research Funds for the Central Universities of China (No. FRF-TP-15-029A1)

摘要/Abstract

摘要：

Tensegrities are a class of lightweight and reticulated structures consisting of stressed strings and bars. It is shown that each prismatic tensegrity can have two self-equilibrated and stable states, leading to a snapping instability behavior under an applied torque. The predicted mechanism is experimentally validated, and can be used in areas such as advanced sensors and actuators, energy storage/adsorption equipments, and folding/unfolding devices.

关键词: tensegrity, structure mechanics, snapping instability, mechanical response

Abstract:

Key words: snapping instability, tensegrity, structure mechanics, mechanical response

中图分类号:

74G60

Liyuan ZHANG, Cheng ZHANG, Xiqiao FENG, Huajian GAO. Snapping instability in prismatic tensegrities under torsion[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(3): 275-288.

参考文献

[1] Skelton, R. E. and de Oliveira, M. C. Tensegrity Systems, Springer, Dordrecht (2009)
[2] Sultan, C. Tensegrity: 60 years of art, science, and engineering. Advances in Applied Mechanics, 43, 69-145 (2009)
[3] Rhode-Barbarigos, L., Ali, N. B. H., Motro, R., and Smith, I. F. C. Designing tensegrity modules for pedestrian bridges. Engineering Structures, 32, 1158-1167 (2010)
[4] Sunny, M. R., Sultan, C., and Kapania, R. K. Optimal energy harvesting from a membrane attached to a tensegrity structure. AIAA Journal, 52, 307-319 (2014)
[5] Fraternali, F., Senatore, L., and Daraio, C. Solitary waves on tensegrity lattices. Journal of the Mechanics and Physics of Solids, 60, 1137-1144 (2012)
[6] Stamenovi?, D. and Ingber, D. E. Tensegrity-guided self assembly: from molecules to living cells. Soft Matter, 5, 1137-1145 (2009)
[7] Veenendaal, D. and Block, P. An overview and comparison of structural form finding methods for general networks. International Journal of Solids and Structures, 49, 3741-3753 (2012)
[8] Zhang, L. Y., Li, Y., Cao, Y. P., Feng, X. Q., and Gao, H. J. Self-equilibrium and super-stability of truncated regular polyhedral tensegrity structures: a unified analytical solution. Proceedings of the Royal Society, A: Mathematical Physical and Engineering Sciences, 468, 3323-3347 (2012)
[9] Koohestani, K. and Guest, S. D. A new approach to the analytical and numerical form-finding of tensegrity structures. International Journal of Solids and Structures, 50, 2995-3007 (2013)
[10] Feng, X. Q., Li, Y., Cao, Y. P., Yu, S. W., and Gu, Y. T. Design methods of rhombic tensegrity structures. Acta Mechanica Sinica, 26, 559-565 (2010)
[11] Li, Y., Feng, X. Q., Cao, Y. P., and Gao, H. J. Constructing tensegrity structures from one- bar elementary cells. Proceedings of the Royal Society, A: Mathematical Physical and Engineering Sciences, 466, 45-61 (2010)
[12] Zhang, L. Y., Zhao, H. P., and Feng, X. Q. Constructing large-scale tensegrity structures with bar-bar connection using prismatic elementary cells. Archive of Applied Mechanics, 85, 383-394 (2015)
[13] Defossez, M. Shape memory effect in tensegrity structures. Mechanics Research Communications, 30, 311-316 (2003)
[14] Li, Y., Feng, X. Q., Cao, Y. P., and Gao, H. J. A Monte Carlo form-finding method for large scale regular and irregular tensegrity structures. International Journal of Solids and Structures, 47, 1888-1898 (2010)
[15] Xu, X. and Luo, Y. Z. Multistable tensegrity structures. Journal of Structural Engineering-ASCE, 137, 117-123 (2011)
[16] Micheletti, A. Bistable regimes in an elastic tensegrity system. Proceedings of the Royal Society, A: Mathematical Physical and Engineering Sciences, 469, 20130052 (2013)
[17] Zhang, L. Y., Li, Y., Cao, Y. P., and Feng, X. Q. Stiffness matrix based form-finding method of tensegrity structures. Engineering Structures, 58, 36-48 (2014)
[18] Guest, S. D. The stiffness of tensegrity structures. IMA Journal of Applied Mathematics, 76, 57-66 (2011)
[19] Fraternali, F., Carpentieri, G., and Amendola, A. On the mechanical modeling of the extreme softening/stiffening response of axially loaded tensegrity prisms. Journal of the Mechanics and Physics of Solids, 74, 136-157 (2015)
[20] Moored, K. W. and Bart-Smith, H. Investigation of clustered actuation in tensegrity structures. International Journal of Solids and Structures, 46, 3272-3281 (2009)
[21] Ali, N. B. H., Rhode-Barbarigos, L., and Smith, I. F. C. Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm. International Journal of Solids and Structures, 48, 637-647 (2011)
[22] Zhang, L., Lu, M. K., Zhang, H. W., and Yan, B. Geometrically non-linear elasto-plastic analysis of clustered tensegrity based on the co-rotational approach. International Journal of Mechanical Sciences, 93, 154-165 (2015)
[23] Zhang, L., Gao, Q., Liu, Y., and Zhang, H.W. An efficient finite element formulation for non-linear analysis of clustered tensegrity. Engineering Computations, 33 (2016) DOI 10.1108/EC-08-2014- 0168
[24] Kebiche, K., Kazi-Aoual, M. N., and Motro, R. Geometrical non-linear analysis of tensegrity systems. Engineering Structures, 21, 864-876 (1999)
[25] Tran, H. C. and Lee, J. Geometric and material non-linear analysis of tensegrity structures. Acta Mechanica Sinica, 27, 938-949 (2011)
[26] Zhang, L., Gao, Q., and Zhang, H. W. An efficient algorithm for mechanical analysis of bimodular truss and tensegrity structures. International Journal of Mechanical Sciences, 70, 57-68 (2013)
[27] Zhang, L. Y., Li, Y., Cao, Y. P., Feng, X. Q., and Gao, H. J. A numerical method for simulating non-linear mechanical responses of tensegrity structures under large deformations. Journal of Applied Mechanics-Transactions of the ASME, 80, 061018 (2013)
[28] Stamenovi?, D., Fredberg, J. J., Wang, N., Butler, J. P., and Ingber, D. E. A microstructural approach to cytoskeletal mechanics based on tensegrity. Journal of Theoretical Biology, 181, 125- 136 (1996)
[29] Oppenheim, I. J. and Williams, W. O. Geometric effects in an elastic tensegrity structure. Journal of Elasticity, 59, 51-65 (2000)
[30] Crane, C. D., Duffy, J., and Correa, J. C. Static analysis of tensegrity structures. Journal of Mechanical Design, 127, 257-268 (2005)
[31] Plaut, R. H. and Virgin, L. N. Vibration and snap-through of bent elastica strips subjected to end rotations. Journal of Applied Mechanics-Transactions of the ASME, 76, 041011 (2009)
[32] Fargette, A., Neukirch, S., and Antkowiak, A. Elastocapillary snapping: capillarity induces snap- through instabilities in small elastic beams. Physical Review Letters, 112, 137802 (2014)
[33] Mao, G. Y., Li, T. F., Zou, Z. N., Qu, S. X., and Shi, M. X. Prestretch effect on snap-through instability of short-length tubular elastomeric balloons under inflation. International Journal of Solids and Structures, 51, 2109-2115 (2014)
[34] Shekastehband, B., Abedi, K., Dianat, N., and Chenaghlou, M. R. Experimental and numerical studies on the collapse behavior of tensegrity systems considering cable rupture and strut collapse with snap-through. International Journal of Non-Linear Mechanics, 47, 751-768 (2012)
[35] Li, T. F., Keplinger, C., Baumgartner, R., Bauer, S., Yang, W., and Suo, Z. G. Giant voltage- induced deformation in dielectric elastomers near the verge of snap-through instability. Journal of the Mechanics and Physics of Solids, 61, 611-628 (2013)
[36] Dai, F. H., Li, H., and Du, S. Y. Cured shape and snap-through of bistable twisting hybrid[0/90/metal]T laminates. Composites Science and Technology, 86, 76-81 (2013)
[37] Avramov, K. V. and Mikhlin, Y. V. Snap-through truss as an absorber of forced oscillations. Journal of Sound and Vibration, 290, 705-722 (2006)
[38] Connelly, R. and Terrell, M. Globally rigid symmetric tensegrities. Structural Topology, 21, 59-79 (1995)

Snapping instability in prismatic tensegrities under torsion

Snapping instability in prismatic tensegrities under torsion

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