An efficient self-stress design of tensegrity shell structures. (English) Zbl 1521.74148
Summary: Distribution and level of self-stress has a profound impact on the structural behavior of tensegrity systems. The problems associated with self-stress implementation preclude designing tensegrity structures for civil engineering application. To achieve the feasible self-stress state of a tensegrity shell structure, an efficient procedure based on solving an optimization problem in conjunction with multi constraint equations on group subdivisions is presented in the current study. Several tensegrity shell configurations are utilized to demonstrate the capability of the proposed procedure. The method provides superior performance compared with the other conventional methods of obtaining desired self-stress distributions. For a given shell configuration, group division is of paramount importance with respect to the regularity and uniformity of self-stress distributions.
MSC:
| 74K99 | Thin bodies, structures |
| 74K25 | Shells |
| 74S99 | Numerical and other methods in solid mechanics |
| 74P99 | Optimization problems in solid mechanics |
Keywords:
group division; singular value decomposition; force density method; optimization problem; multi constraint equationReferences:
| [1] | Tang, Y.; Yin, J., Design of cut unit geometry in hierarchical kirigami-based auxetic metamaterials for high stretchability and compressibility, Extrem Mech Lett, 12, 77-85 (2017) · doi:10.1016/j.eml.2016.07.005 |
| [2] | Bertoldi, K.; Vitelli, V.; Christensen, J.; Van Hecke, M., Flexible mechanical metamaterials, Nat Rev Mater, 2, 17066 (2017) · doi:10.1038/natrevmats.2017.66 |
| [3] | Skelton, RE; De Oliveira, MC, Tensegrity systems (2009), New York: Springer, New York · Zbl 1175.74052 · doi:10.1007/978-0-387-74242-7 |
| [4] | Wang BB (2004) Free-standing tension structures: from tensegrity systems to cable-strut systems. Spon Press |
| [5] | Liew, JYR; Lee, BH; Wang, BB, Innovative use of star prism (SP) and di-pyramid (DP) for spatial structures, J Constr Steel Res, 59, 335-357 (2003) · doi:10.1016/S0143-974X(02)00037-8 |
| [6] | Pellegrino, S., A class of tensegrity domes, Int J Sp Struct, 7, 127-142 (1992) · doi:10.1177/026635119200700206 |
| [7] | Kmet, S.; Mojdis, M., Time-dependent analysis of cable domes using a modified dynamic relaxation method and creep theory, Comput Struct, 125, 11-22 (2013) · doi:10.1016/j.compstruc.2013.04.019 |
| [8] | Fraternali, F.; Carpentieri, G.; Amendola, A., On the mechanical modeling of the extreme softening/stiffening response of axially loaded tensegrity prisms, J Mech Phys Solids, 74, 136-157 (2015) · Zbl 1349.74056 · doi:10.1016/j.jmps.2014.10.010 |
| [9] | Zhang, J.; Ohsaki, M., Form-finding of self-stressed structures by an extended force density method, J Int Assoc Shell Spat Struct, 46, 159-166 (2005) |
| [10] | Connelly, R.; Terrell, M., Globally rigid symmetric tensegrities tensegrites symetriques globalement rigides, Struct Topol, 21, 59-78 (1995) · Zbl 0841.52013 |
| [11] | Vassart, N.; Motro, R., Multiparametered formfinding method: application to tensegrity systems, Int J Sp Struct, 14, 147-154 (1999) · doi:10.1260/0266351991494768 |
| [12] | Sultan C, CorlessM, Skelton RE (1999) Reduced prestressability conditions for tensegrity structures. In: Proceedings of 40th ASME structure dynamic material conference, pp 2300-2308 |
| [13] | Quirant J, Kazi-Aoual MN, Laporte R (2003) Tensegrity systems: the application of linear programmation in search of compatible selfstress states. J Int Assoc Shell Spatial Struct 44:33-50. http://cat.inist.fr/?aModele=afficheN&cpsidt=14991376 |
| [14] | Quirant, J., Selfstressed systems comprising elements with unilateral rigidity: selfstress states, mechanisms and tension setting, Int J Sp Struct, 22, 203-214 (2007) · doi:10.1260/026635107783133807 |
| [15] | Pellegrino, S., Structural computations with the singular value decomposition of the equilibrium matrix, Int J Solids Struct, 30, 3025-3035 (1993) · Zbl 0783.73080 · doi:10.1016/0020-7683(93)90210-X |
| [16] | Yuan, X.; Dong, S., Nonlinear analysis and optimum design of cable domes, Eng Struct, 24, 965-977 (2002) · doi:10.1016/S0141-0296(02)00017-2 |
| [17] | Yuan, X.; Dong, S., Integral feasible prestress of cable domes, Comput Struct, 81, 2111-2119 (2003) · doi:10.1016/S0045-7949(03)00254-2 |
| [18] | Yuan, X.; Chen, L.; Dong, S., Prestress design of cable domes with new forms, Int J Solids Struct, 44, 2773-2782 (2007) · Zbl 1121.74050 · doi:10.1016/j.ijsolstr.2006.08.026 |
| [19] | Quirant, J.; Kazi-Aoual, MNN; Motro, R., Designing tensegrity systems: the case of a double layer grid, Eng Struct, 25, 1121-1130 (2003) · doi:10.1016/S0141-0296(03)00021-X |
| [20] | Tran, HC; Lee, J., Advanced form-finding of tensegrity structures, Comput Struct, 88, 237-246 (2010) · doi:10.1016/j.compstruc.2009.10.006 |
| [21] | Tran, HC; Park, HS; Lee, J., A unique feasible mode of prestress design for cable domes, Finite Elem Anal Des, 59, 44-54 (2012) · doi:10.1016/j.finel.2012.05.004 |
| [22] | Hanaor, A., Prestressed pin-jointed structures-Flexibility analysis and prestress design, Comput Struct, 28, 757-769 (1988) · Zbl 0632.73081 · doi:10.1016/0045-7949(88)90416-6 |
| [23] | Pellegrino, S.; Calladine, CR, Matrix analysis of statically and kinematically indeterminate frameworks, Int J Solids Struct, 22, 409-428 (1986) · doi:10.1016/0020-7683(86)90014-4 |
| [24] | Shekastehband, B.; Abedi, K.; Dianat, N., Experimental and numerical study on the self-stress design of tensegrity systems, Meccanica, 48, 2367-2389 (2013) · Zbl 1293.74303 · doi:10.1007/s11012-013-9754-3 |
| [25] | Chen, Y.; Feng, J.; Ma, R.; Zhang, Y., Efficient symmetry method for calculating integral prestress modes of statically indeterminate cable-strut structures, J Struct Eng, 141, 1-11 (2015) · doi:10.1061/(ASCE)ST.1943-541X.0001228 |
| [26] | Lee, S.; Lee, J., Optimum self-stress design of cable-strut structures using frequency constraints, Int J Mech Sci, 89, 462-469 (2014) · doi:10.1016/j.ijmecsci.2014.10.016 |
| [27] | Ma, Q.; Ohsaki, M.; Chen, Z.; Yan, X., Step-by-step unbalanced force iteration method for cable-strut structure with irregular shape, Eng Struct, 177, 331-344 (2018) · doi:10.1016/j.engstruct.2018.09.081 |
| [28] | Motro, R., Tensegrity: structural systems for the future, Kogan Page Sci (2003) · doi:10.1016/B978-1-903996-37-9.X5028-8 |
| [29] | S.H. Juan, J.M. Mirats Tur, Tensegrity frameworks: Static analysis review, Mech. Mach. Theory. 43 (2008) 859-881. doi:10.1016/j.mechmachtheory.2007.06.010 · Zbl 1342.70013 |
| [30] | N. Ploskas, N. Samaras, Linear Programming Using MATLAB, 1st ed., Springer International Publishing, 2017. doi:10.1007/978-3-319-65919-0 · Zbl 1386.90003 |
| [31] | Shekastehband, B.; Abedi, K.; Dianat, N.; Chenaghlou, MR, Experimental and numerical studies on the collapse behavior of tensegrity systems considering cable rupture and strut collapse with snap-through, Int J Non Linear Mech, 47, 751-768 (2012) · doi:10.1016/j.ijnonlinmec.2012.04.004 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
