Topology Optimization of Tensegrity Structures Considering Buckling Constraints
Publication: Journal of Structural Engineering
Volume 144, Issue 10
Abstract
This paper proposes a general approach for topology optimization of tensegrity structures. The optimization problem is formulated in the framework of a mixed-integer linear programming. Compared with previous approaches, more practical issues such as member overlapping, strut buckling, displacement limits, and multiple load cases are considered in the proposed approach. The member connectivities, internal forces, and cross-sectional areas are used as independent variables. The total weight of the final structure is used as the objective function. The maximum allowed number of struts connected to each node, the maximum allowed number of cross-sectional sizes for each type of members, and the minimum number of nodes used in the final structure can be actively controlled. A novel constraint formulation is proposed to avoid the member overlapping problem. Numerical examples are carried out to verify the proposed approach. The tensegrity structures found by the proposed approach are much more suitable for practical applications, and the approach can be used as a general generator for new types of tensegrity structures for specific application scenarios.
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Acknowledgments
This work was supported by National Key R&D Program of China (2017YFC0806100), Natural Science Foundation of Zhejiang Province (Grant No. LR17E080001), and National Natural Science Foundation of China (Grant No. 51378458).
References
Ali, N. B. H., L. Rhode-Barbarigos, and I. F. C. Smith. 2011. “Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm.” Int. J. Solids Struct. 48 (5): 637–647. https://doi.org/10.1016/j.ijsolstr.2010.10.029.
Barnes, M. R. 1999. “Form finding and analysis of tension structures by dynamic relaxation.” Int. J. Space Struct. 14 (2): 89–104. https://doi.org/10.1260/0266351991494722.
Calladine, C. R., and S. Pellegrino. 1991. “First-order infinitesimal mechanisms.” Int. J. Solids Struct. 27 (4): 505–515. https://doi.org/10.1016/0020-7683(91)90137-5.
Ehara, S., and Y. Kanno. 2010. “Topology design of tensegrity structures via mixed integer programming.” Int. J. Solids Struct. 47 (5): 571–579. https://doi.org/10.1016/j.ijsolstr.2009.10.020.
Estrada, G. G., H. J. Bungartz, and C. Mohrdieck. 2006. “Numerical form-finding of tensegrity structures.” Int. J. Solids Struct. 43 (22): 6855–6868. https://doi.org/10.1016/j.ijsolstr.2006.02.012.
Gurobi Optimization, Inc. 2014. “Gurobi Optimizer reference manual.” Accessed May 25, 2015. http://www.gurobi.com/documentation/8.0/refman/index.html.
Kanno, Y. 2012. “Topology optimization of tensegrity structures under self-weight loads.” J. Oper. Res. Soc. Jpn. 55 (2): 125–145.
Kanno, Y. 2013a. “Exploring new tensegrity structures via mixed integer programming.” Struct. Multidiscip. Optim. 48 (1): 95–114. https://doi.org/10.1007/s00158-012-0881-6.
Kanno, Y. 2013b. “Topology optimization of tensegrity structures under compliance constraint: A mixed integer linear programming approach.” Optim. Eng. 14 (1): 61–96. https://doi.org/10.1007/s11081-011-9172-0.
Lofberg, J. 2004. “YALMIP: A toolbox for modeling and optimization in MATLAB.” In Vol. 41 of Proc., IEEE Int. Symp. on Computer Aided Control Systems Design, 287–292. Piscataway, NJ: IEEE.
Lu, J. Y., N. Li, and G. P. Shu. 2015. “Form-finding analysis of irregular tensegrity structures by matrix iteration.” Adv. Steel Constr. 11: 507–516.
Masic, M., R. E. Skelton, and P. E. Gill. 2005. “Algebraic tensegrity form-finding.” Int. J. Solids Struct. 42 (16): 4833–4858. https://doi.org/10.1016/j.ijsolstr.2005.01.014.
MathWorks. 2014. “MATLAB help document.” Accessed April 20, 2015. https://ww2.mathworks.cn/help/.
Mela, K. 2014. “Resolving issues with member buckling in truss topology optimization using a mixed variable approach.” Struct. Multidiscip. Optim. 50 (6): 1037–1049. https://doi.org/10.1007/s00158-014-1095-x.
Ministry of Housing and Urban-Rural Development of the People’s Republic of China. 2003. Code for design of steel structures. GB50017-2003. Beijing: China Planning Press.
Ministry of Housing and Urban-Rural Development of the People’s Republic of China. 2010. Technical specification for space frame structures. JGJ7-2010. Beijing: China Architecture and Building Press.
Ministry of Housing and Urban-Rural Development of the People’s Republic of China. 2012. Chinese load code for the design of building structures. GB50009-2012. Beijing: China Architecture and Building Press.
Motro, R. 2003. Tensegrity: Structural systems for the future. New York: Elsevier.
Pagitz, M., and J. M. Tur. 2009. “Finite element based form-finding algorithm for tensegrity structures.” Int. J. Solids Struct. 46 (17): 3235–3240. https://doi.org/10.1016/j.ijsolstr.2009.04.018.
Pellegrino, S., and C. R. Calladine. 1986. “Matrix analysis of statically and kinematically indeterminate frameworks.” Int. J. Solids Struct. 22 (4): 409–428. https://doi.org/10.1016/0020-7683(86)90014-4.
Rasmussen, M. H., and M. Stolpe. 2008. “Global optimization of discrete truss topology design problems using a parallel cut-and-branch method.” Comput. Struct. 86 (13): 1527–1538. https://doi.org/10.1016/j.compstruc.2007.05.019.
Skelton, R. E., and M. C. De Oliveira. 2009. Vol. 1 of Tensegrity systems. Berlin: Springer.
Tran, H. C., and J. Lee. 2010. “Initial self-stress design of tensegrity grid structures.” Comput. Struct. 88 (9): 558–566. https://doi.org/10.1016/j.compstruc.2010.01.011.
Vassart, N., and R. Motro. 1999. “Multiparametered formfinding method: Application to tensegrity systems.” Int. J. Space Struct. 14 (2): 147–154. https://doi.org/10.1260/0266351991494768.
Xu, X., Y. Wang, and Y. Luo. 2016. “General approach for topology-finding of tensegrity structures.” J. Struct. Eng. 142 (10): 04016061. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001532.
Zhang, J. Y., and M. Ohsaki. 2006. “Adaptive force density method for form-finding problem of tensegrity structures.” Int. J. Solids Struct. 43 (18): 5658–5673. https://doi.org/10.1016/j.ijsolstr.2005.10.011.
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Information
Published In
Journal of Structural Engineering
Volume 144 • Issue 10 • October 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Dec 4, 2016
Accepted: Mar 30, 2018
Published online: Jul 13, 2018
Published in print: Oct 1, 2018
Discussion open until: Dec 13, 2018
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