This article presents a design methodology based on a stiffness and volume optimization algorithm for three-dimensional nonlinear hyperstatic and pre-stressed structures composed of elements only subjected to axial forces, with a special emphasis on tensegrity structures. The algorithm is based on dimensionless numbers called morphological indicators that allow finding, within a given family of structures, the geometry related to a maximum stiffness or a minimum volume of materials or the best ratio between stiffness and volume. The algorithm takes into account the buckling of the struts and different materials for cables and struts. This article first demonstrates the optimization algorithm and then gives numerical confirmations and examples.
TibertAGPellegrinoS.Review of form-finding methods for tensegrity structures. Int J Solids Struct2003; 38: 5223–5252.
3.
TranHCLeeJ.Advanced form-finding of tensegrity structures. Comput Struct2010; 88: 237–246.
4.
ZhangJYOhsakiM.Adaptative force density method for form-finding problem of tensegrity structures. Int J Solids Struct2006; 43: 5658–5673.
5.
Gomez EstradaGBungartzH-JMohrdieckC. Numerical form-finding of tensegrity structures. Int J Solids Struct2006; 43: 6855–6868.
6.
De JagerBSkeltonE. Symbolic stiffness optimization of planar tensegrity structures. J Intel Mat Syst Str2004; 15: 181–193.
7.
MasicMSkeltonREGillPE.Optimization of tensegrity structures. Int J Solids Struct2006; 43: 4687–4703.
8.
Rhode-BarbarigosLBel Hadj AliNMotroRet al. Designing tensegrity modules for pedestrian bridges. Eng Struct2010; 32: 1158–1167.
9.
Bel Hadj AliNRhode-BarbarigosLPascual AlbiAet al. Design optimization and dynamic analysis of a tensegrity-based footbridge. Eng Struct2010; 32: 3650–3659.
10.
ZalewskiW. The flow of forces. In: Excerpt from notes on structural behavior for architecture students. MIT Press, 1980.
11.
MichellAGM. The limit of economy of material in frame structures. Philos Mag1904; 8(47): 589–597.
12.
SkeltonREDe OliveiraMC.Optimal tensegrity structures in bending: the discrete Michell Truss. J Frankl Inst2010; 347: 257–283.
13.
ZalewskiWKusS. Shaping structures for least weight. In: IASS Symposium “Conceptual Design of Structures”, Stuttgart, 7 November 1996, pp. 376–383.
14.
Quintas RipollV. Sobre el teorema de Maxwell y la optimization de arcos de cubierta. Inf Constr1989; 40(400): 57–70.
15.
Quintas RipollV. Sobre las formas de minimo volumen de las celosias de seccion constante. Inf Constr1992; 43(418): 61–67.
16.
SamynP.Etude comparée du volume et du déplacement de structures isostatiques bidimensionnelles sous charges verticales entre deux appuis. Thèse de doctorat, Université de Liège, Liège, 2000.
17.
SamynP.Etude de la morphologie des structures à l’aide des indicateurs de volume et de déplacement. Publication de la Classe des Sciences de l’Académie Royale de Belgique, collection in-4°, 3e série, tome V, 2004.
18.
LatteurP.Optimisation et prédimensionnement des treillis, arcs, poutres et câbles sur base d’indicateurs morphologiques. Application aux structures soumises en partie ou en totalité au flambement. Thèse de doctorat, Vrije Universiteit Brussel, Brussel, 2000.
19.
Van SteirteghemJ. A contribution to the optimisation of structures using morphological indicators: (in)stability and dynamics. Thèse de doctorat, Vrije Universiteit Brussel, Brussel, 2006.
20.
VandenbeghT.Benchmarking optimization at conceptual design stage with morphological indicators. PhD Thesis, Vrije Universiteit Brussel, 2010.
21.
VandenberghTDe WildeP.A review on conceptual design with morphological indicators. Int J Struct Eng2010; 1(3/4): 280–298.
22.
ZhangPFengJ.Initial prestress design and optimization of tensegrity systems based on symmetry and stiffness. Int J Solids Struct2017; 106–107: 68–90.
23.
AshwearNTamadapuGErikssonA.Optimization of modular tensegrity structures for high stiffness and frequency separation requirements. Int J Solids Struct2016; 80: 297–309.
