Initial form-finding design of deployable Tensegrity structures with dynamic relaxation method

Abstract

The paper studies the initial form-finding problem, includes the initial configuration and stress distribution, of deployable tensegrity structures. The stress distributions in bars are preset as prestressing forces, the configuration of the structure and the stress distributions in cables are searched by a presented dynamic relaxation method. In the method, mechanical characteristics of the deployable tensegrity structures are considered. The compatibility of the configuration and stress distribution of the structure is achieved in an iterative process by continuous modification of the bar lengths while keeping the initial stress in bars and the cable lengths with constant values. The effects of the dummy nodal mass, iteration time step length, and cable stiffness on the calculated results and the convergence performances are investigated and rational selection of these parameters are advised. Several numerical examples are provided to verify the applicability and accuracy of the presented method.

Keywords

Deployable tensegrity structures form-founding dynamic relaxation iterative process selection of parameter

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References

Schek

H.J.

, Force density method for from finding and computation of general networks, Computer Methods in Applied Mechanics and Engineering3 (1974), 115–134.

Connelly

and Terrell

, Globally rigid symmetric tensegrities, Topologic Structurale21 (1995), 59–77.

Connelly

and Back

, Mathematics and tensegrity, American Scientist86 (1998), 142–147.

Dariusz

and Brzezi

, Accuracy problems of numerical calculation of fractional order derivatives and integrals applying the riemann-liouville/caputo formulas, Applied Mathematics and Nonlinear Sciences1 (2016), 23–44.

Zhang

J.Y.

and Ohsaki

, Adaptive force density method for form-finding problem of tensegrity structures, Int J of Solids and Structures43 (2006), 5658–5673.

Pagitz

and Mirats Tur

J.M.

, Finite element based form-finding algorithm for tensegrity structures, Int J of Solids and Structures46 (2010), 3235–3240.

Tran

H.C.

and Lee

, Initial self-stress design of tensegrity grid structures, Computer and Structures88 (2009), 558–566.

, Feng

X.Q.

, Cao

Y.P.

and Gao

H.J.

, A Monte Carlo form-finding method for large scale regular and irregular tensegrity structures, Int. J. of Solids and Structures47 (2010), 1888–1898.

and Luo

Y.Z.

, Form-finding of nonregular tensegrities using a genetic algorithm, Mechanics Research Communications37 (2010), 85–91.

10.

Motro

, Najari

and Jouanna

, Tensegrity systems, from design to realization, Proceedings of the First International Conference: Lightweight Structures in Architecture, Sydney, 11986, pp. 690–697.

11.

Domer

, Fest

, Lalit

and Smith

I.F.C.

, Combining dynamic relaxation method with artificial neural networks to enhance simulation of tensegrity structures, J of Structural Engineering129 (2003), 672–681.

12.

Ali

N.B.H.

, Rhode-Barbarigos

and Smith

I.F.C.

, Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm, Int J Solids and Structures48 (2011), 637–647.

13.

Tibert

, Deployable tensegrity structures for space applications, Ph. D. Dissertation, Royal Institute of Technology, 2002.

14.

Tomas

, Marta

and Pedro

, An iterative method for non-autonomous nonlocal reaction-diffusion equations, Applied Mathematics and Nonlinear Sciences1 (2017), 73–82.