Vol. 6, No. 9-10, 2011

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ISSN: 1559-3959
A finite element for form-finding and static analysis of tensegrity structures

Dario Gasparini, Katalin K. Klinka and Vinicius F. Arcaro

Vol. 6 (2011), No. 9-10, 1239–1254
Abstract
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This text describes a mathematical model for both form-finding and static analysis of tensegrity structures. A special line element that shows constant stress for any displacement of its nodes is used to define a prestressed equilibrium configuration. The form-finding and static analysis are formulated as an unconstrained nonlinear programming problem, where the objective function is the total potential energy and the displacements of the nodal points are the unknowns. Analytical solutions for tensegrity prisms are presented and compared with the numerical results of the proposed approach. A quasi-Newton method is used, which avoids the evaluation of the tangent stiffness matrix. The source and executable computer codes of the algorithm are available for download from the website of one of the authors.

Keywords
cable, element, line, minimization, nonlinear, optimization, tensegrity
Milestones
Received: 4 August 2010
Revised: 10 January 2011
Accepted: 5 February 2011
Published: 15 January 2012
Authors
Dario Gasparini
Civil Engineering Department
Case Western Reserve University
2182 Adelbert Road
Cleveland, OH 44106-7201
United States
Katalin K. Klinka
Department of Structural Engineering
Budapest University of Technology and Economics
2 Bertalan Lajos
Budapest H-1111
Hungary
Vinicius F. Arcaro
College of Civil Engineering
University of Campinas
Avenida Albert Einstein 951
Campinas, SP 13083-852
Brazil
http://www.arcaro.org