Vol. 7, No. 10, 2012

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ISSN: 1559-3959
Form finding of tensegrity structures using finite elements and mathematical programming

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

Vol. 7 (2012), No. 10, 899–907
Abstract

We show that the minimization of total potential energy is the general principle behind the well-known rule of maximizing some lengths of a truss mechanism to define a tensegrity. Moreover, the latter rule is a special case, due to the usual high values of the modulus of elasticity. An innovative mathematical model is presented for finding the form of tensegrity structures, based on the finite element method and on mathematical programming. A special line element that shows constant stress for any displacement of its nodes is used to define a prestressed equilibrium configuration. Form finding is 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. A connection is made with the geometric shape minimization problem, defined by a constrained nonlinear programming problem. A quasi-Newton method is used, which avoids the evaluation of the tangent stiffness matrix.

Keywords
cable, element, line, minimization, nonlinear, optimization, tensegrity
Milestones
Received: 3 November 2011
Revised: 26 October 2012
Accepted: 30 October 2012
Published: 1 March 2013
Authors
Katalin K. Klinka
Department of Structural Engineering
Budapest University of Technology and Economics
2 Bertalan Lajos
Budapest
1111
Hungary
Vinicius F. Arcaro
Institute for Membrane and Shell Technologies
Bauhausstrasse 8
D-06846 Dessau
Germany
Dario Gasparini
Civil Engineering Department
Case Western Reserve University
2182 Adelbert Rd
Cleveland OH 44106
United States