A finite element for form-finding and static analysis of tensegrity structures

Abstract

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.

An improved multi-objective topology optimization approach for tensegrity structures

“…When the topology and the unilateral property of members of a tensegrity structure are given in advance, a procedure, called form-finding, is usually used to determine the nodal positions that can ensure the self-stressibility and stability of the tensegrity structure. There are tremendous literature on form-finding of tensegrity structures, and various form-finding approaches, such as dynamic relaxation procedure–based approaches (Ali et al, 2011; Zhang and Ohsaki, 2006), force density formulation–based approaches (Estrada et al, 2006; Masic et al, 2005; Vassart and Motro, 1999), equilibrium matrix formulation–based approaches (Lu et al, 2015, 2016), and finite element–based approaches (Gasparini et al, 2011; Pagitz and Tur, 2009), have been developed. Because all or partial nodal positions are used as variables in the form-finding procedure, the form-finding procedure has a weak control on the shape of the found tensegrity.…”