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. © 2011 by Mathematical Sciences Publishers.