Algebraic tensegrity form-finding

Milenko Masic

doi:10.1016/j.ijsolstr.2005.01.014

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Algebraic tensegrity form-finding

2005-08-01

130

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Milenko Masic *

Robert E. Skelton

Philip E. Gill

DOI：10.1016/j.ijsolstr.2005.01.014

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Abstract

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This paper concerns the form-finding problem for general and symmetric tensegrity structures with shape constraints. A number of different geometries are treated and several fundamental properties of tensegrity structures are identified that simplify the form-finding problem. The concept of a tensegrity invariance (similarity) transformation is defined and it is shown that tensegrity equilibrium is preserved under affine node position transformations. This result provides the basis for a new tensegrity form-finding tool. The generality of the problem formulation makes it suitable for the automated generation of the equations and their derivatives. State-of-the-art numerical algorithms are applied to solve several example problems. Examples are given for tensegrity plates, shell-class symmetric tensegrity structures and structures generated by applying similarity transformation. (c) 2005 Elsevier Ltd. All rights reserved.

Keywords:

tensegrity

shape constraints

symmetry

nonlinear zero-finding

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