Algebraic tensegrity form-finding
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.
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