Multiparametered Formfinding Method: Application to Tensegrity Systems

Abstract

A method allowing a multiparametered formfinding for prestressed and selfstressed reticulated systems with tensile and compressive members is presented. Known methods, based on geometric analysis and dynamic (dynamic relaxation) considerations have been developed for these systems but they allow generally the evolution of only one parameter. But, in case of shape finding of non-regular new forms or when the sought-after form is subject to a set of geometrical constraints, it becomes obligatory to elaborate a multiparametered form-finding process. The proposed numerical method, which is described in this paper, exploits the force density method, already used for form finding of pure tensile structures. However, equilibrium matrix of pure tensile structures as cable nets systems, admits always an inverse, which might be false when tensile and compressive members coexist in the system. In this paper, different processes allowing to define prestressed (or selfstressed) equilibrium geometry are described. Except for the relational structure which is considered as known at the beginning of the process, two sets of form-finding parameters can be identified for this method: prestress (or selfstress) coefficients of members and coordinates or redundant nodes. The proposed method does not yield a unique geometry but it is very convenient for a multiparametered formfinding, and has produced very interesting results, especially for Tensegrity Systems. Application of this method of multiparametered formfinding to Tensegrity Systems, provides the designer with an efficient way to achieve interesting new selfstressed geometries, such as the generation of double-layer grids by agglomeration of Tensegrity modules.