Mechanisms of prestressed reticulate systems with unilateral stiffened components

The stability of space reticulate systems is dependent on the existence of mechanisms. The methods that have been developed to determine them are mainly based on the calculation of a basis of the mechanismsʹ vectorial subspace by computing the kernel of the transpose equilibrium matrix of the structure. However, they can only consider a bilateral stiffness of the members, which applies to the case for systems composed of bars with traction and compression stiffness. Nevertheless, some classes of reticulate systems, like tensegrity systems, use unilateral rigidity components such as cables. The objective of this paper is to develop a method for calculating the mechanisms which can take into consideration the presence of components with unilateral rigidity. In this case, specific mechanisms associated with these elements may appear; these are referred to as “unilateral mechanisms”. An approach is therefore proposed in order to write a basis of their vectorial subspace. It is included in a methodology devoted to the analysis of space structures with initial stresses. The process is based on the identification of the possible prestress states and of the bilateral mechanisms and, next, to the characterization of the unilateral mechanisms.