A numerical analysis of infinitesimal mechanisms

The paper presents a numerical algorithm, based on Koiter’s theory of the elastic stability, for detecting the order of infinitesimal mechanisms, i.e. kinematically indeterminate systems of pin-jointed bars. In cases of one degree of indeterminacy the algorithm improves, in terms of computational simplicity and efficiency, an analogous algorithm proposed by Salerno in 1992. This is shown to be due to the vanishing of the terms higher than the third-order of the asymptotic expressions of the energy, owing to the use of the Green strain measure and a mixed (displacement and stress) formulation of the problem. Moreover, the proposed algorithm is able to provide a correct definition of mechanism in cases of several degrees of indeterminacy, mainly for structures like those first studied by Connelly and Servatius in 1994, which the paper will treat in depth