Continuum Models for Systems in a Selfstress State

Abstract

We present a procedure to determine continuum equivalent properties of systems in selfstress state; this procedure is based on the energetic equivalence between the discrete model and the continuum model. This equivalence expresses the identity between strain energy and the selfstress energy developed in both models. Research of equivalent continuum media is made in the vicinity of the non-deformed configuration. The application of this procedure to tensegrity systems is validated on three types of modules, the simplex, the regular quadruplex (vertically homogenized) and the half-cuboctahedron quadruplex (horizontally homogenized). The equivalent rigidities and the coupling terms obtained on these modules are presented and compared to those obtained by a direct method (finite element method). Particular interest is paid to the influence of selfstress on the equivalent rigidities and the coupling terms of the continuum model.