Continuum modelling of a beam-like latticed truss: identification of the constitutive functions for the contact and inertial actions

The derivation of a continuum model apt to give a compendious description of the mechanical behaviour of a latticed structure is envisaged here as a procedure leading to the identification (of the constitutive parameters) of a "coarse" model starting from a prescribed "finer" one. The fine model considered describes a planar modular beam whose module is made up of a pair of rigid diaphragms connected by straight elastic bars; diaphragms and bars have both mass. The coarse model is a one-dimensional continuum endowed with Euclidean structure. An interesting result is that the value of the density of the inertial actions at a point depends not only on the value of the acceleration at that same point - as is usually taken for granted in conventional continuum models - but also of its first and second derivatives with respect to the material coordinate.