An Augmented Lagrangian Formulation for the Analysis of No-Tension Structures with Unilateral Supports

Abstract

Object of the paper is a class of structural problems that will be abstractly defined by the following three sets of equations:

• the compatibility equation C(u) = ε, where the operator C:u —>D is assumed linear (and so is its dual C’ that relates the internal stress a to the external actions f ∈ u’);

• the constitutive equation f (ε) = σ, assumed to be a monotone lower semi-continuos map from D to D’. Therefore the map is obtained from a generalized potential, that turns out to be lower semi-continuos and convex. This means that the material behaviour is reversible;

• the external force field, supposed to derive from a functional that is assumed to be lower semi-continuos and convex. The functional defines also the (non-linear) static and kinematic boundary conditions (eventually unilateral).