Abstract

We study the equilibrium problem for bodies made of a no-tension material, subjected to distributed or concentrated loads on their boundary. Admissible and equilibrated stress fields are interpreted as tensor-valued measures with distributional divergence represented by a vector-valued measure, as outlined in two 2005 papers by Lucchesi et al. Such stress fields are generalizations of ordinary functions, which allows us to consider stress concentrations on surfaces and lines. The general framework for this approach is presented first and then illustrated on examples of two-dimensional panels under different loads. In the general framework we determine weak divergences and the surface tractions of several stress field measures via the (surface) divergence theorem. Combinations of these stress fields are shown to give the solutions for the panels, which we assume to be clamped at the bottom, and subjected to various loads on the top and possibly on the sides of the panel. The shapes of the singular lines and stresses are explicitly determined in these cases.

Keywords

masonry panels, equilibrium, divergence measures

Authors