  We formulate and discuss the relationship between polyhedral stress functions
and internally self-equilibrated frameworks in 2D, and a two-mesh technique for
the prediction of the stress field associated with such systems. We generalize
classical results concerned with smooth Airy stress functions to polyhedral
functions associated with arbitrary triangulations of a simply-connected
domain. We also formulate a regularization technique that smoothly projects the
stress function corresponding to an unstructured force network over a
structured triangulation. The paper includes numerical examples dealing with a
benchmark problem of plane elasticity, and the stress fields associated with
tensegrity models of a cantilever beam and an elliptical membrane.
