Geometric stress functions, continuous and discontinuous

Abstract

AbstractIn his work on stress functions Maxwell noted that given a planar truss the internal force distribution may be described by a piecewise linear, $$C^0$$ C 0 continuous version of the Airy stress function. Later Williams and McRobie proposed that one can consider planar moment-bearing frames, where the stress function need not be even $$C^0$$ C 0 continuous. The two authors also proposed a discontinuous stress function for the analysis of space-frames, which however suffers from incompleteness. This paper provides a discontinuous stress function for n-dimensional space frames that is complete and minimal, along with its derivation from an n-dimensional continuous stress function. The continuous stress function generalizes both Günther’s and Maxwell’s stress functions.