Geometric Stress Functions, Continuous and Discontinuous

TL;DR

This paper introduces a complete and minimal discontinuous stress function for n-dimensional space frames, extending previous work on continuous and piecewise linear stress functions for planar trusses and frames.

Contribution

It provides a novel, complete, and minimal discontinuous stress function for n-dimensional space frames, derived from a continuous stress function.

Findings

Provides a complete and minimal discontinuous stress function for n-dimensional space frames.

Derives the discontinuous stress function from an n-dimensional continuous stress function.

Extends the theory of stress functions to higher dimensions and discontinuous cases.

Abstract

In his work on stress functions Maxwell noted that given a planar truss the internal force distribution may be described by a piecewise linear, $C^0$ 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 $C^0$ 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.