On the correspondence between 2D force networks, tensegrity structures and polyhedral stress functions

TL;DR

This paper explores the relationship between polyhedral stress functions, 2D force networks, and tensegrity structures, introducing a two-mesh technique for stress prediction and generalizing classical results to polyhedral functions.

Contribution

It presents a novel framework linking polyhedral stress functions with self-equilibrated frameworks and introduces a regularization method for stress field approximation.

Findings

Validated the approach with numerical examples

Extended classical stress function results to polyhedral cases

Demonstrated stress prediction in tensegrity models

Abstract

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.