The force as a function: Towards analytical graphic statics for spatial structures
Abstract
One of the most influential early works in graphic statics is one of Maxwell, where he introduced the idea of a discontinuous stress function and the use of a 3D projective polarity for a planar problem. A recent work gave an analytical description with the goal to provide explaining power, treating planar forces as linear functionals (moment functionals) forming a 3D vector space, so force and form diagrams of planar problems can be interpreted in a 3-dimensional way. The linear combination of these moment functions can naturally be used as a discontinuous stress function since the Airy stress function is known to correspond to moments of planar forces. The main contribution of this work is to present a dimension independent way of treating forces as functions, that returns the known stress-functions of planar and spatial graphic statics. This is done by relying on the multi-linear function definition of Grassmann-algebra.
Cite
@article{arxiv.2104.02313,
title = {The force as a function: Towards analytical graphic statics for spatial structures},
author = {Tamás Baranyai},
journal= {arXiv preprint arXiv:2104.02313},
year = {2021}
}