Graphic Statics as a Legendre Transform

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• Professor Allan McRobie
• Friday 21 October 2022, 15:00-16:00
• CivEng Seminar Room (1-33) (Civil Engineering Building).

If you have a question about this talk, please contact Jamie Clarkson.

This somewhat impromptu talk is to describe a few things that I have been thinking about in my research of late. It will be more of a discussion piece than a polished fait accompli.

After a brief overview of some recent work in 2D and 3D graphic statics, this talk will focus in on a few fundamentals. These can be found in James Clerk Maxwell’s 1870 paper “On Reciprocal Figures, Frames and Diagrams of Forces” and they relate to the notion of a stress function. Encouraged by Bill Baker to read Maxwell’s original papers, I was quite taken aback at how little I was aware of the basics of my own subject. This short talk will look at Maxwell’s notion of a “Diagram of Stress”, involving a stress space wherein the only stress is a simple, constant, isotropic pressure from which (almost) any other stress field can be constructed. This leads naturally to the conclusion that “form” and “force”, the two fundamentals of graphic statics, are a Legendre transform pair. I will show how this understanding can be extended to include moments, and finish with a brief glimpse at how this may find applications in the design of materially-efficient structures, including shells and gridshells.

Recommended pre-reading: JC Maxwell 1870, “On Reciprocal Figures, Frames and Diagrams of Forces”, Trans RS Edinburgh, XXVI , Pt1, pp 1-40, section: “General Theory of Diagram of Stress in Three Dimensions”. https://archive.org/details/dli.granth.111835/page/178/mode/2up

This talk is part of the Engineering Department Structures Research Seminars series.

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