Tag Archives: Folding

Research Tutorial

Dynamic Arches...

Tinkering about with SystemModeler a little further, I've managed to finally build a sprung arch, complete with dampers on the revolute joints.  I'm intending on using this principle in my research to create folded structures, so it's interesting to see what effect the spring stiffness will have on the behaviour of the arch during the unpacking process - specifically looking at the accelerations on the masses at key points.

The thing that I was struggling with was creating a structure that had a set of equations that could be solved, the key concept I was initially missing was the closing of the structure with the special type of revolute joint to complete the chain.  Without this special revolute chain the equations are essentially unsolvable, so it's important that one of these joints sits in the system somewhere.

Sprung Arch

Another concept is that the structure in the video has 3 straight segments, each 1m long; but the supports are only 2m apart.... forcing the arch to pop into a stable shape that balances the weights at each of the joints.  This is essentially what makes the arch wobble when solving the initial set of equations.  Next step is applying external forces and measurement points along the structure for displacement etc...

General Research Tutorial


Part of the work that I've been undertaking on Mathematica is to create a series of sheets that will calculate the geometry of a cable-chain arch with a set of given parameters.  In part I’m interested in how the cable-chain arch can behave as a deployable structure and looking to build on the work of (Li, Vu, & Richard, 2011) to see how practical a cable-chain structure can be made with regards economy, efficiency, and robustness.  Essentially a cable-chain structure is a curved arch that is sub-divided into straight sections, with cables spanning across the base of two struts as can be seen in the figure below.  Simple versions of these types of structures are widely used for the likes of temporary and deployable aircraft hangers to create large open spans.


Now that I’ve got the makings of a simple Mathematica sheet up and running and I’ve taught myself some rudimentary programming and graphics manipulation skills I’ve managed to start to knock together what I feel are some high quality illustrations for my thesis.

I’ve done this with a mixture of Mathematica to create the base diagram, which I save as a PDF.  I then import the PDF into OmniGraffle to annotate the diagram and then export to a PNG file to maintain the transparent background, this figure I can then host for linking into blogs etc.  Below is a sample figure which shows how the number of segments (nSeg) affects the internal area available for habitation within a typical parabolic arch.

Cable Arches

Given that both of my brothers are colour blind and I’ve never done the test, I’m not convinced on my choice of colour schemes, but the good news is that it won’t take long to change if it turns out I’ve made my figures look like something off the set of Austin Powers.

So far I’m finding OmniGraffle quite limited compared to Visio that I’ve been using for my diagrams for perhaps 20 years or so.  I decided to use OmniGraffle though as most of my writing work is done on a Mac, although I also have a PC so I can always create the more complex diagrams on Visio if need be, especially as I’ve managed to get a legitimate copy from work for £12.

I'd love to hear how other engineers and academics approach creating technical figures and sketches on their Macs though, I've a feeling that I'm really missing out on something and there's got to be a much slicker workflow out there.


Li, Y., Vu, K. K., & Richard, J. Y. (2011). Deployable Cable-Chain Structures: Morphology, Structural Response And Robustness Study. Journal for the International Association for Shell and Spatial Structures, 52(168), 83-96.



Keeping it real...

One of my colleagues has discovered an absolute gem of a piece of software called Physion that lets you mess about with various bits of structure, motors, gears, and other things all in a real time physics environment.  Now the tutorial videos themselves are pretty impressive, but with a little bit of JavaScript some of the things the Physion community has been creating are absolute works of genius.

This simple piece of software has been an endless source of entertainment for the past couple of weeks for the structural engineering lectuers and they've been busy creating models of shaker tables, backfilled arches with granular fill, disproportionate collapse simulations, and all sorts of other random stuff that simply looks cool when brought to life with real time physics.

I've to deliver a technical lecture in a few weeks for the Institution of Structural Engineers, but one of the things that I was struggling with was describing how some deployable structures and other lightweight structures can be susceptible to the effects of disproportionate collapse when the removal of a critical member occurs. I knew I wanted to do something along the lines of an animation to show this, but wasn't sure what was the best way to go about it... until I discovered Physion.

I know the animation above is not the most exciting in the world, but it shows what happens when a critical member, either the restraint cable at the end of the pantograph beam, or any internal element is removed from the structure. The removal of just a single element brings about the complete collapse of the structure, this effect is known as disproportionate collapse and is an important concept for structural engineers to understand.  All buildings in the UK are designed to resist this effect to increase the safety of buildings in the event of accidental damage occurring.

The circular elements introduced at the beginning of the video are just there to create some weight on the structure to show that it's stable and can support a sensible amount of load when the structure is undamaged.  Then using the delete tool, I've tried to show a couple of different failure mechanisms, there's no sound on the animation as I intend to talk about this during the technical lecture I'm delivering.  We've already done some work on creating structurally stable pantographic beams with our MSc students here at the University, complete with additional safety mechanisms to prevent the failures above happening and it's a research topic that is ongoing in our team. The original motivation was to see if we could use it to create a deployable bridge, perhaps in scenarios that have happened recently in Cumbria when the bridges were swept away by flood water... and it's a concept that's expanding.

At times I find life as an academic frustrating compared to being in industry, then I remember that they pay me to play with things like this for a living and I feel lucky...