# Tag Archives: Modelling

## Cable-Chains...

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.

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.

References:

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.

Research

## Sticky backed plastic...

One of the fun parts of my job is that I get to tinker about with software and see how it could be used, either for my research or for my teaching.  Over the summer, the MSc students will be undertaking their dissertations and most of the topics that I set are generally quite playful so as to maintain their interest and enthusiasm, but equally, they're highly demanding...  One of the topics that I'm interested in is the use of cardboard as a structural material and how this can be formed into innovative shapes and forms.  One of the initial difficulties can sometimes be encountered relates the geometry and the formation of organic forms.  This is where 3D modelling can come in handy, and I've slowly been trying to learn 3D Studio Max to help generate the geometry so I can unpick the structure to create templates.  Whilst these models can help me understand the geometry and overall shape and massing of models, it can be a large leap into constructing them and physically realising the componentry to create scaled physical models.  This is where my latest toy comes into play, it's created by AutoDesk and it's called 123DMake and it's attractively priced at £0 and is available for PCs and Macs and can convert 3D model files into cardboard planes that can be fitted together to make all sorts of intricate shapes...

I've only just started messing with the software, but I'm quite optimistic that I will be able to create some really creative forms and shapes with the software over the summer, I just need to get some cardboard and a nice sharp knife lined up, or sweet talk someone into lending me their laser cutter.  I know that it doesn't sound likely that cardboard can be used as a structural material, but it's being used successfully to make crash helmets that pass a multitude of safety tests and even more impressive is that cardboard is being used to create a temporary cathedral in New Zealand following the recent earthquakes...  Cardboard structures are not as uncommon as you might think, Frei Otto for example constructed the Japan Pavilion for the Hanover Expo... go have a rummage in your recycling bin, you might just have enough for a bungalow... at least 123DMake will give you a nice template to cut out and stick together for your next housing project...

## Mathematica...

One of the reasons that I started this blog was so that I could mess about with embedding some Mathematica files to help with testing out some ideas.  For this to make sense it's easiest if I embed a few simple examples in this blog post.  Now if you want to interact with these examples, I'm afraid you're going to have to download the Wolfram CDF player, which is completely free and works on PC's and Mac's alike.  Imagine it as a sort of PDF viewer but it lets you interact with the files as opposed to a PDF which is typically just a static and lifeless document.

Consider the following equation:

Most text books would draw the graph for this over whichever range they deemed to be suitable and then students would try and learn from these dull and boring diagrams.

Now this is how I was taught maths and in fairness, it's pretty dull and it's difficult to gain any form of intuition as to how it might behave if the 2 became a 3 for example, this is where Mathematica's CDF files come in handy because it has some nice tricks for letting you explore maths in an interactive fashion... let's consider the following equation, from the previous graph most people wouldn't really know how it would affect the graph.

But if we crank this through Mathematica we can create a really nice interactive widget that can be shared with anyone for free!  As you change the slider, the graph updates in real time, and if you want to know what number you're changing 'a' to be then simply click the little + sign next to the slider itself to expand the input values beneath it.  In fact if you think that messsing with sliders is far too much like hard work, then simply click the little play button in the top right and the widget will work the sliders for you... sit back and watch the pattern.

If you're not familiar with Mathematica, you may be concerned that this sort of widget is really difficult to create, but actually I'm still on Chapter 3 on the text that I'm working through and the code is incredibly simple to create this kind of interactive learning tool and I've replicated it below to show how few lines of text can create this level of interaction.

Manipulate[ Plot[ Sin[a x], {x, -10, 10}], {a, 1, 5}]

Essentially this code starts with "I want a slider widget", "Plot me a graph of Sin(a.x) over a range of values for x from -10 to 10", then "make the slider vary a from 1 to 5".

Now this seems ok, but the Manipulate command is actually incredibly powerful and with a little more twiddling, high quality interactive 3D plots can be created, so let's consider the following expression.

This expression has four variables: f,g,x, and y.  Of course, I bet you're dying to know what the graph looks like for this function so you can boost your maths skills...

This is where the CDF player starts to flex its muscles a little, not only can you mess around with the sliders to change the values of f and g... but you can click and rotate the 3D graph itself to get a better view of how you think it's working.  For me this level of interaction is a real opportunity for playing with the maths to help build up a level of intuition and feeling of how the maths will behave.  And once again the code to get it to work is fairly straight forward even for a novice such as myself.

Manipulate[Plot3D[(f ) Sin[ x] + (g)  Sin [y], {x, 1, 10}, {y, 1, 10}], {f, -10, 10}, {g, -10, 10}]

Now here's the rub, a full Mathematica licence is the best part of £1,000 for a lecturer to use, in these hard times that's a lot of money.  But because I carry 'dual' status as I'm studying 2 degrees as well as working full time as a lecturer I was able to pick up a student licence for roughly £80.  Normally the cost for a student licence is a shade over £100 but it is possible to reduce the normal student price by 15% by using the discount code PD1637 at the Wolfram store checkout and I still retain the full functionality of sharing my CDF files via export.

I hope this helps someone, if you've any feedback on this post or would like to ask any questions, please get in touch or leave a comment below.

General

## 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...