In this first section, we’ll get our bearings by taking a look at the course structure. This will give you a good idea of what to expect. We’ll also introduce our main focus for this course - cablenet structures. This will provide some historical context for the technical analysis to follow. 

This course assumes that you’ve completed the prerequisite course on 2D cable analysis; we’ll elaborate on why it’s critical that you cover that course first if you want to get the most from this course. 

In this section, we’ll take the theory used to develop the 2D non-linear stiffness matrix and extend that to 3D. This really involves two steps, updating how we calculate the element transformation matrix and then updating the local element stiffness matrix. 

The task here isn’t difficult, the hard work was done in establishing the 2D stiffness matrix in the prerequisite course. We'll focus on whiteboarding the theory here before diving into code a little later.

Blender is a trusty 3D Swiss army knife that makes all of this modelling possible. So, since we’re moving from 2D to 3D, we’ll need to update some of the utility scripts we wrote previously for data import and export. 

But it won’t be all coding in this section, we dabble in some 3D modelling and generate our first simple cablenet model to serve as our test-bed structure for the next section.

Now it’s time to roll up our sleeves and dive into our main solver code. In this section, we’re going to be doing the bulk of the work to update the 2D solver we wrote previously. We’ll also be implementing all of the transformation and stiffness matrix theory we whiteboarded earlier. 

Once you’ve completed this section you will have converted your 2D cable analysis code into a 3D solver…and we can start experimenting with some structures.

When we studied 2D cable analysis previously, we analysed a 2D cable-stayed antenna tower. So, now that we’ve built ourselves a 3D toolbox, the obvious first task is to build a bigger 3D cable-stayed lattice tower to see how our solver crunches through that! 

This section will be our first complete run-through of the analysis workflow, from modelling in Blender, to analysis in our solver to results visualisation back over in Blender.

In this section, we’ll focus on how we can get the most out of Blender’s modelling and simulation tools. We’ll start by exploring a relatively new feature in Blender; geometry nodes. This functionality gives us the ability to procedurally model and parameterise our geometry. This will be a taster on geometry nodes - after which you can decide if you want to investigate further beyond this course.

Next, we’ll explore Blender’s cloth simulation tools, one of Blender’s many physics engine toolboxes. Although this tool is not designed for structural simulation, it serves as an excellent way of approximating net and membrane geometry which we can use as a starting point for our structural analysis. 

This process of exploratory form-finding is one of the most creative and enjoyable parts of studying these structures and serves as a nice counter-balance to our focus on programming and mechanics!

In this section, we’ll bring together our 3D solver with what we’ve learned about form-finding using Blender’s simulation tools. We’ll focus on the modelling and analysis of a hyperbolic paraboloid cablenet structure. For the structure itself, we’ll draw inspiration from a fabric membrane structure by Frei Otto from 1955. 

This will give us a good opportunity to discuss the relationship between form-finding and pre-tension. Again, this will be another good demonstration of the typical modelling-analysis-visualisation workflow. 

In this final section, we’re going to finish strong! We’ll use everything we’ve learned so far to build a model of one of Frei Otto’s finest membrane structures, the so-called ‘Dancing Fountain’ from the Cologne Federal Garden Exhibition in 1957. 

We’ll use all of the tools at our disposal to build the initial geometry, simulate the minimum surface under tension and then analyse the cablenet force distribution under self-weight. Naturally, we’ll bring it all back into Blender for final visualisation.

The successful completion of this structure sets a great high-water mark for your understanding of cablenet structures and of the tools you’ve just built. This should leave you confident enough to explore the behaviour of non-linear cablenet structures in the wild.

As with every DegreeTutors course, you should also be confident in extending the code beyond what we finish up with at the end of the course. 

In this appendix, I’ll walk you through exactly how to build the axial force and deflected shape visualisation we implemented in the course. Once you see and understand how this is done, you can easily extend this to build other structural data visualisations in Blender.