What you'll learn
Section 1: Introduction and Course BreakdownsIn this short introductory section, we’ll take a tour of the course, section by section, to give you an idea of what to expect as you move through the course. We’ll also briefly discuss the course prerequisites.
Section 2: ‘Heavy’ cables – the linear solutionIn section 2 we’ll start our analysis of cable behaviour. Cables very often undergo changes in their geometry under loading, either due to cable extension, directly applied loads or flex in the cable supports – they are the classic example of a non-linear structure. In this section, we’re going to establish a linear (closed-form) cable solution that ignores non-linear effects. This will provide a baseline case to test our non-linear code against later.
Section 3: Getting Comfortable with Non-linearityIn section 3, we’ll start to talk about non-linear structural behaviour, before focusing on geometric non-linearity in particular. The aim of this section is to take any mystery out of the term ‘geometric non-linearity’. We’ll also explore, at concept level, how we might set about solving for the behaviour of a non-linear structure. We’ll introduce the Newton Raphson method which informs the main architecture of the solver code we’ll write later on.
Section 4: The Non-linear Stiffness MatrixOne of the central elements of a matrix-based non-linear structural analysis is a stiffness matrix that can capture the influence of large deflections of the structure. In section 4 we’ll focus on deriving a form of non-linear element stiffness matrix that can do just that. Familiarity with the material in the prerequisite course will be helpful here.
Section 5: Building our 2D Solver ToolboxNow that we have a stiffness matrix that can reflect progressive stiffening or softening due to large deformations and we understand, conceptually at least, how to iterate towards a solution, it’s time to build out the code that can bring these ideas to life. In section 5, we’ll do the bulk of our code development. In bitesize chunks, we’ll build our solver, bit-by-bit. By the end of this section, you’ll have a functioning non-linear solver.
Section 6: Visualising the ResultsAfter building a solver, next, we need to turn our attention to visualising the output results. This is the focus of section 6. We’ll build out the data visualisation that brings our solution to life and allows us to explore how the structure evolves towards its final equilibrium state.
Section 7: ‘Heavy’ Cables – the Non-linear SolutionIn section 7 we’ll return to a conversation we started at the very beginning of the course. We’ll use our new solver to simulate the cable we kicked the course off with. We’ll compare our code’s results with our earlier linear solution. We’ll be able to closely approximate the linear solution but also observe the emergence of non-linear behaviour as the axial stiffness of our cable is progressively reduced.
Section 8: Modelling Initial Geometry in BlenderIn section 8 we’ll take a break from pure coding and detour over to Blender, the free 3D modelling tool we’ll be using to generate structural geometry. If you’ve taken some of my other structural analysis courses you’ll be familiar with how we use Blender. If you’re completely new to Blender, I’ve included an appendix section at the end of the course to help you get set up and familiar with Blender.
Section 9: Mixing Cables and Bars in the Same ModelIn the final section of the course, we’ll expand our code to handle structures that consist of both bar and cable elements. One of the features of a cable is its inability to resist compression. Our code doesn’t yet capture this behaviour – we’ll address that in this final section of the course. We’ll also complete the modelling and analysis of a cable-stayed lattice tower – a classic example of a conventional and commonly found structure that utilises geometrically non-linear cables.
Who this course is for
- Students and professional engineers who are familiar with methods of linear structural analysis and want to learn about non-linear behaviour.
- Anyone who has taken my linear 2D truss analysis course and wants to extend their analysis capabilities beyond linear structures.
- Students and professional engineers who want to learn more about how to implement iterative methods of analysis in Python.
Course Completion Certificate
- Download your personalised Certificate of Completion once you’ve finished all course lectures.
- Applying for jobs? Use your Certificate of Completion to show prospective employers what you’ve been doing to improve your capabilities.
- Independently completing an online course is an achievement. Let people know about it by posting your Certificate of Completion on your Linkedin profile or workplace CPD portfolio.
Lecture 1: Introduction and Course Overview
Lecture 55: Antenna Tower - Modelling and Analysis
Introduction and Course Breakdown
‘Heavy’ Cables - the Linear Solution
Getting Comfortable with Nonlinearity
The Non-linear Stiffness Matrix
Building our 2D Solver Toolbox
Visualising the Results
‘Heavy’ Cables - the Non-linear Solution
Modelling Initial Geometry in Blender
Mixing Cables and Bars
Appendix - Introduction to Blender
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Frequently Asked Questions
Absolutely. Even if you watched the full course, if you’re not satisfied, contact me in the first 30 days and I will give you a full refund, no questions asked. It would be helpful if you could tell me how I can improve the course for other students.