What you'll learn

**geometric non-linearity**and when it should be considered.

**account for large deflections and changes in geometry**.

**Newton-Raphson solution algorithm**that seeks to converge on the final state of the structure.

**open-source modelling tools**to quickly generate structural geometry.

Description

**After completing this course, you’ll have built an iterative numerical solver for cable and truss structures that exhibit geometric nonlinearity due to large deformations.**

**This is known as geometric non-linearity and requires a more sophisticated solution strategy**.

**the objective here is to build your understanding of the behaviour and the best way to do this is by implementing what you learn by building your own solver**.

**Examine the evolving behaviour of your structure as loading is incrementally increased.**

**Our solver implements an iterative algorithm, so a solution that converges is not always guaranteed!**Weโll be leaving the relative comfort and certainty of linear analysis behind – welcome to geometric non-linearity!

Course prerequisites

**Even if you have a theoretical understanding of the direct stiffness method, I still recommend that you complete my course on applying the direct stiffness method to truss structures.**That course is called, The Direct Stiffness Method for Truss Analysis with Python and itโs my entry point into matrix-based structural analysis.

**Get familiar with Python and how I implement the direct stiffness method in that introductory course first.**This will leave you in a great position to tackle this course and really focus on whatโs new and challenging about analysing non-linear structures.

Course Breakdown

**Section 1: Introduction and Course Breakdowns**

In this short introductory section, weโll take a tour of the course, section by section, to give you an idea of what to expect as you move through the course. Weโll also briefly discuss the course prerequisites. **Section 2: โHeavyโ cables – the linear solution**

In section 2 weโll 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, weโre 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-linearity**

In section 3, weโll 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 โgeometric non-linearityโ. Weโll also explore, at concept level, how we might set about solving for the behaviour of a non-linear structure. Weโll introduce the Newton Raphson method which informs the main architecture of the solver code weโll write later on. **Section 4: The Non-linear Stiffness Matrix**

One 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 weโll 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 Toolbox**

Now 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, itโs time to build out the code that can bring these ideas to life. In section 5, weโll do the bulk of our code development. In bitesize chunks, weโll build our solver, bit-by-bit. By the end of this section, youโll have a functioning non-linear solver. **Section 6: Visualising the Results**

After building a solver, next, we need to turn our attention to visualising the output results. This is the focus of section 6. Weโll 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: โHeavyโ Cables – the Non-linear Solution**

In section 7 weโll return to a conversation we started at the very beginning of the course. Weโll use our new solver to simulate the cable we kicked the course off with. Weโll compare our codeโs results with our earlier linear solution. Weโll 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 Blender**

In section 8 weโll take a break from pure coding and detour over to Blender, the free 3D modelling tool weโll be using to generate structural geometry. If youโve taken some of my other structural analysis courses youโll be familiar with how we use Blender. If youโre completely new to Blender, Iโve 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 Model**

In the final section of the course, weโll 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 doesnโt yet capture this behaviour – weโll address that in this final section of the course. Weโll 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.

*The codes developed in this course are for*

**educational purposes only**and are not tested or certified for use beyond the educational scope of this course. Always employ your own engineering judgement first and foremost, regardless of what the computer says!## Course Completion Certificate

- Download your personalised Certificate of Completion once youโve finished all course lectures.
- Applying for jobs? Use your Certificate of Completion to show prospective employers what youโve 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.

Course preview

### Lecture 1: Introduction and Course Overview

### Lecture 55: Antenna Tower - Modelling and Analysis

Course content

### Introduction and Course Breakdown

### โHeavyโ Cables - the Linear Solution

### Getting Comfortable with Nonlinearity

### The Non-linear Stiffness Matrix

### Building our 2D Solver Toolbox

### Visualising the Results

### โHeavyโ Cables - the Non-linear Solution

### Modelling Initial Geometry in Blender

### Mixing Cables and Bars

Appendix - Introduction to Blender

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