Course overview

Develop a custom-coded analysis pipeline for 2D and 3D plate and shell structures, a roadmap from theory to solver

Finite Element Analysis of Plate and Shell Structures in Python

Uncover the role uncertainty plays in structural behaviour with the First Order Reliability Method

Uncertainty, Risk and Reliability Part 1 - Probabilistic Modelling of Structural Failure

Unlocking the Fundamentals of Shell Behaviour with Analytical Modelling and Membrane Theory

Analytical Modelling of Plate and Shell Structures: Part 2 - Shells

This course is part 1 in a two-part series exploring the analytical modelling of plate and shell structures. In this first part, we’ll be exploring 2D plates. By the end of this course, you will have a good understanding of how to analyse both circular and rectangular plates using purely analytical means - so no finite elements or numerical methods - just fundamental closed-form solutions. In addition to learning about the specifics of plate behaviour, you should also walk away with a better understanding of how to develop analytical models in the form of governing differential equations. You’ll also have a few new tools and techniques that you can use to unlock tricky math problems using Python.

Section 2 overview

Geometric considerations and assumptions

Shell structures in the built environment

Fundamental load resistance mechanisms

Deformation curvature for 2D plates

Curvature and axis rotation

Undeformed shell curvature

Section 3 overview

Coordinates, limitations, assumptions and the plan

Establishing the radial and hoop strain

Jumping to stresses via Hooke’s Law

Determining the stress resultants

Equilibrium of the infinitesimal element

From equilibrium to the governing differential equation

Evaluating the shear force term

The influence of plate boundary conditions

Case study #1: Simply supported with edge moment

Case study #2: Simply supported with UDL

Case study #2: Further investigation & visualisation

Case study #3: Built-in with central point load

Case study #4: Built-in annular plate with UDL

Case study #5: Simply supported with linearly varying load

Case study #5: Code solution and plotting

Building a 3D visualisation of plate deflection

Section 4 overview

Setting up our derivation

Stress and strain analysis

Equilibrium and the governing differential equation

Stress distributions

Fixed and simply supported boundary conditions

Free edges

The corner effect

Navier’s solution for rectangular plate deflection

Determining plate moments

Case study #6: Navier’s solution for UDL

Case study #7: Navier’s solution for linearly varying loading

Case study #8: Navier’s solution for patch loading

Case study #9: Navier’s solution for point loading

Building a ‘Plate Calculator’ script

Course wrap up and certificate of completion

A practical guide to the analysis of circular and rectangular plates under load, from first principles.

Analytical Modelling of Plate and Shell Structures: Part 1 - Plates

The aim of this course is to provide an introduction to the behaviour of reinforced concrete in bending and shear. By the end of the course you should understand the mechanical models we use to characterise reinforced concere behaviour. You’ll also develop an understanding of the rules and analysis techniques prescribed by Eurocode 2 for the analysis and design reinforced concrete structures. In addition, towards the end of the course, we’ll also explore how we can use Python scripting to speed up repetitive manual calculations.

Who is this course for?

The optional role of Python in this course

The relevant codes for this course

Actions on structures

Ultimate limit state design

Serviceability limit state design

Worked example #1: Determining ULS actions

Worked example #2: Determining ULS actions

Material properties

Cross-section analysis

Ultimate moment capacity

Worked example #3: Basic section design

Worked example #4: Calculate section moment capacity

Worked example #5a: Over-reinforced sections

Worked example #5b: Automating the search for x

Doubly reinforced sections

Worked example #6: Doubly reinforced section design

Worked example #7: Calculating doubly reinforced moment capacity

Flanged beam design

Worked example #8: Flanged section moment capacity

Worked example #9: Flanged section design

Shear behaviour in beams

Reinforced shear resistance (Variable Strut Method)

Worked example #10: Bending and shear design

Worked example #11: Shear design example

Longitudinal shear in flanged beams

Worked example #12: Transverse shear reinforcement design

Section 5 overview

Designing singly reinforced sections

Expanding to doubly reinforced sections

Expanding to singly reforced flanged sections

Determining the correct analysis case

Under-reinforced section analysis

Over-reinforced section analysis

Doubly reinforced section analysis

Flanged section analysis

An introduction to ultimate limit state design for bending and shear with optional calculation automation using Python.

Fundamentals of Reinforced Concrete Design to Eurocode 2

After completing this course, you’ll have developed a complete workflow for the modelling and analysis of non-linear 3D cablenet structures. We’ll expand beyond what we covered in our study of 2D non-linear cables by adapting the tools we built previously, for the analysis of non-linear 3D cablenet structures. However, instead of just modifying our existing code, we’ll spend time fleshing out a complete workflow that takes you from initial form-finding of cablenet geometry, right through to iterative stiffness method simulation to identify the cablenet deflections and tension profile.

Introduction and course overview

Course prerequisites

Moving to JupyterLab

Cablenet structures

Building the 3D transformation matrix

Extending the non-linear stiffness matrix

Generate a simple cablenet

Extending our Blender export scripts

Visualising axial forces and deflections in Blender

Updating our notebook structure

Basic updates to our preprocessing code

Implementing a basic 3D plot

Fixing the 3D scale problem

Implement support type visualisation

Implementing 3D arrows

Implementing 3D annotations

Building the transformation matrix

Calculating the pre-tension force vector

Building the stiffness matrix

Calculating the internal force system and axial forces

Recap of the main loop logic

Updating the results plot - phase 1

Updating the results plot - phase 2

Updating the results plot - phase 3

Using Pandas DataFrames to represent our data

Visualising deflection and axial force data in Blender

Model generation in Blender

Solving the antenna tower

Saving and exporting all simulation data

Building a results viewer notebook

Section 6 overview

Simulation initial geometry in Blender - Part 1

Simulation initial geometry in Blender - Part 2

The relationship between form-finding and pre-tension

Procedural modelling with geometry nodes [Optional]

Section 7 overview

Accommodating different cable types

Generating initial geometry and pre-tension

Analysis iteration 1 - Establishing pre-tension

Analysis iteration 2 - Adding props and stay cables

Section 8 overview

Form-finding the initial geometry

Roof pre-tension simulation

Full structure pre-tension simulation

Applying load to the pre-tensioned structure

Course wrap up

Blender data-viz - Structure setup & force data

Blender data-viz - Blocking out the code

Blender data-viz - The transformation matrix

Blender data-viz - Generating materials from force data

Learn how to combine parametric modelling, exploratory form-finding and iterative analysis techniques to simulate 3D tensile structures.

Modelling and Analysis of Non-linear Cablenet Structures using Python and Blender

In this course, you’ll build an iterative numerical solver for cable and truss structures that exhibit geometric nonlinearity due to large deformations. This course focuses on building the understanding and tools to analyse structures that undergo large deflections when loaded. Large changes to the geometry of a structure can alter the internal stress distribution. This is known as geometric non-linearity and requires a more sophisticated solution strategy. We’ll place particular emphasis on cable and catenary structures as these are classic examples of structures whose deformation under load can lead to geometric non-linearity.

Deriving a linear heavy cable equation

Accounting for cable self-weight

Problem-specific boundary conditions

Solving for max cable tension

What is non-linear structural behaviour?

Large deflections and geometric non-linearity

An iterative solution strategy

The linear stiffness matrix

Additional force due to large deflections

The local non-linear stiffness matrix

The global non-linear stiffness matrix

Initial setup and data import

Plotting the initial configuration

Blocking out the main convergence loop

Building the transformation matrices

Adding pre-tension to each member

Solving for displacements

Updating the internal force system

Building a convergence test function

Calculating axial forces

Allowing for smaller external force increments

Generating a text summary output

Adding self-weight calculation

Plot setup and data selection

Plotting the undeformed structure

Building a colour scale

Plotting the deformed structure

Adding axial force labels

Plotting the applied forces

Plotting the reactions

Exploring the convergence behaviour

Modelling the cable with large axial stiffness

Introducing non-linearity by reducing the axial stiffness

Linear vs. Non-linear comparison for a simple truss

Simulating initial catenary geometry

Basic geometry data export

Exporting cable definitions

Exporting restraint data

Exporting force location data

Section 9 overview

Modifying our code for different element types

Analysing a combined cable and bar structure

Removing slack cable elements

Antenna tower - modelling and analysis

Course wrap up & Certificate of Completion

How can Blender help us?

Downloading and installing Blender

Blender overview and interface

Object versus edit mode

Rectilinear modelling

Organic modelling

Build an iterative solution toolbox to analyse structures that exhibit geometric non-linearity due to large deflections.

Non-linear Finite Element Analysis of 2D Catenary & Cable Structures using Python

This course is for anyone who wants to understand multi-degree of freedom (MDoF) structural dynamics. The course is built around the theme of seismic analysis and determining the response of structures to earthquake-induced ground motion. In reality, that’s just one form of excitation; when you complete the course, you’ll be able to handle ground motion as well as any directly applied dynamic loads such as wind loading or blast pressure waves, for example. Once you complete this course, you’ll have a toolbox full of dynamic analysis tools and the knowledge and confidence to apply them to your projects.

Course prerequisites and do I need to know Python?

Getting your coding environment set up

El-Centro N-S ground acceleration record (.csv)

20 Largest Earthquakes in the World as of September 2021, USGS

Overview of earthquake ground motion

Build the knowledge and tools to decode the dynamic response of real-world structures to real-world loads.

Multi-Degree of Freedom Dynamics, Modal Analysis and Seismic Response Simulation in Python

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Course Bundles

The Direct Stiffness Method Course Bundle

The Structural Dynamics Course Bundle

The 2D and 3D Beam and Frame Analysis Course Bundle

The Getting Started in Structural Analysis Course Bundle