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Analytical techniques are great for modelling the simplified behaviour of plate and shell structures, but we quickly run into their limitations when we stray beyond the limiting assumptions that the models are built upon. This is where finite element modelling comes into its own. In this course, we begin our exploration of finite element analysis of plate and shell structures by building our own solver based on the incredibly versatile Reissner-Mindlin theory. This approach will ultimately allow us to model both thick and thin plate and shell elements, resulting in an extremely versatile and accurate analysis pipeline. Building your own solver will give you a much deeper understanding of the underlying theory. That said, we’ll also cover how to implement the same solutions using OpenSeesPy and Pynite - two free and open-source Python libraries. To complete our plate modelling and analysis toolset, we’ll also cover mesh generation using GMSH, another incredibly powerful open-source meshing library. Once you’ve completed this course, you’ll have a complete workflow for the analysis of plate structures, backed by a fundamental understanding of the Reissner-Mindlin theory that powers it all! Our full journey into plate and shell modelling will span two courses. In this course, part 1, we’ll focus on plates. In part 2, we’ll build on what we’ve learned here and expand our study shell structures. 

Welcome to the course - roadmap overview

Housekeeping - Python, prerequisites and tips for success

Plate theories and why Reissner-Mindlin?

High-level primer - what are we trying to do?

Section overview - The Mechanics of Plate Elements

The displacement and strain fields

Relating stress and strain - the constitutive matrix D

From stresses to stress resultants

The role of shape functions

The strain-displacement matrix, B

The Jacobian’s role in calculating B

Pause, recap and regroup

Section overview - Virtual Work and Calculating the Element Stiffness Matrix

How Virtual Works leads to the element equations

A primer on numerical integration

Numerical integration applied to our element

Setting up our stiffness matrix calculation

Calculating an element stiffness matrix

Calculating the shear and bending stiffness

Calculating the equivalent nodal force vector

Section overview - Expanding to a full plate element solver

Procedurally generating a rectangular mesh

Defining plate constraints

Defining the self-weight force vector

Building the structure stiffness matrix

Solving the system and extracting reaction forces

Plotting the plate displacements

Building an evaluation grid for stress resultants

Calculating the moments and shears

Visualising the plate bending moments

Extracting shear forces

Visualising the plate shear forces

Adding strip and edge masking to the shear plot

Adding magnitude clipping to the shear plot

Building an interpolation utility function

Section overview - Benchmarking against OpenSeesPy and Pynite

Building an equivalent OpenSeesPy model

Extracting OpenSeesPy displacements and reactions

Extracting OpenSeesPy moments and shears

Visualising OpenSeesPy moments

Visualising OpenSeesPy shears

Building an equivalent Pynite model

Extracting displacements and reactions from Pynite

Extracting moments and shears from Pynite

Visualising Pynite moments and shears

Qualitative comparison across models

Max-displacement parameter sweep across models

The role of shear-locking

Adapting for shear-locking and comparing again

Section overview - Meshing with GMSH and Python

Generating a QUAD mesh with GMSH

Visualising the custom mesh

Correcting the element node order

Implementing mesh openings

Implementing specific nodal positions

Converting our code to a utility function

Section overview - Custom mesh finite element analysis

OpenSeesPy custom mesh plate analysis

OpenSeesPy custom mesh deflection benchmark

Custom mesh Reissner-Mindlin plate analysis

Custom mesh analysis results - reactions

Custom mesh analysis results - deflected shape

What's going on with our deflection?

A plan for fixing our Reissner-Mindlin element

Section overview - Eliminating zero-energy displacements

The substitute transverse shear strain matrix - part 1

The substitute transverse shear strain matrix - part 2

The natural shear interpolation matrix

Modifying shear stiffness for the assumed transverse shear strain field

Implementing point loads in our custom FE solver

Implementing patch loading in our custom FE solver

Wrapping up and what next?

An analysis pipeline for thick and thin plate structures, a roadmap from theory to toolbox

In this course, you’ll learn how to unlock the enormous potential of Blender as a tool for engineering modelling and analysis. Over the years, Blender has popped up in various EngineeringSkills courses as a structural modelling and visualisation tool. Now, we’re going to take the next step and build a custom addon that will streamline our modelling and analysis workflow. You’ll learn how to use Serpens, the intuitive and user-friendly node-based development addon that has revolutionised addon development in Blender. We’ll combine this with custom scripting using Blender’s Python API to develop V1 of the StructureWorks addon. Once you complete this course, you’ll have built an addon that turns Blender into a 3D truss analysis app, but more excitingly, you’ll be more than capable of extending it way beyond what we cover in the course. Once you’ve built your first addon, you’ll be hooked!

Welcome and course overview

A look behind the scenes

How to take this course

Getting help and community resources

Blender and Serpens setup

Visual Studio Code setup for Blender

Saving your work (and your sanity!)

Section overview - Serpens 101

Serpens 101 - The basics

Implementing a basic N-panel

Triggering action from the user-interface

Refactor with function nodes

Nodes versus Python scripts

Exporting your addon

Section overview - Itemising structure elements and nodes

Setting up a nodes collection

Building the nodes collection update loop

Building the update logic for elements

Sub-panel setup

Building the node list table

Building the node coordinate table

Implementing row select functionality for nodes

Building the element number table

Building the element definition table

Implementing row select for elements

Section overview - Building the materials library

Getting our material properties set up

Panel layout - material list layout

Panel layout - building user-input fields

Creating new structural materials

Updating the material list

Deleting materials from the library

Changing the active material

Updating material properties from user input

Synchronising structural and Blender materials

Refactoring to use portals for reduced duplication

Updating material display properties

Assigning specific materials to active elements

Selecting elements by material (and deselecting)

Section overview - Building the sections library

Getting the Serpens properties setup

Full panel layout

Creating new cross-sections

Deleting cross-sections

Changing the active cross-section

Updating the sections library based on user input

Updating cross-section display properties

Assign, select and deselect elements

Section overview - The Restraint Management Panel

Setting up the restraint properties

Building the restraint panel interface

Implementing the restraint toggles

Adding restraints to the collection

Clearing all restraints

Adding list manipulation controls

Implementing restraint sorting

Removing duplicate restraints

Section overview - The Applied Forces Panel

Setting up the force properties

Self-weight and nodal force inputs

Building the force display list

Adding and clearing all forces

Force list manipulation controls

Sorting forces

Consolidating force records

Section overview - Adding custom mesh assets to the scene

Creating force and restraint mesh assets

Force and restraint visibility properties

Setting up the mesh update node functions

Wiring the update restraint mesh nodes

Loading template force and restraint objects

Creating restraints in the 3D view

Wiring up the clear mesh function

Clearing restraints from the 3D scene

Updating the mesh update function for forces

Setting up the force mesh update function

Updating and clearing forces from the 3D scene

Implement restraint and force visibility toggle

Section overview - Implementing 3D truss analysis

Panel and property setup

Setting up the structural analysis

Collecting the data and blocking out our script

Validating and unpacking all input data

Review of truss analysis code - part 1

Review of truss analysis code - part 2

Packaging results back into Serpens properties

Implementing analysis reset

Section overview - Building data tables and a deflected shape

Results panel and visibility setup

Building row select functionality

Building the nodal displacement table

Building the axial force table

Building the reaction force table

Deflected shape UI and property setup

Setting up the deflected shape function

Writing the deflected shape generator

Deleting the deflected shape

Section overview - Exporting data

Setting up the model export panel

Building the export function

Unleash the power of Blender by building custom tools to speed up your workflows

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