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

In this course, we’re going to build a full Isoparametric Finite Element solver. This unlocks our ability to model and analyse any 2D structural form. When we combine our finite element analysis solver with knowledge of the theory of plane stress and plane strain, this course will equip you with the ability to model 3D structures using 2D finite element models. We’ll build in the ability to simulate the influence of point load forces, distributed forces and body or self-weight forces. When you complete this course, you will have built your own 2D Finite Element solver, but more importantly, you’ll understand precisely how it works and what every single line of code does! This will give you the knowledge, experience and confidence to extend your solver and add the new features that matter to you.

Introduction and course overview

What you should cover before this course

Section 2 overview

Bar stiffness using generalised coordinates

Bar stiffness using shape functions

Quad elements and shape functions

The strain-displacement matrix, B

The Jacobian Matrix, J

Calculating the strain-displacement matrix

Accounting for plane-stress/strain

The equivalent surface force vector

The equivalent body force vector

Section 3 overview

Gauss numerical integration scheme

Numerical integration in 2D

Calculating the element stiffness matrix

Stiffness matrix convergence

Section 4 overview

Generating a simple quad mesh in Blender

Exporting mesh data from Blender

Exporting support and point load data

Importing support, loading and mesh data

Section 5 overview

Setting analysis parameters and plotting the structure

Building the global force vector

Defining the element stiffness matrix

Assigning the element stiffness coefficients

Building the structure stiffness matrix

Solving the structure

Visualising the deformed structure

Generating detailed text output

Euler-Bernoulli deflection validation

Section 6 overview

Generating the stress calculation grid

Visualising the stress calculation grid

Calculating the strain and stress fields

Visualising the normal stress distribution

Building normal strain/stress contour plots

Building shear stress/strain contour plots

Building a stress/strain interpolation query function

Visualising stress distributions at a vertical section

Euler-Bernoulli stress validation

Section 7 overview

Implementing self-weight in our analysis

Correcting self-weight reactions

Distributed loading - Interpolation limits

Distributed loading - Data export from Blender

Importing distributed loading data

Surface force vector - Setup

Surface force vector - Integration

Updating the global force vector and validating

Orthogonal surface forces

Section 8 overview

A recap of principal stresses

Calculating principal angles and stresses

Sorting principal stresses

Identifying max ten/comp principal stresses

Visualising the principal stress magnitude field

Visualising the principal stress vector field

Combining the magnitude and vector fields

The von Mises failure theory

Visualising the von Mises stress field

Perimeter stresses and updating plot edges - Planning

Perimeter stresses and updating plot edges - Coding

Section 9 overview

Generating 2D geometry in Blender

Meshing complex geometries

Exporting an irregular mesh

Generalising our solver

Stress distribution masks

Course wrap up

[BONUS] Cantilever model and analysis walkthrough

Understanding the 2D stress element

The stress transformation equations

Visualising transformation equations

Principal stresses and principal planes

Finding maximum shear stresses

2D stress analysis worked example

Stress analysis Python worked example

Understanding Mohr's circle of stress

Mohr's circle worked example in Python

Use the Isoparametric Finite Element Method to build an analysis tool for 2D structures in Python.

Finite Element Analysis of Continuum Structures in Python

Finite Element Analysis of Plate and Shell Structures in Python

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

Frequently asked questions