# FINITE ELEMENT ANALYSIS

## The Direct Stiffness Method for Truss Analysis with Python

### Build your own finite element truss analysis software using Python and tackle large scale structures.

After completing this course…

• You’ll understand how to use the Direct Stiffness Method to build complete structural models that can be solved using Python.
• You’ll have your own analysis programme to identify displacements, reactions and internal member forces for any truss.
• You’ll understand how common models of elastic behaviour such as plane stress and plane strain apply to real-world structures.

## Beam & Frame Analysis using the Direct Stiffness Method in Python

### Build a sophisticated structural analysis software tool that models beams and frames using Python.

After completing this course…

• You’ll understand how to model beam elements that resist axial force, shear forces and bending moments within the Direct Stiffness Method.
• You’ll have your own analysis software that can generate shear force diagrams, bending moment diagrams, deflected shapes and more.
• You’ll understand how to model rotational pins within your structures, inter-nodal distributed loading and realistic flexible supports.

## 3D Space Frame Analysis using Python and Blender

### Develop tools to model and analyse complex 3D space frame structures using Python.

After completing this course…

• You’ll understand how to apply the Direct Stiffness Method to solve 3D space frame structures.
• You’ll have your own analysis programme to identify displacements, reactions and internal member forces for any 3D space frame.
• You’ll be able to use Blender, a powerful open source 3D modelling software to build, visualise and export your structural models.

## Finite Element Analysis of 3D Structures using Python

### Build your own complete 3D structural analysis software in Python using the Direct Stiffness Method

After completing this course…

• You’ll understand how to expand the direct stiffness method to full 12 degree of freedom beam elements in 3D space.
• You’ll have developed a complete 3D finite element analysis solver to simulate structures consisting of beam and axially loaded bar elements.
• You’ll have the skills to efficiently build detailed structural models in Blender and export these for analysis in your own Python solver.

## Finite Element Analysis of Continuum Structures in Python

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

After completing this course…

• You will have the tools to analyse continuum structures using your own Isoparameteric Finite element Python code, developed from the ground up.
• You will understand how the plane stress and plane strain approximations allow us to analyse 3D structures accurately with 2D planar models.
• You will be able to use open source tools to generate structural models and mesh data that can be analysed with your FE code.

## Non-linear finite element analysis of 2D catenary & cable structures using Python

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

After completing this course…
• You will understand the concept of geometric non-linearity and when it should be considered.
• You will understand how to modify the axially loaded element stiffness matrix to account for large deflections and changes in geometry.
• You will have implemented a Newton-Raphson iterative solution algorithm that seeks to converge on the deformed state of the structure.
• You will have a workflow that leverages open-source modelling tools in Blender to quickly generate the initial structural geometry.

## TUTORIALS

### 3D Truss Calculator – Quick Start Guide

Welcome to this quick start guide on how to use the 3D truss analysis toolbox. In this tutorial, we’ll work through the solution of a sample 3D space frame (pin-jointed) structure. We’ll determine reaction forces, axial forces and nodal displacements. By the end of this tutorial, you’ll be comfortable using the toolbox to analyse your own structures. In the video accompanying this tutorial, we’ll also use the Blender modelling template file provided to model and analyse a structure from scratch. Like the 2D toolbox, students in particular, should find it helpful as a quick and easy tool for generating structural response data.

### Free Truss Calculator – Quick Start Guide

This is a quick start guide for our free online truss calculator. Follow this short text tutorial or watch the Getting Started video to quickly orientate yourself with this handy free tool. We’ll walk through the process of analysing a simple truss structure. By the end, you’ll be comfortable using the truss calculator to quickly analyse your own truss structures. Students, in particular, should find it helpful as a quick and easy tool to test manual solutions against.

### Finite Element Analysis and Structural Behaviour Modelling Case Study

In this post we will use the Tintagel footbridge as a case study to explore structural behaviour and show how we can build up an understanding of the structure through analysis of increasingly refined finite element models models. We’ll apply this iterative approach by starting with a simple beam model and incrementally working towards a full 3D finite element model. Throughout this post we’ll make use of finite element analysis codes developed in DegreeTutors courses.

### Truss Analysis using the Direct Stiffness Method

In this tutorial we examine the Direct Stiffness Method and work our way through a detailed truss analysis. By the end of this complete introduction, you should understand the basic ideas behind why the method works, how to implement it for truss analysis and you should understand the power and scalability of the technique. Once understood, the direct stiffness method opens the door to structural analysis of large scale complex structures.

# The Direct Stiffness Method for Truss Analysis with Python

## Build your own finite element truss analysis software using Python and tackle large scale structures

Play Video

The aim of this course is to equip you with the tools and knowledge to build your own truss analysis software using the Direct Stiffness Method. In this course you’ll develop a truss solver that can determine axial forces and deflected shapes for pin-jointed truss structures.

Understanding structural analysis theory and hand-analysis techniques is an essential requirement of any competent engineer. It informs our intuition of structural behaviour and provides a foundation from which we can analyse complex structures.

However, most large structural analyses leverage the speed of structural analysis software. And modern structural analysis software is dominated by matrix analysis methods like the direct stiffness method. In this course you’ll implement these techniques to build your own version of a structural analysis software.

You DO NOT need to be a Python programming guru to take this course. If you’ve taken any of the prerequisite courses – or even if you’re just familiar with basic programming ideas like functions, loops and variables that will be plenty to get you started.

# Beam & Frame Analysis using the Direct Stiffness Method in Python

## Build a sophisticated structural analysis software tool that models beams and frames using Python.

Play Video

In this course we’ll be focusing on building a beam and frame analysis programme in Python using the Direct Stiffness Method. Once you’ve completed this course you’ll have developed from scratch, your own structural analysis software tool that can generate bending moment diagrams, shear force diagrams, and defections for beam and frame structures.

Engineers today typically rely pretty heavily on structural analysis software. While understanding hand analysis techniques forms the foundation of our understanding of structural behaviour, once things scale up on real world engineering projects, finite element analysis software becomes incredibly useful. If you’re wielding these sophisticated tools, as a student or practicing engineer, it makes sense to have a good understanding of what’s going on behind the scenes.

This course follows on from our course on truss analysis using the direct stiffness method with Python. If you’ve completed that course, then this course is the natural next step. We’ll take our fundamental understanding of the direct stiffness method and supercharge it by expanding to consider beam elements resisting bending and shear. The code we develop in this course, will be able to handle, pinned members, inter-nodal loading and even flexible supports.

You DO NOT need to be a Python programming guru to take this course. If you’ve taken any of the prerequisite courses – or even if you’re just familiar with basic programming ideas like functions, loops and variables that will be plenty to get you started.

# 3D Space Frame Analysis using Python and Blender

## Imagine, build and analyse 3D space frames using the Direct Stiffness Method in Python

Play Video about 3D-Space-Frame-Analysis-with-Python V2 | DegreeTutors.com

In this DegreeTutors course, we leave the two-dimensional world and expand our horizons into the world of three-dimensional structural analysis! After completing this course, you’ll be able to turn a structure from your imagination, into a 3D model that you can analyse using the Direct Stiffness Method, implemented in Python.

We’re going to build on what we learned in our study of The Direct Stiffness Method for Truss Analysis with Python. We’ll expand the code developed in that course to accommodate 3D space frame structures.

You’ll see that expansion of the Direct Stiffness Method from 2D to 3D is readily achieved with some logical alterations to our code. You should only take this course after first completing the prerequisite course. This will give you the foundation you need to get the most from this course.

Once our analysis code is complete, we’ll turn our attention towards how best to generate the geometric data that defines our structure. For this we’ll turn to a powerful open-source 3D modelling tool called Blender . By harnessing some simple 3D modelling tools, we open the door to analysing the behaviour of any structure. We are limited only by our imagination! With its powerful 3D modelling tools and Python API, Blender is an excellent fit for our structural analysis workflow.

You DO NOT need to be a Python programming guru to take this course. If you’ve taken any of the prerequisite courses – or even if you’re just familiar with basic programming ideas like functions, loops and variables that will be plenty to get you started.

# Finite Element Analysis of 3D Structures using Python

## Build your own complete 3D structural analysis software in Python using the Direct Stiffness Method

Play Video
In this course we’re going to dive deep into the world of 3D structural analysis by building a 3D structural analysis programme using Python. After completing this course you’ll have built your own 3D finite element solver and have a workflow you can use to model and analyse complex 3D structures that would otherwise require expensive commercial software packages. Building on a family of Python-based structural analysis courses, this course will take your level of ability and self-reliance in structural analysis to yet another level by expanding to consider full 3-dimensional beam bending. In this 14.5 hour video course, we go beyond axially loaded 3D space frame structures covered previously, to build out a feature rich, general 3D solver that can simulate:
• Interaction between 6 degree of freedom axially loaded bar elements and 12 degree of freedom beam elements.
• Localised rotational releases in the form of pins.
You DO NOT need to be a Python programming guru to take this course. If you’ve taken any of the prerequisite courses – or even if you’re just familiar with basic programming ideas like functions, loops and variables that will be plenty to get you started.

# Finite Element Analysis of Continuum Structures in Python

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

Play Video

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. When you complete this course you will have built your own 2D Finite Element solver, but more importantly, you’ll understand exactly how it works and what every single line of code does!

Once complete, you can use your solver to show:

• deflected shapes
• normal stress and strain fields
• shear stresses and strains fields
• principal stress magnitudes fields
• principal plane orientations
• von Mises stress fields

We’ll build in the ability to simulate the influence of point load forces, distributed forces and body or self-weight forces. Once you complete this course you’ll have the knowledge, experience and confidence to extend your solver and add the new features that matter to you.

You DO NOT need to be a Python programming guru to take this course. If you’ve taken any of the prerequisite courses – or even if you’re just familiar with basic programming ideas like functions, loops and variables that will be plenty to get you started.

# Non-linear finite element analysis of 2D catenary & cable structures using Python

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

Play Video about Nonlinear-finite-element-analysis-of-2D-catenary-&-cable-structures-in-Python | DegreeTutors.com
After completing this course, you’ll have built an iterative numerical solver for cable and truss structures that exhibit geometric non-linearity due to large deformations.

This course focuses on building the understanding and tooling necessary to analyse structures that undergo large deformations when loaded. These large changes to the geometry of a structure can alter the internal stress distribution within the structure. This is known as geometric non-linearity and requires a more sophisticated solution strategy.

This course will build on the understanding developed in previous DegreeTutors courses and in particular our linear 2D analysis course, The Direct Stiffness Method for Truss Analysis with Python. It is strongly recommended that you complete this course first before tackling non-linear analysis.

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. However, the code developed can be equally deployed to flexible truss structures.

The tools developed in this course are not meant as a replacement for commercial non-linear solvers (we’re not going to be rebuilding SAP2000! :) – 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.

This course is divided into 9 sections:

• Introduction and course overview
• ‘Heavy’ cables – the linear solution
• Getting comfortable with non-linearity
• 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 in the same model

The final code will be capable of handling structures like the one pictured above that consist of a mixture of axially loaded cable (tension only) and bar (tension and compression) elements. Our solver implements an iterative algorithm, so a solution that converges is not always guaranteed! We’ll be leaving the relative comfort and certainty of linear analysis behind!

You DO NOT need to be a Python programming guru to take this course. If you’ve taken the prerequisite course – or even if you’re just familiar with basic programming ideas like functions, loops and variables that will be plenty to get you started.