# How to solve a Finite Element problem using hand calculations

Basically, when we want to determine the forces and displacements in a certain structure using Finite Element Analysis (FEA), what we are doing is creating a system of equations that relates the stiffness of the elements to the displacements and forces in each node. When we run a simulation, we do not see all the calculations. For that reason, today I want to illustrate a simple case that can be easily solved by hand applying that methodology.

Before getting started, just think of a spring. Everyone has come across the Hooke’s law at a certain point during school. It states that the force in the spring is proportional to a constant “k” multiplied by the variation in length of the spring. FEA follows the same principle, but in this case the “k” constant is the stiffness matrix and the variation in length is a vector of displacements and rotations, depending on the case.

Let’s study a simple static case. Our structure consists of two bar elements connected at a common node, where a load “P” is applied. The other two nodes have both horizontal and vertical displacements constrained (see the boundary conditions). For this particular case, the reactions in nodes 1 and 3 and the displacements of node 2 are requested. I have solved the problem by hand following a few steps that, based on my experience, can be generalised for more complex problems. Pretty much, the summary of the methodology is: Continue reading

# D is for “Ductile Damage”

The FEA dictionary is back and it’s time for letter D! Today I will introduce you to one of the methods to introduce damage in your material models.

Although it was created based on the failure of metals, this damage model can be used to introduce the degradation of mechanical properties for other types of materials. This option is available in Abaqus/Standard and Abaqus/Explicit and it requires the definition of the ideal elastic-plastic behaviour of the material, a damage initiation criterion and a damage evolution response. Please note that if any of the requirements cited before is not defined, the material properties will not be degraded.

In Abaqus there are different options for the damage initiation criterion and basically they can be classified as follows:

• Criteria for fracture of metals (ductile and shear).
• Criteria for necking of sheet metal.

# A is for Abaqus

Happy New Year everyone! After a well deserved Christmas break I’m back with some more engineering topics. In this occasion I want to introduce a new series of brief posts about Finite Element Analysis. The idea is to cover one topic for each letter of the alphabet (i.e. from A to Z). Let’s get started!

Motivated by the “A-Z Challenge” that I followed for the first time thanks to Dr David Jesson, the idea of doing something similar has been growing in my head for some time. However, in this case I won’t be writing a post every day but, hopefully, once a week a new one will be published.

I had some doubts about the topic, but after meeting some of the members of the Formula Student Team of the University of Seville (Spain), I thought it would be a great idea to do some kind of simple Finite Element guide. In particular, this guide will be focused on the commercial package Abaqus. Some of you might be wondering why I’ve chosen this particular software, and the reason is pretty obvious: it is one of the most used FE packages in industry and loads of students struggle to understand how it works, especially if their first experience with FEA involved Ansys. Don’t get me wrong, I started using Ansys as well and I don’t want to give the impression that I have a problem with it. The thing is though, that a lot of people tend to learn how to model things in Ansys by heart and because of that, they won’t be able to reproduce the same models in other packages.