## B is for “bar” and “beam” elements

New post about FEA! In this occasion, I bring you some theoretical background for two types of elements which are very useful for modelling certain structures: bars and beams.

Let’s start from the beginning. A bar is basically an element which can resist only axial loading. Therefore each of its nodes has one degree of freedom, i.e. a displacement along the longitudinal axis of the element. On the other hand, each node of a beam presents not only one but three degrees of freedom: displacement in the longitudinal axis, displacement in the transverse direction and rotation.

As you should already know, Finite Element Analysis requires the a stiffness matrix (K) so, in order to illustrate this, in this post I will show you how the K matrix can be derived for bar elements. Note that the process for obtaining the stiffness matrix of a beam element is similar but a bit more tedious.

## 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.

## The importance of checking contacts in FEA

This week I wanted to write a brief post regarding a very common problem that can be found when running and post-processing Finite Element models: the correct definition of contact algorithms.

During this week, I had a conversation with other engineers about some issues related to the TIED CONTACT definition. In these terms, any commercial FE package gives you the opportunity to define this type of contact in a relatively easy way: you select the nodes or surfaces (master and slave) and then the pre-processor shows some kind of symbol in order to highlight that the contact has been established. However, the symbols and the fact that you have followed the standard steps of the software do not mean that the parts are going to behave as expected. Continue reading “The importance of checking contacts in FEA”

## Modelling foam cores in LS-DYNA

It´s been a while since the last time I wrote about Finite Element Analysis. For that reason, this week I would like to express some of my concerns about two material models which are available in LS-DYNA for crushable foams.

Crushable foams are widely used in the aerospace and automotive industries due to their energy absorption capabilities and their low weight. This means that companies can take advantage of those properties in order to produce lightweight vehicles, improving the efficiency in terms of fuel consumption while making the structures safer for the occupants.

In these terms, original equipment manufacturers (OEMs) normally use foams as the core of sandwich structures, in order to combine the properties of different materials. Nevertheless, both the manufacturing process and the experimental tests are usually expensive and time consuming, and this can lead to non-profitable results. Because of that, FEA has become an extremely powerful tool for analysing and predicting the behaviour of structures. The fact that the set up of the FE models usually requires simple tests reduces the cost of the process, even more if we take into account that once the models are validated, they can be used for predicting other type of scenarios which would be extremely expensive to test in reality.

## About Hashin´s failure criteria in FEA

When using Finite Element Analysis (FEA) for studying composite materials, one of the most used failure criterion is the one which was proposed by Hashin in 1980. This theory is included in all the main FEA packages and, probably, you are more than familiar with this particular model. However, what you might not know is that the failure criteria that you are defining is not exactly the Hashin’s one. If you want to know why, this is your place.

Since the available failure criteria at that point presented some inconsistencies, in 1980 Hashin developed a new criteria which differentiated between failure modes. His theory considered four different ways in which the material could fail:

## FEA for beginners (Part IV): Material models

Every time you use Finite Element Analysis you need to assign a material model to all the components. Since there are plenty of them, one question arises: which one should you use for your particular case?

To begin with, there might be more than one material model which can provide an accurate solution to your problem. However, it is likely that one of them will present some advantages when compared to the others, such as computational time or the number of parameters which have to be defined. When you have spent time working with a certain kind of material (e.g. metals) you will have gained some experience that will help you choosing between different options whenever you face a similar Finite Element model. But, what happens when you are new and you don’t know where to start?

## FEA for beginners (Part III)

One of the dangers of FEA is that it provides results, even if they are wrong. Hence it is the engineer’s responsibility to critically analyse and validate them. In these terms, one of the most common rookie mistakes is “hourglass”. If you want to learn what it is and how to correct it, this is your place.

To begin with, let me introduce two different concepts: underintegrated elements and fully integrated ones. Underintegrated elements are only evaluated at one single integration point, whereas fully integrated ones have more than one. In order to illustrate this idea, Figure 1 is introduced.