Author Archives: Ignacio Carranza Guisado

Classic question about the use of a Cantilever beam for designing vehicle structures

Good afternoon everyone! I know it’s been a while since the last post but I’ve been (and still am) very busy with all kind of simulations, tests and writing papers and my doctoral thesis. Hopefully, I’ll manage to write some more articles during the summer! I recently had a conversation with some senior engineers from a F1 team regarding Cantilever beams and some erroneous assumptions which are commonly made, so I wanted to discuss it with you! Hope you enjoy this brief post!


A few weeks ago, I had the chance to speak with three top F1 designers and we had a chat about a certain question regarding the use of the Cantilever beam as a tool to design some vehicle structural components. First of all, let’s remind what this type of configuration is. A Cantilever beam is a structure which is fully constrained at one end, having a vertical load applied at the other end of the beam to study the effect of bending, as illustrated in Fig. 1.

cantilever1

Figure 1. Schematic of a Cantilever beam

This type of structure is very useful when designing certain components, since they can be simplified to this well-known beam, reducing the number of variables and being able to define simpler design targets. The thing is that usually, in reality, the components usually have some part of its length reinforced (e.g. thicker walls), so two questions arise: why is this non-homogeneous beam common and where should that reinforcement be placed?

We agreed that a lot of people answer very quickly that it should be placed at the free end of the beam, i.e. where the load is applied. According to these people, the reason for this is pretty obvious, since that end will suffer the greatest deflection (I will write another post soon where I derive this and discuss some ways to calculate it by hand!). Hence, if that region was reinforced, the deflection would be smaller and the structure would be better in terms of bending performance. But, is this true? Let’s have a thought.

Consider the structure from Fig.1 and try to analyse it with simple structural mechanics. Firstly, we need to determine the reaction forces and moment at the fixed end caused by load P. Applying equilibrium as shown in Fig.2, the following results are found:

cantilever2

Figure 2. Equilibrium applied to the Cantilever beam

cantilever4

Then, applying equilibrium to a portion “x” of the beam from the fixed end (see Fig. 3), the stress distribution can be easily calculated by applying, once again, equilibrium:

cantilever3

Figure 3. Equilibrium applied to a section of the Cantilever beam

cantilever5.PNG

While the axial stress is null and the shear stress is constant along the length of the beam, the bending moment depends on the position. This means that the maximum moment that the structure experiences is located precisely at the fixed end, rather than at the loaded point! Therefore, the fixed end is the region which suffers the most, resulting in designers adding extra material or other types of reinforcements in that area, in opposition to what other people mights have thought! If you don’t believe this, you can always hold a small stick in one had and apply a vertical displacement on the free end with your other hand: the stick will bend and break at the end that you’re holding!

My point with this post is that this simple question can be asked to you in an interview, and you should not jump into the first “logical” response that comes into your mind. Just spend some time thinking about the problem and you’ll see how basic structural mechanics can help you! And you thought you would never use all these basic theories you were taught at university…

About Tsai-Wu failure criterion

Predicting material failure is always a challenge, especially when it comes to composites and advanced materials. There are plenty of theories that try to provide a numerical approach to solve this complex problem, such as Maximum Stress/Strain Theories,¬† Hashin, Tsai-Hill or Tsai-Wu. Although all of them brought something valuable to the table, some of them don’t seem to be that precise when accurate results are needed. In these terms, Tsai-Wu is my least favourite criterion and I’ll explain the reasons for that.


First of all, Tsai-Wu is an interactive failure criterion for composite materials. This means that the theory takes into account the interaction of different stress components in order to predict failure. Basically, the criterion uses equation 1 (subjected to the condition given by equation 2) to calculate an index and, if its value is one, then it means the material is failing. Please note that i,j=1,2,…,6, where subindices 1 to 3 represent normal stress components and 4 to 6 are shear stress components. In the original publication, authors explain how the different coefficient can be determined through experimental tests (e.g. compression, tension, biaxial…). So far, so good.

01

Equation 1

02

Equation 2

Problems start when people adapt this approach to introduce failure in Finite Element (FE) analyses. This theory does not include any damage evolution, so if you define failure as soon as the index reaches 1, then elements will be deleted from the model straight away. To be fair, if you are just trying to get estimations for composites, this is not that bad, since they are supposed to fail as soon as they reach a certain level of stress. The main issue is when users use this interactive failure criterion for other materials. For example, for a three dimensional case, equation 1 can be rewritten as follows:

06

Equation 3

Now consider a material which has similar strengths in the 3-principal axes and assume that the positive and negative shear strengths are equal. Then, using the expressions from equation 4 (where the parameters represent the tensile, compressive and shear strengths), we know that: F1=F2=F3; F11=F22=F33; F4=F5=F6=0; F44=F55=F66.

03

Equation 4

There are an infinite number of ways to determine the interactive coefficients so, how do we solve this problem? Some people suggests biaxial tests but another effective way to overcome this issue is to make the following assumption (as suggested in literature):

04

Equation 5

Firstly, this assumption satisfies the stability condition (equation 2) and secondly, it proves to be quite satisfactory for composite materials. Generalising this idea, we find the following:

05

Equation 6

Okay, so now consider that our material exhibits an elastic-perfectly plastic behaviour in compression. This would mean that the specimen should keep deforming under constant load after the yield (or maximum) compressive stress was reached. Hence, the criterion would predict failure once that value was reached, and no plastification prior to failure would be considered. For instance, consider uniaxial compression once the yield stress is reached, as shown in Figure 1:

Capture

Figure 1

Using all the equations which were introduced before, we have:

07

Equation 7

Therefore, in FEA elements would be deleted after that point, whereas in reality we would expect the material to keep deforming. That being said, more problems appear in cases where the structure is subjected to mixed loading conditions, since the criterion would then predict premature failure.

This post does not intend to state categorically that this theory is useless, that is not what I mean at all! But lately I have seen companies offering FE services using this type of approach, not taking into account that the material under consideration might not be compatible with the assumptions made for this criterion. I just needed to highlight this bad practice that I’ve noticed, so sorry if I’ve offended anyone!

Speed Read F1

Every year, with the start of the Formula 1 season, a lot of people ask about the rules, concepts, technology and history of the sport. For that reason, Stuart Codling recently wrote a new book called “Speed Read F1”, which tries to cover the keys to understand the basics of Formula 1. If you want to find out more about this book, keep reading this review!


Believe it or not, I first heard about this book on Twitter, where a considerable amount of motorsport journalists shared their excitement about the release of this book. I was curious so I decided to check who the author of this book was and I was shocked when I found out that it was written by Stuart Codling, who is a well known automotive and motorsport expert (you can find his articles in prestigious magazines such as “F1 Racing”). After that, there was no doubt I needed to get my hands on this book!

Let me start the review with the structure of the publication. The book is divided in seven sections based on different aspects of the sport: Technology; Drivers; Rivalries; Racing Circuits; Flag to Finish; Staying Alive; Taking Care of the Business. From my point of view, this division is very clever and helpful for new fans and people who just want to learn the basics of something in particular. Although the book is 159 pages long, it is written in a way that encourages the reader to finish it as quick as a Lewis Hamilton’s fast lap. In addition, another thing that I particularly enjoyed is that every subsection counts with three brief paragraphs on the left margin where the reader can find interesting information about something funny, history and a person of interest (always related to the main topic of the subsection).

Now, with regards to the content itself, I must admit that I got hooked from the beginning, which covers all the main technical aspects of the sport… but that may be because of my engineering background and my previous knowledge of F1. Besides, the chapter about rivalries provides amazing facts about old drivers that I never got the chance to see on the track, so I am sure almost everyone will learn at least one new thing while reading this section. Furthermore, another detail that I would like to highlight is that after each chapter, the author includes a glossary. This glossary is a very useful F1 dictionary that new fans will definitely take advantage of, mainly because it explains specific topics in a very simple way. Now you will be able to understand every word you hear during a Grand Prix on TV!

That being said, I must warn you that sometimes there is a bit too much of information in a very reduced amount of words. If you are not used to scientific papers or technical books you may struggle and will probably need to read certain paragraphs a few times. Also, as a non-native English speaker, I found it curious that in the book some words are written in British English whereas others are written in American English, such as “carbon fiber” (American) instead of “carbon fibre” (British). This is nothing bad, don’t get me wrong, but it made me pay more attention whenever I read something like that, especially about materials… And I found something that is not an accurate fact about composite materials. The author, in order to provide some background, gives a definition of carbon fibre that only applies to certain types of composites… I know this is a silly comment, but I am very picky when it comes to materials science!

Overall, I think it is a nice book to read if you are new to the sport or just a casual fan. However, I wouldn’t recommend it to people who have followed Formula 1 for a long time. From my point of view, this book should target an audience which is willing to get involved in this motorsport world. So, if you are one of these new fans, I definitely encourage you to get a copy of the book. After reading it (and it is very easy to read!), “rookies” will be able to speak about most things F1 related with people who have been enjoying the sport for ages. You won’t need to be asking all sort of basic questions anymore!

Coding subroutines in Abaqus

If you are an advanced Abaqus user, I am sure you have heard a word which some people try to avoid at all costs: subroutines. Today, I write about them as well as about my recent experience coding one for my research.


First of all, lets start with the main question: what is a subroutine? It is a script that, when run in parallel with the Finite Element (FE) model, allows users to request features which are not defined by default in the commercial software Abaqus. This FE package recognises a lot of different types of subroutines for both implicit and explicit simulations, depending on the information that we want to include, recalculate, modify, request… In other words, subroutines are useful when we want something that is not already available within the software and we need it in order to produce acceptable results.

Consider, for instance, that we were trying to simulate the response of a certain material, but the material model which was available in Abaqus did not quite reproduce the correct behaviour. What could we do then? The first option would be to contact Dassault Systemes to ask if they had any kind of expansion (with its corresponding extra cost, not too many things are given for free these days I’m afraid); sometimes, since a lot of users request the same thing, it is the company itself the one that creates the official subroutine. This option would save time and effort, but it would also affect our wallet. The second option would be to create a new material model from scratch. How could we do that? Well, we would need to code a UMAT (implicit) or a VUMAT (explicit) subroutine. In order to do so, we would need to learn how to code in Fortran, which is the only language supported by Abaqus (I know, this is a bit of a pain since Fortran is basically obsolete, but hey! It’s always good to learn something new!). We would also need to install two compilers and link them to the FE package, which once again is not straight forward (don’t worry, I’ll try to write another post to explain this). Some people might say that giving up would be the third option, but to me that attitude would be unacceptable, so don’t you dare! Read more

Spanish university to collaborate with the development of intelligent materials

The University of Alicante (Spain) is taking part in a project that will develop intelligent materials for aerospace, automotive and transportation industries. The main aim will be to improve the safety of occupants and the durability of the components.


Researchers from the Department of Civil Engineering from the University of Alicante and the tech company Applynano Solutions are carrying out this project known as MASTRO, which stands for Intelligent Bulk Materials for Smart Transport Industries. The project is part of the Horizon 2020 programme, which is the biggest investment system for R&D in Europe.

Their goal is to develop intelligent materials for the transportation sector. In particular, the aerospace and automotive industries will be the main targets. Amongst other innovations, ¬†these materials will be able to monitor their own deformations and they will also be capable of heating and defrosting their surfaces. Besides, thanks to their capability to repair and protect themselves from damage, they will improve their efficiency, their durability and users’ safety. At the same time, manufacturing and maintenance costs will be reduced, as well as emissions.

In order to develop these materials, different matrices will be used, including polymers, concrete and carbon nanomaterials. Their functions will be based on three processes: the variation of electric resistivity when a material is subjected to a mechanical load, the relation between the heat that is generated and the electric flux, and electrostatic discharge.

One the one hand, the Spanish university will work on the development of the function related to perception of strain and damage on structures made of reinforced concrete. In addition, the previously mentioned institution will also focus on the heating of surfaces made of asphalt and concrete in order to avoid the formation of ice.

On the other hand, Applynano Solutions will work on the development of the carbon nanomaterials, the manufacturing of composites and the production of prototypes.

These are exciting news for the European research community, since not only Spain but also institutions from United Kingdom, Portugal, Italy, France, Germany and Sweden will collaborate with the MASTRO project. Hopefully, we’ll see encouraging results in the near future! I’ll keep you updated!

How to receive automatic notifications when your FE simulations are done

If you are a regular Abaqus user, I am sure that eventually you will need to run models for long periods of time. It can be quite annoying to go back to the office just to check if the simulation has finished to then find out that it is still running. For that reason, I’ve coded a simple python script that sends an automatic e-mail to the user once the simulation is completed or aborts due to errors.


While you run FE models that take a huge amount of computational time to finish, it is likely that you will be working on other things, such as experimental tests, reports, meetings and so on. Obviously, we want to check our results as soon as they are ready, but in order to do so we need to be checking our computer every now and then. This can be particularly annoying when you leave a simulation running for a few days and you are doing things out of the office. Hence you need to go and check if the model is done… and then you realise it’s still there, calculating more stresses and strains and that your trip to the office was a waste of time. To overcome this problem, I decided to create a python script to send a notification directly to my e-mail every time my analyses finish. I will try to explain you the basics so you can use this code on your computer. Read more

The Secret Science of Superheroes

Do you like science? Are you a comic geek? If your answer to both questions is “yes”, then “The Secret Science of Superheroes” is your book!


Last August I got myself an autographed copy of “The Secret Sicence of Superheroes”, thanks to Dr David Jesson and Dr Mark Whiting (University of Surrey) and I must say I don’t regret it at all! The book is distributed by the Royal Society of Chemistry and it was edited by Mark Lorch and Andy Miah. When I first heard about this book, Dr David Jesson told me that the whole thing was completed in just one weekend during an event in Manchester and that each chapter was written by a different author and it related a specific superheroe topic with the author’s field of expertise. Interesting, right?

I would review every single chapter, I really would, but… then you wouldn’t read the book! So, I’m just going to talk very briefly about the things I enjoyed the most. Basically, the text is written for a general audience, introducing the scientific concepts as the authors try to make their point. Read more

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