Dear Reader,

Happy Easter: I want to first of all wish a Happy Easter to christians all over the world who are celebrating the death and rising of Jesus Christ during this period. I hope you do get time to reflect and enjoy. In my personal family, we are doing the same, and for those who are non-christians, I hope you take the season to rest and recharge your batteries.

Welcome to new subscribers: In the last week, I had 20 new subscribers join the CM Videos Insider Group. To those new members of this family, you will therefore be receiving this newsletter as the first from me. I excitedly welcome you to the Group and I hope you keep in touch with me with questions and the like of any sort of support you need from me. We are here to help you create effective computational modelling solutions to any existing computational challenge you are grappling with. Hence, I am thrilled that you are here.

This week, being the Easter week, I will offer a short reflection as I would not want to take too much of your time. Here are the issues I am going to reflect on:

1. Technical Reflections: The Mathematics of Element formulation
2. Inspiring YouTube Videos: Is it RVE or Unit Cell?
3. Quote for the week: Your mind and empty glass!

Technical Reflections

The Mathematics of Element Formulation

One of the chapters in my FEM textbook which I authored in 2018 is titled exactly as the above: The Mathematics of Element Formulation. It is also a topic of a lecture that I give as part of my MSc class on Finite Element Applications. This is an aspect of finite element modelling that most users do not always engage with as the focus always is about choosing existing elements within the element library and using same to do your modelling. A lot of users do not really know that the behaviour of an element is defined by a mathematical formulation. This is similar to material models that drive the mechanical (material) behaviour of materials in a finite element scheme.

Definition wise, let us consider the following perspective of the Mathematics of Element formulation:

In the above definition, here are some things that characterize element formulation (highlighted above in bold)

• Lagrangian arguments: This refers to a polynomial description of the behaviour of an element which defines consistently the behaviour of such element. It involves polynomial interpolations.
• Shape functions: This is a polynomial description used to perturb nodal behaviours according to a prescribed boundary condition. It is the bedrock of element formulation.
• Isoparametric natural coordinates: This is a local coordinate system which defines what an element does at the element level. It takes values between -1 and +1.
• Mapping function: This is a mathematical relationship that connects the behaviour of an element at the isoparametric natural coordinates to the cartesian (global level) coordinate system. Element behaviours are defined such that with a mapping function, one can interconvert cartesian coordinates positions to isoparametric natural coordinates system and vice versa.
• Displacement,s strains, stresses, etc: This are the objective of most FEA slutions. These are derived based on formulations of an element, and hence making it very powerful.

Modern FEM solvers implement these as a standard, thereby making it possible to predict element behaviour within an FEA solution.

If you are interested in these sort of discussions and would want me to make a video exploring this issue further, then send me a direct message on my social media platforms (see foot of this email.

Inspiring YouTube Video

Is it RVE or Unit Cell?

This section is a new addition to my newsletter features with a view to highlighting videos that I have seen, and really enjoyed within the week. The focus will always be computational modelling issues or allied matters that affect the welfare and progression of students at MSc and PhD levels.

I filmed and published this video a while ago. I really liked it and it took me a long time to edit it properly and make sure the story I tell with it was understood. Here is the video, titled: Unit Cell or RVE Modelling: How to know which one to use?

The video was aimed at clearing the common confusion between Representative Volume Elements and Unit Cells. I defined these and established conditions in which an RVE is preferable to use over a Unit Cell. If you have ever wondered which is which and how do you determine what RVE or Unit cell to use for your modelling problem, then it may be worth your while to watch the above video. Please let me know if you find the video helpful and what you use for your modelling problems - RVEs or Unit cells?

Quote for the week

Your mind as an empty glass

My quote for the week is taken from a podcast I listen to regularly hosted by Andrew Wommack. He teaches about christian principles for life. The quote goes as follows:

It is possible that the quote actually originates from someone else but I first heard it from Andrew. It is so important for one to consider what goes into ones mind. The phrasing of the mind as an empty glass is important as it makes you realize that whatever you are thinking of now has been allowed to go in there. Things do not just pop into our mind, we actually have to open our minds to welcome those thoughts.

As a result, we must be carefully what we allow into our minds. As a student of computational modelling, it is easy to say to yourself "I will never finish that modelling" or "I am not good at coding" or "If only I paid attention to when this concept was taught, I would not be struggling now." Although all of these are well meaning, they can also start building self-doubt in your and this is not good.

I am taking this as my quote for the week just to help you understand that you are the gateway of what goes into your mind. If you want to see positive outcomes in life, then think positive things. If you make this a habit, the accummulation of such positive thoughts will manifest a life of such great outcomes and outputs that you would wonder how did I get here.

That is it for this week's newsletter. I hope these reflections bless you. If you enjoyed them, then do recommend to your friends to join the community through this link:

Take care and catch you next week.

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