The Transformative Power of Dirichlet Boundary Conditions in FEM | Rulers of the AI eco-system | Standing on Shoulder of Giants

Published about 2 years ago • 7 min read

Dear Reader,

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Aim of the newsletter: The aim of this newsletter is to offer reflections on computational modelling issues whilst also dropping some background the scene information about CM Videos YouTube channel and CM Videos Ltd. Also, I will offer you reflectiosn on my self-development journeys as well as my quote of the week where again I offer some insights into ideas that motivate me. I also offer discounts to subscribers whenever I launch products from the CM Videos Ltd. If you know anyone who would benefit from these, then do forward this email to them. Thank you.

Focus for this newsletter: For this week, I am discussing another principle of FEM that is taken from my book and something I feel needs computational modellers like you to consider. Here are the issues I am reflecting on today:

  1. Technical Reflections: The transformative power of Dirichlet Boundary Conditions in FEM
  2. Behind the Scenes at CM Videos: Techno-utopians rule the AI eco-system.
  3. Scholarly Tip of the week: Why you need to stand on Shoulder of Giants

Technical Reflections

The Transformative Power of Dirichlet BCs in FEM

What is a Dirichlet Boundary Condition: Users of Finite Element Modelling understand the importance of Boundary Conditions. What is not always clear is if these users understand the necessity of accurate representation of BCs for models they create. In my view, beyond the quality of mesh used for a simulation, the boundary condition is the next most important principle of the finite element framework. So, adequately understanding what it is and the different types of Boundary Conditions to be used for different solutions is central to effective modelling.

  • The Dirichlet Boundary Condition is one of the most important boundary condition types. It is generally regarded as a first-type boundary condition because it is truly the very first type of boundary conditions most users understand.
  • It is also called a kinematic uniform boundary condition (KUBC) which suggests that it enforces a certain kinematics (flight path) to a given set of nodes in the model. It is always recreating a uniform behaviour because the nodes associated with this type of boundary condition take a pre-determined value in a uniform manner.
  • Also, this type of boundary condition is also described as homogeneous displacement boundary condition. This is a restrictive definition as it considers only displacement as a variable that will be associated with this boundary condition. Whilst this is true, and it is the most common example of this type of Dirichlet BC, however there are other types of variables that apply here beyond displacement such as velocity, temperature, angular displacement and so on.
  • One important feature of this type of the Dirichlet Boundary Condition is that the model variable is set to a defined value and the equations for it is often given thus:

Model Variable = C where C = constant.

An Illustration: The figure below is an example where a user decides to apply a 3 mm displacement on the front edge of a steel plate with a hole in the middle, fixed at the back. Then, most users will understand that the boundary conditions of the front will require setting the nodes on the front edge to a displacement of 3 mm. Two nodal sets are identified namely XFront and XBack which will be prescribed with Dirichlet Boundary Conditions.

How would the above be implemented equation-wise as well as within ABAQUS. The figure below illustrates how to do so for two nodal sets: XBack and XFronts. What we can see in theis example is that the model variable (displacement in this case) is set to a constant pre-defined values of either 0 or 3mm. The displacements are for x- and y-axes for this 2D problem as well as rotational displacement about the z-axis which again is set to zero. The inset images with the equations is how the implementation of this can be done inside ABAQUS.

The Power of Dirichlet BC: The key take-away from this reflection about Dirichlet BCs is that it has a transformative power within FEM. Here are used cases where this type of BC will work well:

  1. Validation of strain-controlled experiments: If you are looking to validate a model with experimental data for a certain displacement simulation, then you have to use the Dirichlet BC. It is comparable to strain-controlled experiments. This is because of the requirement to prescribe a definite value to the model variable. This value can be same used for the experiment.
  2. Uniform edge displacements: If you are interested in recovering a uniform edge displacement, then this type of BC is important for doing so. This again is because of the requirement to impose a definite value to the domain.
  3. Beyond displacements, other variables apply: The Dirichlet BC applies beyond just displacement. If you want to do a thermal study involving temperature specified isothermally at certain regions in your model, then the prescribed temperature (isothermal heat) can be achieved solely by using a Dirichlet BC.
  4. No Dirichlet BC, no dynamics: Most dynamic studies require you to specify velocities which captures a time-dependent evolution of displacement. So, for the edges or regions in the model where velocities are applied, then you do need to use a Dirichlet BC to specify those velocities. So, if there were to be no Dirichlet BC, then there would be no dynamics assessment.

Those are just a few of the used-cases where a Dirichlet BC will apply. If you are interested in reading more about this, then please read my book chapter on Boundary Conditions accessible via the Springer website of my authored textbook: Finite Element Applications .

Behind the Scenes at CM Videos

Rulers of the AI eco-system

On the CM Videos YouTube Channel's community tab, I ran a poll last week where I wanted to understand which partisan groups of AI users there are among viewers of my YouTube Channel. I had always been skeptical about people's position in the AI discourse. While I am a open advocate of AI, I felt there is more conservativeness around adoption of AI by my audience.

So, I was pleasantly surprised by the outcome of the poll shown below.

Although there were only 27 votes at the time of writing, I was surprised that most of the respondents (about 74%) are Techno-utopians - those who have positive outlook on AI and thinks it can lead to great wealth in future. I am not sure if this high preference is because most of the viewers of my channel are computational modellers and so already have a favourable disposition to technology and any resource that can help enhance simulations (which is the mantra of AI tools).

It was also interesting to see that none of the respondents identify as Techno-pessimists - those who openly oppose AI use. A healthy 26% are sitting on the fence, and classed under what I have coined as Techno-utopian-pessimists. In conclusion, the Techno-Utopians, in line with the poll results, are the rulers of the AI eco-system. I am one of those and this gladdens my heart.

Scholarly Tip of the Week

Why you need to stand on Shoulder of Giants

The image above is taken from the Google Scholar website and I am drawn to the motto: Stand of the shoulders of giants. Why does Google say this database is a shoulder of giants? How does this affect your research career?

When I started my academic career as a PhD student, there was no Google scholar so I remember attending trainings on how to search through Web of Science, Web of Knowledge, EBSCO databases and other academic databases. If you ever wanted to get a journal, you would have to search through multiple databases.

Then on the cusp of finishing my PhD, Google Scholar was born in line with Google's objective of "organising the world information and make it universally accessible and useful." All of a sudden, we could now search through Google Scholar and find most of the journal papers we were interested in. There was no more the drudgery of moving from one database to another. Google's organization objective mearnt that the Google Scholar Framework is the search engine that looks at these databases and extract the papers I need.

Therefore, Google scholar becomes a giant that we can stand on to peer into the near boundless databases of academic publications and books, which grants better visibility to our research and research outcomes.

If you are a researcher (student or industry) and you have not be using Google scholar, my scholarly tip for you this week is that you have to start immediately. There is a true giant in the academic space and you would be better hitching a ride on his/her shoulder - that giant is Google Scholar.

That is the end of this week's newsletter. It ended being longer that I intended but I guess the creative juice was flowing and I went along with the reflective muse and here we are.

Thanks again for reading these reflections. Let me know if there is anyway I can support you or if aspects of this reflection impacts on your research.

Also, let me know what you particularly like in these newsletters. I want to know how it has been affecting your research (positively or negatively, please let me know).

I will catch you next week but in the mean time, do have a wonderful weekend. Bye bye!

Thank you for reading this newsletter.

If you have any comment about my reflections this week, please do email me in a reply to this message and I will be so glad to hear from you.

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Lets keep creating effective computational modelling solutions.

Michael

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I am an university academic, author and content creator who specializes in all things computational modelling. Please join over 800+ computational modelling enthusiasts who read my weekly (Friday) newsletters where I reflect on finite element modelling, engineering, AI and personal development journeys. I also offer insights on different aspects of the academic journey that have led to my becoming an Associate Professor.