Theory of Periodic Boundary Condition implementation in FEM

This is a lecture discussing the philosophy behind periodic boundary conditions (PBC) within finite element modelling. Periodic boundary conditions are very important for analysis of micromechanical systems with a heterogeneous media. The commercial FEM solvers do not have an automatic way of implementing this without the user having to resort to creation of plugins to do so. In this video, I am teaching about the theory behind PBC so that the user can be equipped to develop bespoke tools that can help them implement PBC for any type of 2D RVE. I have shown how canonical equations can be created from a periodic mesh of the 2D RVE. These canonical equations can be introduced into ABAQUS, for example, using a *EQUATION command. #pbc #abaqus #cmvideos

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Time stamps
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You can quickly navigate through the videos using these chapters.

00:00 Intro
01:30 Boundary conditions types
03:54 Example of PBC use in micromechanics
06:08 Reference book about PBCs
07:23 The Principle of PBCs
10:25 Periodic & non-periodic meshes
12:43 Implementation of PBCs: Canonical Equations
17:54 Implementation of PBCs: The ABAQUS case
24:53 Outro

--Related Videos---

✔️** Link to journal publication about non-periodic meshes

✔️*Link to Michael Okereke's Finite Element Applications textbook
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[ChaseMortensen]

I have two questions, that I am still confused on. Hopefully you can answer. 17:38

First, why did you not connect node 3 to anything? Why was N4 and N1 used instead of N3 and N2.

Second, Lets assume you are applying a uniform displacement in the Z-direction that starts at NC and goes to ND. what corner/retained nodes would I use to connect my internal nodes?

[hosseinmalekinejad]

Honestly the best channel in this regards which I have ever seen. Thanks a bunch Dr.

[mariogalindoq]

Your videos are very good. Thank you. I appreciate the way you have to present and explain the topics. Definitively your videos are between the bests in abaqus explanation. Please continue creating more videos.

[nishantmistry]

Thank you Dr. Okereke for a detailed explanation about PBC. I would be waiting for your video on application of PBC on non-periodic meshes.

[Aman-bjhe]

This video is very helpful. Eagerly Waiting for next two videos . Thanks for uploading this . This is the only video of PBC on YouTube to describe it in such a nice manner.

[junlichen]

Thank you DR. Okereke for the video of PBC, I hope you can publish some videos about the detailed PBC settings or whole simulations of woven fabric under tension

[sandeepkr.gautam]

Thanks you Dr. Okereke for such amazing lecture. 🙏🙏🙏🙏🙏

[sathishkumar-ufsr]

Thank you for the video. Was waiting for one like this.

[athinakontopoulou]

Thank you very much for your videos, Dr Okereke! They are all very helpful! It would be very interesting to learn how to apply PBCs on non-periodic meshes!

[jackjohn]

Thank you for making this video. Great help！

[abushaidsujon]

Hi Dr. Michael. Thank you very much for making the concept of PBC so lucid. Could you please make a video on non-periodic mesh ?

[subratkumarmaharana]

Thank you very very very from india..best wishes from my research team

[oluwaseyiayeni]

Hello Dr Okereke, I really learnt a lot on this video. I am definitely subscribing to the channel. I am not an ABAQUS user, I have been using COMSOL for modelling and simulation so I couldn't implement the ideas in the video. Regardless of this, I learnt a lot from the explanation. Do you use COMSOL? If yes, can you do a lecture on using Periodic flow conditions in Fluid Mechanics using COMSOL? Thank you.

[weisun]

Excellent video with high quality! I am quite interested in set a period boundary condition for non-period mesh. Could you please make one? Appreciate that!

[chunxuyan]

great video, hope your non-periodic mesh tutorial coming soon!!

[joonabil]

Very interesting video to understand the Periodic Boundary Condition. But I would like to understand the difference between the representative volume element (RVE) and studying a normal specimen as the simulation of lab experiments and also the difference RVE and X-symmetry or Y-symmetry sections. Thanks in advance

[Wand]

Dear Dr. Michael, just noticed that the corner node N3 isn't tied to anything, just having trouble understanding how is this gonna work?

[muhammadzakihauna]

Thank you for the video! I just wondering is is possible to apply PBC in a macro-scale model while we're intersting in discretizing full-scale model into smaller finite periodic model? Also, quite found a few resource in YT showing PBC application with the thermal analysis. Appreciate if you could emphasize on that!

[panfang]

Hi, Dr, Michael. Thanks very much for your video. I am recently researching helical structures, which also use PBC. However, that is more complicated because the canonical equation used inside is nonlinear and sometimes has a displacement coefficient. Therefore, I have to use the user-defined MPC inside ABAQUS, which I think is not so easy to implement and I still have some confusion about this subroutine. Could you please take a video and share with us some experience?

[johnsonezenwankwo]

EasyPBc was not created by just
a youtuber. He's a distinguished academic, Sir. Nice video!