The Finite Element Method | Part 12: The Frame Element

[@donaldkhanye9011]

Hello Dr CEE, This FEM lecture series is quite something else, and yes, it is very satisfying to say the least. Thank you so so much for doing this series. I have completed the example, and at first, I was a bit distressed because my results did not match 100% with the results in the referenced text (for example I got the global displacement u2 = 4.95305mm compared to Dr. Logan u2 = 5.007mm …. this trend propagated to other displacement vectors and down to the local forces acting on the elements (for example my f’1x was = 14.814 N v/s Dr. Logan f’1x = 14.950 N; my m’1 = 37.577 x 10^6 N-mm v/s Dr. Logan m’1 = 38,049,902 N-mm, and so on…….) Although the above results were about 99% similar, and I also recalled Dr. CEE mentioning something about the degree of accuracy of the computing tool used…., I still could not help to wonder why were the results not exact? after checking and re-checking my set-up and also panicking (^_^) of course. I decided to re-run my set-up using the US units, and lo and behold, the US units results computed 100% exactly and to the dot 😊. I know that this exercise was “practically immaterial”, however it was the “theoretical impact” which I wanted to explore. I guess it is safe to say that any early rounding off of numerical input values to the FEM should be done consciously. 15:31 Yep; you are definitely right T.A. CEE, Dr. CEE voice is indeed carrying extra joy in this video lecture (I wonder why, but I am glad it is, he deserves it) and the other good thing is that his joyful feeling is contagious. I am feeling it all the way here as well (much like in the matrix - pun intended). I am sensing something here with regard to the 2D frame culmination equations. When we derived the “rotation or the transformation matrix” for the 2D-truss element, we included the v’-displacement term which strictly speaking, we should not have cared about it back then as it had no added benefit on the case of a 2D-truss (axial force) element. I think we derived that v’-displacement term for this moment right here 😊, this is where we care about the v’-displacement term, and more specifically because we now have shear force along v’-direction on the beam element. This is some next level foresight and it is part of the reason why the series is so satisfying. It is now starting to sink in for me as to why we would have to derive the v’ and w’ transformation terms for the 3-D frame equations. Furthermore, I think (I may be wrong here) that the “recommended reading” by Dr. CEE on chapter 4 (specifically example 4.3) was aimed to jump start the concept of “combining” FE equations. I never got that particular exercise right but I am inspired by today’s lecture in combining the “beam-and-truss element” equations to go back and have another go at example 4.3 😊 = beam-and-spring element. 06:18 😊 😊 😊, I can’t help but to laugh when Dr. CEE calls the [T-transpose]*[k’]*[T] an abomination. But I do agree 1000% with the sentiments; it certainly does not help to jump the steps of finding k’ and T and go straight to find k (by using the combined ….. , sorry scratch that, I mean by using the abomination) if one intends to find the local (pains) forces. I think that this combined equation is included in the text because it may be considered suitable and attractive to someone who just want to do a quick (and blind, but numerically correct) computations of global displacements and global forces, it may also be attractive to a “programmer”? 09:52 [Assemble], I see the new “dash-and-slash” one-step_ish-approach. I’d say that it is always very good to see various approaches and this gives one options to choose from when it comes to assembling. I would like to add that including examples in your lectures is superb, I can only imagine how much guessing and unsureness of the various application assumptions and techniques would ensue without your essentially well explained and thought-out examples and exercises. I am really enjoying these videos, and of course I don’t know where to put the HUGE “2D FRAME SIZED” shout-out 😊 Thank you Dr. CEE for shining the light for all to see. Regards, DK

[@CivilEngineeringEssentials]

Hi there Engr. DK, welcome to the world of numerical accuracy, where an error of 2-5% is usually acceptable. Oh you cought that right. The reason why I continued v' displacement in trusses although inconsequential was to prepare for this. I could not say that out loud back then, as we were at the start. ^_^ Yep, that example of 4.3 was also aimed at getting some ideas to prepare for this. I kind of unapologetically hate the approach of just using a singular global stiffness matrix. "Pssst. I am preparing a udemy course on programming the finite element method, which is the reason why I already see the shortcomings of this approach.". Also also, STRADO. I tried to do the global stiffness matrix in a more speed-runnerish way as it would start to bore people who are following the series since its start. You are most welcome, thnx a lot for all the support and stay tuned for more content, CEE

[@criticizemyanmar]

would you reply if we ask some questions sir?

[@CivilEngineeringEssentials]

Of course. I usually reply within a day. 👍

[@criticizemyanmar]

@@CivilEngineeringEssentials where can I ask you? by email or by comments here?

[@CivilEngineeringEssentials]

@@criticizemyanmar comments are better. So all people benefit from our discussion.

[@criticizemyanmar]

@@CivilEngineeringEssentials ok sir.