I can recommend the lecture notes by Dennis Kochmann: ethz.ch/content/dam/ethz/special-interest/mavt/mechanical-systems/mm-dam/documents/Notes/IntroToFEA_red.pdf

Thank you so much! :)

I studied Computational Science in Engineering :)

I don't have a specific book to recommend. but I love the lecture notes by Dennis Kochmann: ethz.ch/content/dam/ethz/special-interest/mavt/mechanical-systems/mm-dam/documents/Notes/IntroToFEA_red.pdf

@DrSimulate thanks. Do you study at ETHZ?

@@CrazyShores I did my PhD there with Laura De Lorenzis :)

Thanks and welcome :)

Thanks for this very motivating comment and thanks stopping by again and again :)) I hope I understand your comment correctly. Are you asking about the part of the video when I say that the functionals input is infinite-dimensional? The key point here is that the function u has no finite basis. If we want to express u as a linear combination of trigonemetric functions, then we would need infinitely many of those. If we take a finite number of trigonemtric functions, we only get an approximation of u.

@DrSimulate Yess u got my point correctly.Even while writing the previous comment i also came to conclusion which u mentioned)) Again thank u for ur efforts.Always recommending ur channel for all my students and co-workers))

I hope I can cover these topics in the future... :)

Though choices :) Maybe you can check the webpages of the institutes and what type of thesis topics they offer and if you find one institute very interesting, you can mostly choose courses offered by this institute...

@@5eurosenelsuelo Thanks for showing up again :) yes you are absolutely right! Because this video is about minization, I focus on functions/functionals with a scalar output. Because only scalars can be minimized. Vectors cannot be minimized (we could, however, minimize the norm of a vector, which would again be a scalar).

@@MohamedHanafy-g6b Thank you so much!

yeah without t his video, I would never understand the weak form !! I did my exam on Trusses analysis with FEM the 28/01, I am sure I did extremely well.

@@AhmedAli-ew2eh Thanks, and greetings from Berlin. I was never there but heart only good about TUM :)

@@corridourthoughts very intelligent question! :) In fact I was also wondering about this before I produced this video. But now I think I have a satisfying answer: It helps to think of the problem in finite dimensions. Take the function f(x) from the video. Let's assume we want to minimize this function. But let's also say that we want to fulfill the constraint that x1=2. Think of this as a plane through the plot of f. For this constraint, we cannot find a point (x1,x2) such that all directional derivative of f are zero. Because for x1=2 there is always a nonzero slope in the x1 direction. Therefore, we have to change the necessary condition for the minimum. We have to constrain the directions v such that they have no contribution in the x1 direction. We have to set v1=0. For the functional F, we observe the same. It's just more difficult to visualize. But if we constrain the function u(x) at any point x, we should also set the test function to zero at this point.

@@aziz0x00 Good luck!

@DrSimulate it was great :D ! Thank you.

Next upload will be in about 2 weeks :)

Thanks :) are you referring to a specific equation or a rigorous mathematical treatment of the problem in general?

Gern :)

Thank you so much! I'm very glad that it helped you to understand! :)

Thanks! :)))

I would say that the terms "dilatiational strain", "hydrostatic strain", "volumetric strain" can all be used interchangeably. The mean normal strain is something else. The dilatiational/hydrostatic/volumetric strain is a tensor, but the mean normal strain should be a scalar value.

I start counting the shape functions with 0. So, N1 is already the second shape function with N1(x=0)=0 :)