Approximate Solutions - The Ritz Method

Finding approximate solutions using The Ritz Method. Showing an example of a cantilevered beam with a tip load.

Governing Equations: Weak Forms vs Strong Forms:

The Galerkin Method:

0:00 Finding the exact solution for the tip loaded cantilevered beam
3:53 The Ritz Method - Mathematical and historical background
10:46 The Ritz Method - Finding a suitable shape function
14:40 The Ritz Method - Formulating the potential energy expression
20:10 The Ritz Method - Minimizing the potential energy with respect to a
22:12 Comparing exact and approximate solutions
24:22 Quick recap

[Alina-ekjr]

After years of engineering you’re the first one to properly explain to me how and why to choose a certain shape function and not just throw it in the excercise. Never thought much about it but that just gave me so much clarity!!

[SMD]

I watch these to go to bed. No disrespect of course, you’re teaching is absolutely wonderful

[Sjbak_mountain]

Now i can digest a bit and see the fundamental workframe of FEM. I appreciate

[soroushasadian]

One of the best instructions I've ever had. Thank you sir

[simonlourenco]

Your video was amazing ! Thanks ! I'm french but still, i understood everythings you've said. It was very clear, everythings was defined and explained. I feel very lucky to have found this video. Many thanks !!

[Omar-sjwl]

Always great to see a new video from you.

[jv]

Keep up the great videos! hopefully in the future a video on plates and shells can be done, I feel that there isn't enough satisfactory material on this available.

[Alliban]

If I try to derive an equation in general, I will always apply the input (here force P) in positive direction in order to avoid confusion. This can also be achieved by using an appropiate coordinate system. Otherwise, the sign of the input quantity has to be contrary to what follows from the coordinate system which may give rise to error.

[ergonautus]

Very interesting! You are very good with explaining notation in all your videos. It helps a lot when trying to understand transformations and such. Thanks!

[andcunsan]

Piece of gold finaly I have a feel on one of the "ingredients" of finite element method

[talalsyed]

nicely explained thank you very much...

[teny]

Thank you very good video! I was surprised you didn't talk about the Rayleigh quotient, which is really useful to find the approximate natural frequencies of a system, but then again the video was more focused on static problem

[mcastanonf]

Great! You are the best, can you please run one of this examples using Newton’s second law?, simple supported beam with a uniform load along the entire beam. Thanks in advance

[mrkaplan]

At the start of your videos, bell sound is too loud, specially when using headset, could you do something about it?

[mathunt]

Excellent video. Is there a way to choose a shape function? You seemed to pluck the one you gave from thin air.

[nabin]

Do you have a textbook or a set of textbooks you refer to while making these videos? Thanks for these videos. Much appreciated.

[GranHerrmanno]

15:39: Why there is no factor "1/2" in the work of the external force P?

[raduandreimatei]

If I could add some constructive criticism you talked a lot in terms of the "Ritz method" and instead of calling things by their practical name, e.g., saying "we apply the Ritz condition" instead of we just extremize the potential energy functional, things became a bit confusing and unrelated to variational calculus, which from what I understand is a core principle of this method. Another thing I would like to mention is that you already know the steps you take but we don't when we solve problems so by calculating W, xx in advance because you know you're going to need it afterwards, it kind of breaks the natural flow of the solution of the problem that a person who doesn't know the results in advance has to experience and it becomes confusing so sticking to the process that a person who is solving it for the first time would is less confusing in my opinion. Great content, I hope this comment doesn't make it seem otherwise.

[steveshaver]

Hi!

Can you explain how your variational method is a “true” variational method, when it is not derived from an Euler Lagrange equation?

[jimbojones]

Hi Freeball - love your videos!

Just wondering if you're pf Zimbabwean or South African origin. I hear a bit of it in your accent - I'm from Zim originally myself!