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the explanation was speechless

How to learn any numerical analysis

*Understanding the Volumetric-Deviatoric Split in Continuum Mechanics* * *0:00** Introduction:* Explains the concept that changing an object's shape is often easier than changing its volume, highlighting the different resistances matter exhibits to these changes. Water is used as an example of a nearly incompressible material. * *0:30** Modeling Material Behavior:* Emphasizes the need to distinguish between volume and shape changes in material models, introducing the volumetric and deviatoric components of stress and strain tensors. * *1:05** Strain Tensor Focus:* Focuses on the volumetric-deviatoric split of the strain tensor under the small strain assumption, acknowledging that different measures are needed for large deformations. * *1:52** Visualizing Strain:* Visual examples demonstrate how different strain tensors affect a volume element, showcasing purely volumetric (shape-preserving), purely deviatoric (volume-preserving), and combined deformations. * *3:18** Shear Strain:* Explains that shear strains are purely deviatoric, meaning they change the shape without affecting the volume. * *4:14** Normal Strain Analysis:* Analyzes how normal strains affect a volume element, demonstrating how equal normal strains result in purely volumetric deformation. * *5:23** Volume-Preserving Condition:* Derives the condition for volume-preserving (deviatoric) deformation using the small strain assumption, showing that it occurs when the trace of the strain tensor is zero. * *7:18** Volumetric-Deviatoric Split Formula:* Presents the formula for splitting the strain tensor into its volumetric and deviatoric parts, explaining how each part relates to volume and shape changes. * *8:26** Example Calculation:* Demonstrates the split using a specific strain tensor, visualizing the volumetric and deviatoric deformations and their combined effect. * *9:05** Stress Tensor Split:* Briefly discusses the equivalent split for the stress tensor, noting that the volumetric part relates to pressure and the deviatoric part to shape-changing stresses. A future video will explore this further in the context of linear isotropic elasticity. I used gemini-1.5-pro-002 on rocketrecap dot com to summarize the transcript. Cost (if I didn't use the free tier): $0.02 Input tokens: 14676 Output tokens: 436

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Your channel has recieved a good amount of subscribers, I believe. Keep up with the good content.

Amazing explanation!! Thank you, It would be great if you could make videos on Non-linear continuum mechanics in the future!!

I have a Ph. D. in mechanics and years of experience as a researcher. Your video is amazingly well explained and quite pedagogical. Congratulations!

Nice video, thanks for the explanation, keep it up :)

Thank you for these videos. This is one of my favourite channels. I hope you do some videos on isogeometric analysis.

I had to rewatch it a few times because it's not a simple topic but the explanation is absolutely fantastic. Thank you very much for sharing.

Looking forward to see your video about linear isotropic elasticity! I am currently doing my thesis partially on anisotropic linear continuum mechanics, where I study phonon tunneling and it's quite a challenging subject

Your videos are amazing. Weiter so!

Wow, this explains it so well, I’m amazed

banger vid

At 10:08, what is the word that you are using "Finite Element Undas" ? Please explain this

Oh my god, what a great video!

Small correction: at 3:56, rotating the function does change its second derivative! Translating it side to side rather, doesn't

where was this video 4 years ago when I was taking the FEA class? Haha I got thru it but this video would have been tremendously helpful. Well done!

Really awesome!

Great explanation! I found today this channel. Explained in an easy and understandable way. Congrats!!

You are a trully amazing teacher!

Thank you for your great explanation.

nettes Video. "Ansatz" kann man m.E. mit approach übersetzen.

Hello, what software do you use for making the graph ?

Beautiful explanation! Thanks 😀🙌👏

Excellent job! Fantastic explanations accompanied by excellent visual aids!

The quality of your videos is insane, thanks a lot!!!

This is a master class!

Literal God !

Thanks for the video ☺️

Thank you very much.

Talking about weak formulation needs to include theory of distributions and the space of test functions (continuously differentiable functions of order n and compactly supported )and Schwartz space. Nevertheless it is an excellent video. I’m an engineer myself but since I decided to get also a degree in applied math and having taken courses on real analysis and functional analysis while studying as well PDEs more rigorously, things make sense .

Dutch accent adds a lot of credibility.

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Thanks so much for your great effort in explaning the stuff beautifully.

Another great intuition explained visually.

Thanks!

Brilliant!

Thank u

Thank you sir

Im speechless how good this video is! The visualisazions are helping a lot! Best video about this topic on TH-cam

Thanks

Omg best video on finite element ever. Ive only learn up to level 2 and got brief introduction to level 3 for structural engineering. This video give me better insight on the latter

Thank you ❤

First thank you so much for this video, I have a question does FEM work only if the starting equation is u(x)´´ = f(x) does the problem or the differential equation has to have this form ?

Informative! and Loved it!

Thank you for your effort in making such an insightful video. More cheers to you. Waiting for more such videos from your channel

I have taken multiple course in FEA but your explanation incredible and amazing!!! Please continue this series of videos.