Understanding the Finite Element Method

Watch the extended version of this video (without ads!) on Nebula! nebula.tv/videos/the-efficien...
You can read the article version of this video here - efficientengineer.com/finite-...
The finite element method is a powerful numerical technique that is used in all major engineering industries - in this video we'll explore how it works.
We'll look at why it's useful to split the body being analysed into small elements and the different elements types that can be used. We'll also cover the key concept behind the finite element method, which is the stiffness matrix, including how the element stiffness matrices are derived, using techniques like the Galerkin method of weighted residuals. Once we have the element stiffness matrices we can assemble them into a global stiffness matrix that describes how the body will displace for a set of applied loads and boundary conditions.
FEM is a complex topic, and this video is really just an introduction. For those of you who would like to explore the topic in more detail, I recommend the book Fundamentals of Finite Element Analysis by David Hutton.
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The Efficient Engineer is a channel aimed at mechanical and civil engineers. The mission is to simplify engineering concepts, one video at a time!
Follow me on Twitter: / efficiengineer

[@TheEfficientEngineer]

Thanks for watching! FEA is a fascinating topic - reply here with some of the interesting things you've analysed using FEA! And remember you can watch an extended version of this video (without ads!) on Nebula - nebula.tv/videos/the-efficient-engineer-understanding-the-finite-element-method-extended-version.

[@RealEngineering]

Wish I had this in college. Fantastic work!

[@UkranianStallion]

hi I'm your fan, Never thought seeing you here 😁

[@abdulhafizuddin95]

im an engineering student.. both channels help me a lot.. Thank you for your great work

[@erockromulan9329]

@@abdulhafizuddin95 Go to grad school!

[@MrFujinko]

@@Bustical Basic modus operandi for these engineering channels.

[@SeanRhatigan]

High Praise 🙏

[@greekmusicetc]

As a computational mechanics masters student, I can easily say this was way more efficient in introducing me in FEA than the whole first semester :)

[@keywang7378]

During the lectures, professors always dive into infinite derivation of equations (like strong form and weak form) without clear explanation of what are the physical meaning. It is definitly a torture especially for the students who are not good at algebra and numerical method...

[@user-hr6tb9fh8k]

This should be played at the beginning of every lecture throughout the semester.

[@bogdanboiii1154]

@@keywang7378 There's not necessarily any physical meaning behind it. Take for example the principle of virtual work. There is no such thing as "virtual work", but it follows from the weak formulation.

[@purplepinkclouds8882]

Where do you study? Planning on starting a graduate track in computational mechanics next year - curious about your experience.

[@jaimeduncan6167]

@@keywang7378 I half agree with you, but I don't understand what a student that is not good at algebra will be doing in a finite element class. The intuition is useful for everybody.

[@hari-sankar]

I am a guy knee-deep in FEM (it being part of my job) and in my 8 years of experience in the field, I can vouch for the fact that nothing that I have seen on the internet has so elegantly defined the topic with such lucidity. Thanks and subscribing.

[@olevel_maths1470]

FEM structural analysis kzbin.info/www/bejne/i3m1oK1oo86iibc

[@Catloverss95]

Finite element structural analysis basics kzbin.info/www/bejne/gaXHiKJvasihbNk

[@amitjose3739]

i took FEA as a unit in university and this 18 minute video still taught me stuff i did not know.

[@robindesai]

can you do analysis of my design please

[@basitashraf4129]

I need help. Can i contact you?

[@storminmormin14]

Taking an entire semester and smashing it down to one video.

[@SpokewTheBoss]

As a CAE professional, I can say this is a very illustrative video. I will definitely recommend it to my students. Also, I am waiting for more on this, going beyond the linear static problem. Thank you

[@Sanatana12345]

Hello sir/ Madam can you please tell some excellent sorces for studying Mechanical engineering softwares specially CAE🙏

[@Sanatana12345]

@Chetan Sonigara okay brother , thank you for the reply 🙏

[@SpokewTheBoss]

@@Sanatana12345 Sorry, I thought I already answered. The already mentioned book looks like a good beggining. If you are looking for a commercial software to learn practical FEM I think the best for this purpose is MSC Apex (Student Edition) with its Apex Curriculum Kit. Regards, Javier

[@Sanatana12345]

@@SpokewTheBoss Thank you for your reply 🙏👍

[@Catloverss95]

Finite element structural analysis basics kzbin.info/www/bejne/gaXHiKJvasihbNk

[@Agol2012]

Do you realize how many lives did you just saved with this AWESOME video.

[@olevel_maths1470]

FEM structural analysis kzbin.info/www/bejne/i3m1oK1oo86iibc

[@Catloverss95]

Finite element structural analysis basics kzbin.info/www/bejne/gaXHiKJvasihbNk

[@BrunoVieiraC]

10 minutes was enough to teach me the basics that the teacher couldn't do in a whole semester. I have no words to thank you enough for the video. Keep up the excelent work!

[@The_Professor123]

I think FEA is one of the coolest engineering courses!

[@lamtran2993]

Any recommend books or materials to get into it ? I am currently studying it, too.

[@The_Professor123]

@@lamtran2993 I would recommend the book "Introduction to the finite element method" by Ottosen and Petersson.

[@cutlmathews9473]

It also depends on the professor :-/

[@girin1512]

Nopes CFD is

[@udbhav5079]

Nonlinear FEA...🥶🥶. Tangent matrix goes brrrrr...

[@DolfocarAli]

The best 18min i have ever spend on a video and i will watch it again now 😋

[@nirvlogswithfun]

kzbin.info/www/bejne/a3rLf6CKpbd0jZo

[@rainman6272]

This is the video I will point everyone to when they ask me about understanding FEA. Everything was so clear and augmented with excellent animations and representations.

[@FEAnalyst]

FEA is my job, field of scientific research and hobby. And yet so far I haven’t seen such a good, clear, and comprehensive but not too long explanation of the Finite Element Method before. When it comes to the next videos, as others already suggested, I’d like to watch your video about buckling.

[@TheEfficientEngineer]

Thanks Jakub, appreciate it! Will have a think about a video on buckling.

[@dehno12]

My daily prayers have been answered with this video! Assignment due in 2 days, what perfect timing! Thank you for doing these videos

[@nirvlogswithfun]

kzbin.info/www/bejne/a3rLf6CKpbd0jZo

[@olevel_maths1470]

FEM structural analysis kzbin.info/www/bejne/i3m1oK1oo86iibc

[@Catloverss95]

Finite element structural analysis basics kzbin.info/www/bejne/gaXHiKJvasihbNk

[@RahulNatha]

I recollected all the topics I learnt in FEM in college by watching this less than 20 minute video.

[@nirvlogswithfun]

kzbin.info/www/bejne/a3rLf6CKpbd0jZo

[@EflavioCalavort]

@@nirvlogswithfun loka

[@chiragdugar8183]

Can you suggest a channel on KZbin to learn complete finite element analysis?

[@Catloverss95]

Finite element structural analysis basics kzbin.info/www/bejne/gaXHiKJvasihbNk

[@dadhad8055]

@@chiragdugar8183 i have question can you help me please

[@SAXASIANGUY]

Have a project due tomorrow for FEA. This came in at just the right time

[@dhanushyakumarkamatam2310]

Dude, me too.

[@christianjauhari2673]

Same here for my final project

[@zaidiebhat681]

@@christianjauhari2673 hahaa...same

[@abhishekkuksal5700]

@@dhanushyakumarkamatam2310 may I know where do you study? Thank you

[@MrFujinko]

Imagine being this irresponsible...

[@davidannenkoff4173]

I recently became a teacher and I have to dust my FEM theory off. I went through a lot of videos and articles in order to build my course up and your video is by far the best one, and I mean by far. Visually, mathematically, verbally, it's the best one on all aspects! Huge respect for your work!

[@pranav3813]

One of the best ultra quality, extremely interactive, highly lucid and coherent engineering content I ever saw in KZbin!! I bet this one deserves the place in top 10 videos in KZbin the way the content is created!

[@KontoVonMir]

Just became a level 2 patron, since I appreciate your work and it's so helpful to visualize scenarios that are hard to imagine based on text and notes/drawings. FEM was one of my classes in University in Germany and once you exceed a certain level of complexity (which is basically valid for all engineering subjects, not just FEM) many people check out. So thank you for filling that gap and making engineering easier to understand for those who want to learn!

[@PREYAS_PATEL]

After struggling to understand the theory of FEM, I came across this and this is the best explanation I could ever have. Great audio visual, great explanation. Would definitely recommend it to my peers.

[@moustachio9936]

As a mechanical fabrication and production masters student, I can easily say this was way more efficient in introducing me in FEA than the whole second semester :)

[@MerkleCAE]

You can see directly how much work went into the video. Good videos on the subject are rare! Very nice

[@andreasjauss3838]

University education should start with overview and "what is the sense of" information like this first and then jump into the details and big literature like Bathe etc. Very few university professors are good with didactics wasting the time of their students. Good education methodology like this is rare - congradulation !

[@markproulx1472]

It’s funny that you mentioned Bathe. I had him for a grad level class. I was utterly lost because of the complete absence of context.

[@scienceskills]

Bathe is an amazing teacher. His book, "Finite element procedures" is a jewel.

[@urosmarjanovic663]

There is soooo much math you need to cram down to become an engineer that you can often lose the point of it. Dry math, without its actual appliance is really hard for most of people. Yet you need it as much as you can have it.

[@abdulwariskenue1012]

Phenomenal work! You just summarized all the key aspects of FEM in under 20 minutes.

[@dudiek12]

The fact that this video is so good is the fact that It focuses on the idea standing behind using FEM and show it gently how it's used. I wish everyone had such introduction to the topic on universities.

[@jonathandoemel2775]

This is the most straightforward overview of FEA I have ever seen. Fantastic work!

[@McPlaySpot]

This channel is a treasure. I really appreciate your work. Thank you so much.

[@nirvlogswithfun]

kzbin.info/www/bejne/a3rLf6CKpbd0jZo

[@olevel_maths1470]

FEM structural analysis kzbin.info/www/bejne/i3m1oK1oo86iibc

[@jmy3592]

Me too

[@cheeios2mc773]

I fully agree.

[@sekargreen7703]

First of all Thanks a lot..my prayers were answered by this video. Really it is very difficult to be in CAE field without proper understanding of FEM concepts. Literally I am screwed up by my own mind daily to know the things right. This video means a lot to me. It answered almost all my doubts in FEA theory. one thing which made me connect is visual representation to understand the concepts because I went in reading many blogs,websites even some other KZbin videos too but I didn't get confidence in FEM now it did. From now on my work in my job going to be different. I gained much confidence. Onceagain thank you.

[@jamal919]

I really enjoyed building these matrices in my undergrad classes. I have switched field since then to fluid dynamics, but it was a joy to watch this video and remember the memories.

[@ManuelRamsaier]

These are the best animations I've seen on this channel. Beautifully explained and illustrated. Wonderful video. I will send my students your way :)

[@mohamedsalih178]

Superb graphics. Absolute clarity of concepts. You’re doing a great service to the engineering profession. Keep innovating

[@JavierMeseguerdePaz]

Wow, this video is just perfect. Accurate, comprehensive, easy to understand... Thanks for making it!

[@JohnChuprun]

Amazing topic and delivery, this deserves such wide recognition for its ability to explain.

[@guilbas1]

It blows my mind how well explained this is. Much better explained than in university courses. Amazing work!

[@keshav.poudel]

Whole semester completed in short great video❤️

[@omarm.3952]

I agree. I've had a professor who couldn't even bother explaining these fundamental concepts in simple terms like in this video.

[@vaibhavtoshniwal]

As a CAE Engineer, I can say that this has to be one of the best video which illustrates the concepts with in depth knowledge in 18 min. Great Work !

[@olevel_maths1470]

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[@Catloverss95]

Finite element structural analysis basics kzbin.info/www/bejne/gaXHiKJvasihbNk

[@ananias-]

it took me a month studying all day long to understand this concept but this animation makes it clear and easy! Of course when you do all the calculations by hand you will get to understand whats goin on more in detail. thank you for this cool resource

[@FiferSkipper]

What an excellent video. Thanks for not avoiding the linear algebra, your clear connection between the model concept and the computation is quite elegant. I am definitely watching this again...

[@AmeenTopa]

As someone who is specialized in FEM software, I can say you did a great job. I will share this video on my channel!

[@Gumball_W]

@Music, raw. Yeah, but FEM courses at universities tend to be really messy, boring and poorly explained. At least in my country ;-)

[@AmeenTopa]

@@Gumball_W Yup. The same case here. It's not only about the information and knowledge that we share, the way how we present it is important too.

[@Sanatana12345]

@@Gumball_W you are also from India

[@Gumball_W]

@@Sanatana12345 No, I’m from Poland

[@Sanatana12345]

@@Gumball_W okay brother

[@CAME18471]

Amazing video. You are one of the best science divulgation channels on KZbin!. Congratulations and please, keep producing this kind of material!

[@Catloverss95]

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[@vishalgarg3629]

One of the most amazing and simple explanations I have seen for a numerical method without any clutter. Keep up the good work 🙂

[@emctres3]

This are simply the best lectures, the voice, animations, topics, incredible. Thanks.

[@saisrirajnallam]

Don't have words to describe how incredible this channel....any how thanks a lot for this lot of information 🙏🙏😭😭🙏

[@olevel_maths1470]

FEM structural analysis kzbin.info/www/bejne/i3m1oK1oo86iibc

[@omidahmadfaqiri9495]

Thank you so much for your excellent videos!

[@olevel_maths1470]

FeM structural analysis kzbin.info/aero/PLg_GL42KJkmG7maeWMd6JKguJlQHoTNa4

[@shivendragangwar1253]

The best video you can find and have the most important information about FEM in just 18 minutes. Amazing!!!!

[@topian789]

I am working in academia and offer CAD/CAE trainings to potential users. Often I recommend this video to the participants in introductory training on FEM. You have nailed it to the point. I am grateful for effort that you have invested. 👍

[@normanmommu1]

Just got my dream job as a FEM Engineer, and I am loving it!

[@TheEfficientEngineer]

Congrats on the job! :)

[@MAnasK-wy2wr]

Where do u work?

[@W204_Muj]

How much math is involved? What software are you using?

[@erockromulan9329]

One of my favorite pieces of code I wrote during my undergrad was a general code that assembles a global stiffness matrix for any connection of elements and nodes. I made it robust enough to walk out of my final exam within 10 minutes because all I had to do was input the givens in the problem. FEM is such a good topic of engineering!

[@manavputtyah7568]

Damn that's cool! I wish I knew it !

[@erockromulan9329]

@@manavputtyah7568 Relate your DoFs from your element stiffness to where they connect on the global node DoFs. Hope that helps!

[@manavputtyah7568]

@@erockromulan9329 thanks buddy. I'll give that a try ❤️❤️❤️

[@ericmeehan298]

Wow, I really wasn't expecting this high quality of a video when I began searching for this subject. Really wonderful job, thank you!

[@Mau365PP]

We are so lucky for having this KZbin channel, THANK YOU

[@Gumball_W]

Finally a video about FEA 😃 It’s really awesome explanation. It would be great if you could continue this topic and make a video for example about basics of nonlinear analyses or about shells. However, there’s also another topic that’s really needed in this series - buckling / structural stability.

[@olevel_maths1470]

FEM structural analysis kzbin.info/www/bejne/i3m1oK1oo86iibc

[@MrPicklock]

I did a whole 270 hours course on FEA last year - this really wraps it up very nicely!

[@olevel_maths1470]

FeM structural analysis kzbin.info/aero/PLg_GL42KJkmG7maeWMd6JKguJlQHoTNa4

[@nightheist2191]

From ?

[@MrPicklock]

From what?

[@thesoupin8or673]

I'm in an FEA class right now, and this is exactly what we're learning rn. Incredible explanation

[@christopherschaefer8279]

The creation and editing of this video was very well done! It is a great introduction to the topic, at-large.

[@priyansutank]

Yeah from first video on this channel, I wished this topic on this channel and it's here....

[@nirvlogswithfun]

kzbin.info/www/bejne/a3rLf6CKpbd0jZo

[@gustavoexel5569]

Although it was mentioned at the beginning of the video that FEM can be used to solve Fluid Mechanics, Heat Transfer and Electromagnetism problems, it really shouldn't be used for such applications, since those kind of problems relies heavily in conservation of energy, mass, momentum... While using the Finite Elements Method the differential equation is integrated in the non-conservative form, using other methods such as the Finite Volumes Method will guarantee conservation of those properties for any mesh size, which is really important. When the spacial and temporal meshes tends to 0, all methods converge to the same solution, but since it isn't possible to have an infinitely refined mesh it is important to select the right method for different kinds of problems. In the same way the FVM also can solve solid mechanics problems but in certain situations the FVM can handle first derivatives badly, as well as the FEM handles second derivatives badly, both scenarios leading to instabilities.

[@potatopotato9308]

So, the problem with FEM is that the result will be influenced a lot by mesh dimension?

[@nitinmuthe2337]

Can't wait for your video on modal analysis. I've always wondered about the computation going on in the solver behind the scenes.

[@RRC5074]

What a perfect timing, God send indeed. I was just asking myself this question few hours ago, wondering where I could get a good source to understand and here you come along. THANK YOU!

[@duchungtran9914]

As a ME student, I decided my concentration to be robotics and spent a lot of time coding in C. However, there are other two techniques that I am really interested in: one is FEM, and the other is CFD

[@Catloverss95]

kzbin.info/www/bejne/i3m1oK1oo86iibc

[@zhengwang1402]

I agree

[@hakankosebas2085]

topology optimization too plssss, I wonder how that magic works

[@TheEfficientEngineer]

Definitely an interesting topic, and not the first time it's been requested. Will give it some thought!

[@arkhonkharon6367]

It's not really that magical when you think about it. Topology Opt is one of the types of shape optimization (three "Topo"s (-metry and -graphy are the others)). With topology here you essentialy create an envelope ( for example a brick), give it features you need (holes, connections etc.) and then you run a FEM simulation on that, with the loads and boundary conditions you need applied. It will "map" the stresses on the discretized brick, "normalize"(read: assign importance from 1 - very important to 0 - chuck that nonsense) to the elements based on how much they are f.e. stressed, then you chuck the ones you don't need that much and recompute. Repeat that a number of times (it can get quite sophisticated here) and voila, you have a shape that uses the material it needs, with reduced weight while preserving the stiffness (or "compliance") you specify. Assuming of course, your model is approximately accurate to reality. It's based on taking away unnecessary material. Now Generative Design, oh boy that's a different beast. That be how nature does its thing (think how your bones grow to support the load). This one is based on lattices and GROWING the part, that's some magic right there.

[@krisztianprim8850]

Bruh. This is exactly what youtube is meant to be. This is so professional, high quality I can't believe I'm actually watching this.

[@mortenabel1978]

This video is brilliant! Best FEM explanation I’ve ever heard.

[@ansonjohn3876]

Today was my exam. Why you exactly uploaded after my exam😅

[@TheEfficientEngineer]

Noooo, sorry! Hope it went well.

[@ansonjohn3876]

@@TheEfficientEngineer 🥰 exam was so easy because FEM is my fav subject. Thankyou for your reply🥰🥰

[@TheEfficientEngineer]

Awesome

[@wanshurst2416]

@@ansonjohn3876 it's easy because it's easy. There are way harder courses than fem

[@AlgoDar]

Best FEM explanation on KZbin! Keep going.

[@nishantkumarsahu6308]

Thanks for this awesome video on FEM. The way of explanation along with the animation is truly fantastic and lucid.

[@DefinitelyNotJoao]

Wow this is the best video on FEM I've seen and the animations are fantastic! Great for quick summary after having learned this a couple of years ago.

[@KorepMater]

Gosh, I am speechless. Great video and explanation, I was watching it until the end without any stop in between. Thanks for such an incredible job, I will share it with others during my Ph.D. studies

[@pagliaran_]

One of the best video that I've seen on mechanics, great job, I'm in love for this channel

[@dakshitha92]

What a treasure of simple yet very complex info. Thanks very much. Hats off!

[@alviahmmed326]

Amazing and informative as always. The way you introduce a topic simply is equivalent to 10 classes.

[@blackguardian89]

Absolute gem! Great content! I'm eagerly waiting for the next video tutorial! Thank you!

[@nikhilkulkarni7181]

FEM can't get simpler than this !!! By far the best video on FEM !!! Thank you. I will share this with all my students 👍 Waiting for more on this topic

[@souviksinghrathore5423]

Nicely explained. It's an antique for generations to come.

[@techhunt4922]

This is very amazing. tears in my eyes for understanding the stuff in a simple way.

[@haslan4885]

not only the content itself is great, the animations are amazing too great video, sir!

[@mrshodz]

Cool video. Explanation and visualisation are perfect.

[@xgozulx]

This is amazing, perfectle summarices what I have spent this past month learning thanks! :D

[@calebemartins8266]

Your video is awesome! I'm currently studying FEM at school and you mentioned all the topics learnt in college in a short video. Very well!

[@andresyesidmorenovilla7888]

This is too well explained. Thanks, I understood from you what I couldn't from my professor👍👏

Fantastic video! It doesn't get any more clear than this 👏👏

[@khileshwarrajpuriya5448]

Very clearly and interactively explained!! Thanks for this video.

[@Shabazza84]

Very good visualzation. I learned something people in school usually hate and loved it.

[@jmy3592]

This video is very informative and straightforward. Well done.

[@2112201211]

The clearest and most instigating introduction to FEA I've ever come across.

[@obedtetteh4498]

Well explained and easy to follow.

[@saday4175]

Exceptional, surely the best video on FEA I have ever seen. Diagrams are intuitive, consistent and evolve along with the voice over.

[@olevel_maths1470]

FeM structural analysis kzbin.info/aero/PLg_GL42KJkmG7maeWMd6JKguJlQHoTNa4

[@F1Jackman]

Love your content. Keep up the amazing work!

[@georgeneves4875]

Good Job!! Easy to understand and visualize the concepts.

[@johncahill3644]

This is really well done...very clear and a nice distillation of the classic arguments (reminds me of the old MacNeal Schwendler manual...but a whole lot more condensed). I started FEA with Nastran in the early 80's, still typing each command line in by hand. We got Patran soon after and that made all the difference (as did big clusters of Vaxes and finally a big Cray YMP-28). Abaqus non-linear followed, as did some primitive Computational Fluid Dynamics. Those were exciting times and some very interesting projects!

[@FutureSDO]

Smoothest Transition Ever So nicely edited and well explained

[@Catloverss95]

Finite element structural analysis basics kzbin.info/www/bejne/gaXHiKJvasihbNk

[@rizalpurnawan3796]

What a great introductory explanation. I was searching for a proper introduction in FEA, however, I could not find one before watching this video. I was wondering about how to arrange the stiffness matrix etc. And why differential equations are involved. I tried to observe the approach from engineering, but the literature was lacking of formal mathematical description or sometimes skip them. Then I tried to observe the approach from pure math literature, I ended up only reading methods for solving the differential equation but did know why the differential equation is there. Thanks for your great video!

[@arthas-vk2ds]

Wow, top notch quality engineering content like this is so rare. Thank you so much❤

[@NIKHILSINGH-pg8eo]

This video couldn't have come at a better time. I'm having FEM course this sem. Really great and helpful video

[@DoggieA]

I first heard of FEM 40 years ago in my college senior year, I was totally confused because the presenter did not know what he was talking about. This 15 minute video finally made me understand a little bit about it, thank you!

[@Catloverss95]

Finite element structural analysis basics kzbin.info/www/bejne/gaXHiKJvasihbNk

[@ANJA-mj1to]

Researching many content of this topic - I can say your Presentation is key to all! Like engineer I can say that finite element has become the method of choicr for solving many types of partial differential equation in engineering equations and physical sciences. It is like you have said - important applications include mechanics, FLUID FLOW (for mel), thermodynamics and electromagnetic field. We usually, take what you also say (so this is brilliant who you differnt issue) =The basic idea is very elegant and dates bak to the classic al work like Gelerkin or Rayleigh, Ritz almost a century ago. You have all important topics! 👏👌

[@ProfeARios]

Great video!!! Loved the background music!!! Thank you so much for sharing!!!

[@ashishmehta4283]

Subscribed and shared this channel. Thank you for creating this

[@harikply08]

superb!!!!!The most simple video I have ever seen related to FEM

[@PiratesBlog]

I watched few videos on this channel So valuable and easy to understand

[@paulmunyao8863]

dude, thanks for summarizing my whole numerical methods unit into one 20 min long video

[@longtranthanh4778]

So this video is very straightforward. Thank you so much.