Correct Mesh Size - A Quick Mesh Convergence Tutorial

[@noahnorberg575]

When you do your Msc thesis and you find the best teacher who teaches how to do Convergence analysis perfectly! You deserve the best!

[@Enterfea]

Thank you so much Noah! You are very kind!

[@carolinekarishmakella4732]

I love all your videos and your blog. Best explanations . Thank you

[@Enterfea]

Thank you Caroline! I'm really glad that you like my work :)

[@arocenajesussusmerano174]

It was great and so helpful advise..Also the way how you validate using your way of analogy, its so smart and really helpful. Thanks a lot

[@Enterfea]

Thank you Arocena :) I'm really glad that you like the video :)

[@nunoteixeira-robotstructur8358]

Another great video from Enterfea!

[@Enterfea]

Thanks Nuno! I'm glad that you like it :) How is Robot design going?

[@mariogalindoq]

I think you should also compare the displacements. The quad4 presents a locking behavior that you are not looking in your examples.

[@madmanstewy]

Great watch! Also reading the comments always seems informative, like the symmetry realism and convergence, thanks for your wisdom.

[@Enterfea]

Thank you Stuart! I'm really glad that the video was useful for you! All the best!

[@HowtyToo]

sensivity analysis is the answer for all these questions

[@Enterfea]

Hey! A quick Google search told me that: "Sensitivity analysis determines how different values of an independent variable affect a particular dependent variable under a given set of assumptions"... For me, being specific in such cases makes sense, so if I would give someone advice on this (as I do in the video) I would never tell them to "do sensitivity analysis" and leave it at that... While this is technically true, it's not advice... because you can't really act on it unless you already know what to do (in which case you would not be asking). So instead I would say: calculate the model with smaller and smaller mesh and draw a chart of the relation between outcome you want and the mesh size... and hope it will converge, and if it won't this is mostly because of singularity or whatever. To me, that would be practical, and using complex definitions as an "answer" that would fit anything from dentistry to psychology isn't really advice in my book.

[@konstantinossfoungaris8474]

That’s some good stuff. My question is, how many Gauss points have those elements been evaluated with? It appears that the correct result is dependent upon how close to the clamped edge the point lies. If you use 1 point, it evaluates the stress at the center of the element. If you use 4, however, you’re immediately closer to the side. There’s of course the problem of shear locking for over-integrated elements, so that’s a trade-off for your accuracy.

[@Enterfea]

Hey Konstantinos! Those have a single gauss point. As far as I know, I don't get to choose any "better" in Femap. Shear locking is a fun problem for sure BTW :)

[@AwestrikeFearofGods]

10:00 If this example were tension (uniform surface load, applied to the free end) instead of transverse load, then would a single Quad4 element give the perfect answer? Again, assuming a Poisson's ratio of 0.

[@Enterfea]

Is the question really then: "Can a square QUAD 4 element accurately transfer uniform stress perpendicular to one of its edges when it is reasonably supported not to constraint perpendicular deformation"? - luckily it can :) Otherwise, it would be quite difficult to calculate anything in FEA :)

[@russreadsbooks]

Great video. I wish I learned this in college

[@Enterfea]

Thanks, Russell! The only thing I can say here is... me too!

[@theodorrist2721]

Really helpful, thank you so much!!

[@Enterfea]

Thank you Theodor for commenting! I'm glad that you found this useful!

[@mattm6170]

How would you do a mesh convergence study if you were doing an analysis over time ,an impact. Thanks

[@Enterfea]

Hey Matt - to be honest with you, I rarely do impact analysis - this is simply not something we do regularly for my Customers, as there was no need for this. This means, that while I will give you an answer, I cannot honestly say that it is backed with a lot of practical experience, so you know... be careful and all that :) That being said, I would most likely do it the same way. Whatever your goal is in the analysis, this is a "measurable" thing (like max stress, or maybe deformation, or whatever you are after really). Then you can just as well do several runs with different meshes, and see how this "goal measurable thing" changes with the change of element size. But there is one caveat to that, and that is, that in explicit analysis the time step depends on element size (long story) - this means that the smaller elements you define, the smaller time steps you will have to define as well... so the analysis will take "longer squared" in those cases. So I can only guess that it would be a total nightmare (time-wise) to do explicit mesh convergence... still nothing else comes to mind really... If you are in doubt, try first modeling something you can measure yourself (so you will be certain of an outcome) - this way you will know if the mesh convergence "worked" if the outcome will converge to an "expected answer". All the best! Ł

[@ivarkjelberg1317]

Hi, why remove the stress concentration you observe at the fixed end, what if it is correct? Poisson coefficient for an isotropic homogenous material tells us that solid physics is a true 3D problems. A linear induced stress couples, via the off diagonal stiffness tensor, to the other directions, so a fixed end, where the fixation constrains the in-depth tenue of your beam you will get a stress induced effect. I would propose, for such an example, that you cut it in the middle of the beam depth, put a symmetry there, and leave the fixation free to "roll" along the beam depth. You will still see a stress variation along the depth. Even, if you analyse very carefully, you will notice that the beam, at the attachment has a slight warping shape, linked to the bending amplitude. Mesh is different if you solve for the displacements, or for the stress level. As FEM solves directly for the change in length (u,v,w) or the displacements, but stress is related to the spatial derivatives (gradient) of (u,v,w), via the stiffness tensor (Hooks law), so you need far more elements to resolve correctly a stress based on the displacement gradient, than for a mesh to resolve only the displacements. So mesh for the stress, locally, or if you use mesh refinement, use the stress energy, a nice positive value concentrated at high stress levels to drive your mesh refinement. Sincerely Ivar

[@Enterfea]

Hey Ivar! Thank you for dropping in! So nice to read such well-thought-out comments - it really makes me feel grateful! So first of all, thank you! To answer your question - I decided to do so, simply because it's an artificial example anyway, and I wanted to be able to "clearly" show with the hand calculations how this works (and that it does!). You are of course right, there will always be "something extra" there, but I feel that if we would agree that the cantilever is just a middle cutout as you described, then the effect of this would be negligible in most practical cases, wouldn't you agree? Of course, you are 100% right - it would be much easier to converge deformations than stresses. However, in my experience, it's the "deformations" that usually don't have to be that accurate, while designers worry way more about stresses. I guess this leaves the field for a different FEA formulation (that starts with stresses, and derives deformation based on that), but while I've heard about this concept a few times, I don't recall any serious provider offering something like this in a commercial package. Once more, thank you for sharing the insights with us, I'm super grateful that you were kind enough to share your thoughts!

[@ivarkjelberg1317]

@@Enterfea hi just to be clear you do a great job with your videos, really nice. What triggered my comment was that you gave little warnings that here you simplified greatly the model. And as I'm working a lot in the MEMS precision instrumentation domain, these secondary effects such as stress stiffening, beam warping ... are important for the system outcome, so I'm used to go much farther than the first level. However, you are also right for constructions, with larger security factors, some of these secondary effects are just to be ignored. The most important, as you state, remains to be able to clearly identify true "stress concentration" effects versus "FEM model singularities". SOMETHING all FEM modeller MUST master well. And this applies, with its own pecularities for all "physics": structural, as well as ACDC, RF, Optics, HT, CFD, ... and even chemistry :)

[@ivarkjelberg1317]

And I'm not aware of any other "direct" method, to analyse stress, than to correctly resolve displacements, and then to extract the stress, appart if you do it fully analytically, without any "discreditation"

[@Enterfea]

@@ivarkjelberg1317 I totally understand you, and I really appreciate the fact that you took your time to comment and reply! This is what I love about my work - I get a chance to talk with folks who do totally different things than I do, and learn from this as well! I do agree that if you require so accurate outcomes, my simplifications would seem brutal (and in those cases - they are!). It's refreshing to know, that in some regions of engineering such precision is required - this is actually great news for me... Mostly because I was getting worried that I'm "too accurate" for most things - and here we are, discussing the accuracy of a simple cantilever calculations. I hope that one day I will be at the level where such things play a significant role - I feel this would be a great place :)

[@Enterfea]

@@ivarkjelberg1317 There is one I think. I mean, I've talked with a few folks who were way smarter than I am in FEA math (and I admit that I couldn't always catch up!). I think that the idea is, that instead of calculating displacements in the nodes you calculate stresses there... then based on those you calculate strains, and then based on those you calculate displacements... or at least this is what I understood/remembered - sadly I'm not even sure if this was "it" but I think it was something along those lines... sadly I'm unable to point you in any direction with this, and I'm not even sure if such an FEA approach was implemented and is commercially available - this I have never seen for sure! I'm writing this, just to expand on what I wrote, and I REALLY HOPE that I didn't mess up the description too much!

[@mekafime]

I have a K-joint hollow square section but I cant get convergence ... I tried reduce size using sphere but not work.

[@Enterfea]

Hey Fe Lix! Sadly, I have no idea how your model look, what you are trying to achieve, etc. so it's impossible to give advice on such specific things... If you are talking about "mesh convergence" (as opposed to analysis convergence) then perhaps you have a stress singularity in your model and stress will be infinite. Or maybe you still just need a smaller mesh?

[@mekafime]

@@Enterfea Could I send for email? Pls

[@Enterfea]

@@mekafime Sorry Mate, I just can't dive in into problems like that - I would love to help, but between running a company, doing online courses and raising 4 kids, I'm stretched for time very thin, and some time ago I've made a hard decision that I will focus on helping students from my online courses only :(

[@MatteoTomaselli]

Lukasz... great lesson... maybe charts in terms of dofs would add some other informative benefit...ciao ciao

[@Enterfea]

Hey Matteo! Thank you. Well, yea I get your point. However, I always "stick" to element count instead of DoF mostly since it's tangible and easier to "grasp" and I feel that the problem is complex enough anyway. Sure, it would make for a better comparison, but in the end, it's the computing time that I'm after - and to me, that would be the "best metric" although I know it's not the "conventional approach" where indeed DoF's are used. Thank you for pointing that - I feel that I should have at least mentioned it, and I didn't so I really appreciate that you brought this up :)

[@MatteoTomaselli]

Hi Lukasz it's always an honor to see you at work with FEM! ;-)

[@Enterfea]

@@MatteoTomaselli Thanks, Mate! I really appreciate your support :)

[@fortiago]

Regardless the problem you are solving and kind of elements using, you should always check mesh convergence. However, when the problem is too complex, sometimes you cannot refine your mesh, because it gets impossible to solve, and have no ideia of your approximation error....

[@Enterfea]

Hey Tiago! Well, I'm on the fence here. I mean, sure - it would be lovely (although quite boring) to do mesh convergence on each project. But I tend to be more pragmatic in my approach. I do mesh convergence on each "type/solution" of a project. This means, that if I did something "similar" in the past, I think (or at least hope!) I know enough to be able to judge that the similarity is sufficient, and then I would base my mesh on the previous mesh convergence. Otherwise, I would be stuck with a TONS of analysis that takes ages to compute. In a similar case, if you have a huge model doing refined mesh locally (maybe even in different locations in different models) to check what is going on maybe the best approach. What do you think?

[@fortiago]

Experience helps a lot. And solving local problems to verify accuracy seems to be a good alternative too. Thanks very much!

[@Enterfea]

@@fortiago My pleasure!

[@peeolo]

as alwasy, great content from Likas and enterfea. PS totally OffTopic. I love your library. It's so "steampunky"

[@Enterfea]

Thanks Paolo! I'm really glad that you like the content. Yea, I really like the new furniture at our office. I will make a tour (it's one room, so you know, it will be a long tour :P) when we are done with the setup... but our working environment really got upgraded recently :)

[@peeolo]

@@Enterfea it's bigger than my office. One room. Buy...very very very....very small. Like a plate in mesh convergence problem

[@Enterfea]

@@peeolo I think we will both agree that it's not the size of the room that really counts :)

[@peeolo]

@@Enterfea dire. But a Little bit of space it's not a bad thing (i'm country boy, i gronw up in a big farm. I use motocross to going accros the field and the Animals stables. ... I Need space and corn file ;) )

[@Enterfea]

@@peeolo I'm a 100% city-grown, so I guess I don't need that much space (and... I never ride on a motocross, but at least I like corn :P)

[@eartheartbaratheon791]

Cześć. Znasz jakieś fajne opracowania "przykładów z życia"? Nie najprostszych kantilewerów, kostek, itp. tylko bardziej złożonych struktur jak podstawy montażowe (z kątowników, ceowników, itd.), podnośniki, które mają na tyle skomplikowaną budowę że ręczne liczenie sprawdzające jest bardzo trudne lub niemożliwe, a z racji geometrii jest sporo osobliwości i "ciekawostek"? Chciałbym przejrzeć parę przykładów od A do Z, dowiedzieć się jaką geometrię wykluczać, jaką upraszczać. Widzę, że wszyscy lubią potwornie przewymiarowywać tego typu narzędzia...ja nie chcę.

[@Enterfea]

Cześć! Nie znam takiego opracowania, ale też jestem "prawie pewien" że po prostu go nie ma. Oczywiście robimy mesh convergence dla niektórych modeli które liczymy, ale nie mógłbym się dzielić takimi wynikami z uwagi na NDA które mam z Klientami. A to czym mogę się dzielić, robię raczej w płatnych kursach a nie "publicznie". Z czasem człowiek nabiera też doświadczenia, choć takie warto zawsze zweryfikować (jestem na etapie produkcji 10 modeli do testowania które będę później analizował MESem, robił convergence itp. na potrzeby mojego nieliniowego kursu z MES). Boję się że wiedza w tym zakresie jest bardzo trudna do zdobycia (i kosztowna, jeśli oparta o badania) więc nie spodziewałbym się jakichś darmowych poważnych opracowań... ale jeśli jakieś znajdziesz - daj znać! Sam chętnie obejrzę :) Pozdr! Ł

[@eartheartbaratheon791]

@@Enterfea Dzięki za odpowiedź. Wielu dziedzin to dotyczy i w każdej są osoby dzielące się wiedzą :)

[@Enterfea]

@@eartheartbaratheon791 Myślę że w MESie... to mogę być również ja... ale jak pisałem - jeśli znajdziesz takie opracowania - daj proszę znać. Sam chętnie się zapoznam :)

[@ubahabdirashid9622]

MASHAALLAH

[@Enterfea]

Thank you Ubah! I'm glad that you like the video :)

[@manelcamposcosta]

Nice video, please fix the sound, it's really hard to listen with sound like that

[@Enterfea]

Thank you for the comment Mcosta :) I have a decent gear to record sound, but I'm first to admit I have no idea how to use it effectively :( I'm doing my best of course, and I hope that in time things will be better... for now, it is what it is. If you would tell me what you didn't like specifically - it will give me a chance to work on that in the next videos - thanks in advance! Ł

[@manelcamposcosta]

​@@Enterfea I'm so sorry, I can't seem to find why I said that yesterday, today I listened to some parts of the video and could find the problem I was experiencing, at least in the same amount. Yesterday I was felling the volume going up and down, I was probably listening in 1,5 or 1,75x velocity, if think is that when you accent a word you get closer to the mic and I think you should get way from it, basically what I felt was everything ok but in some words you say, the volume goes a little to high and causes a little "pain" that made me harder to concentrate. I think this only felt when you increase the play speed.

[@Enterfea]

@@manelcamposcosta C'mon Mate, there is nothing to apologize for! Clearly you "felt" something was wrong, and I appreciate that you voiced your concerns - this gives me a chance to do things better next time! Yea... the "volume thing" is a mess. Sadly, I have a tendency to move around while I talk, and my mic does not like it. I'm trying to find a "workaround" (other than a neck restraint that is :P) - I'm absolutely certain there is a switch somewhere that "evens out" the volume... I just have no idea where it is... but don't worry - I'm still learning - in time it should be better :)