FEA The Big Idea - Brain Waves.avi

[Music] hello again I get a lot of questions about finite element analysis and I thought that would be a pretty good topic for at least one video probably more as I get farther into it when I get questions about finite element analysis it's never about the real nitty-gritty details that's covered pretty well in books and papers and things like that and sometimes even in theoretical manuals for software the questions I tend to get more of the basic ones what am i doing finite element analysis what's it good for what's all the fuss about where did it come from okay what's what's the big deal here and they'll seem like pretty fair questions I I took a lot of finite element classes and I don't remember anybody going over those for me maybe they thought it was so obvious they didn't need to and I was just too thick to notice these things on my own so for whatever it's worth I'm going to go over that now right now finite element analysis is a way well technically it's a way of solving differential equations but for engineers it's mostly a way of solving structural problems although electrical engineers use it to solve a lot of times electromagnetics problems there's all kinds of anything that's described by a differential equation you can solve using a finite element method if you want to I learned it as a structural analysis tool so that's kind of how I'm going to talk about it and that's really how it was mostly developed at least within the aerospace industry okay so let's talk first it's a way of doing structural analysis that's you always see that it's a structural analysis method structural analysis you see the caption esters Oh what structural analysis mean I must be doing it but I'm not quite sure what that means so listen let's get that out of the way first let's say let's take a really simple example let's say I've got a bridge okay and I'll put the rollers over here so if there's a thermal change you know that gets really hot or really cold that end can move because of strong thermal expansion let's put some beans in here it's pretty obvious why I'm not a British designer let's that's there's probably some kind of standard trust it's a prat trust or a Warren trust or something like that so let's say I've got a bridge here and let's say I've got big truck going across it okay there there's a big truck and it's got weight on it okay pretty obvious why I'm not an artist - okay so let's say this is a big big big truck say it's a hundred thousand pounds so that's what like forty five thousand kilograms which I know is mass not weight but forty five thousand kilograms it's big it's heavy right now the other thing I want to Miz it's not going very fast I don't want to inertia it to matter here I don't want dynamics to matter this is going to be just I'm going to talk about this as a static problem static means moving masses don't matter other than the extent that they produce a weight okay inertia doesn't matter if you can also do a dynamic analysis where you start worrying about vibrations and responses to impulses and things like that but we don't need to worry about that yet okay quasi static that's what we're really assuming here so is the bridge where the truck moves across the bridge there's this weight that I can watch move across the bridge and the loads will change on the bridge as the truck moves across so what do I want to know why would I want to mathematically analyze this whatever that means well I might want to know what the deflections are I want to know if it's good the bridge is going to Sag or something like that but more particularly I probably want to know what the stresses are is the bridge going to fail is it going to dump this truck and the poor driver down into the water so I'll put the water right there pretty sure that truck doesn't float and I'm pretty sure that driver does not want to be in the water so that's what I'm trying to avoid so analysis structural analysis anyway is given the forces or loads of forces find deflections and probably more important stresses but once you're finding one you can find the other right so given forces who want to find deflections or stresses that's what it means to do structural analysis now all we're talking about now is what tools do I have to do that with well if you're an engineering school or engineering technology like I teach or any number of other fields you'll learn a couple of tools and you'll learn them pretty much in order number one we learn statics ok number two we learn strengthen materials why should give it a shorter name huh and three we learned for finite elements actually when I was in school about a thousand years ago they still taught this as matrix methods which turned out to be pretty handy um but it's very closely related well statics why do we do static statics is easy well relatively easy ok statics reduces that trust we just had to basically a geometry problem and you solve it using algebra you know the method of joints or method of sections all right so it's simple well that's good it's we can find stresses but it's only approximate five statics only approximate well those of you who've taken a statics course did the words elastic modulus ever appear in that class did you ever calculate a deflection probably not because we assumed the assumption over here is e is infinite okay there is no deflection that's why it's simple it takes pretty gnarly mathematics and makes it a lot simpler by just saying all right we're not going to worry about deflections we're just going to pretend they don't matter so what that's why this is approximate simple an approximate go hand in hand okay you can calculate approximate stresses but you can't calculate them taking into the into account the effect of deflections that's just the way statics is set up but it's really really handy if you don't believe me go look at any bridge made before well certainly before World War two for nineteen forty maybe but let's go back farther than that before the turn of the 20th century go find some bridge trust but look at the Eiffel Tower something that was built before 1900 that has lots of trust work in it okay well chances are excellent that it was designed mostly using static there just wasn't any other tool at the time so people use statics and generally pretty hefty safety factors well last I checked the Eiffel Tower is still doing just fine it's standing survived a couple of wars and pollution and corrosion all these other things it's still doing fine people still use it go look at the Brooklyn Bridge in New York City in the US well that bridge was designed long before the car was around and it's holding cars and trains and trucks and everything else it's doing just fine still in service well it's well over a hundred years old now so clearly statics must work likes a pretty hefty safety factor well let's say we want a more accurate [Music] type of analysis would go to strength and materials now we do take into account deflections we do take into account the fact that elastic modulus is some finite number okay okay still pretty simple let's call it pretty simple it's not as simple as as statics okay takes into account deflections and that's pretty useful because all real structures deform right when I sit on my office chair over there it creaks a little bit and settles a little bit its deforming us I would actually be a little worried if it didn't would be very comfortable if it didn't okay so it's pretty simple counts for deflections hard to do complex structures okay what if we had that bridge I just drew up here and I told you you had to account for all the deflections on it and calculate the stresses then what started out as maybe a long homework problem now becomes much much more of a big deal okay and that's because of elastic modulus being an actual number and not just infinite now deflections are something we need to account for all right so that brings us to finite elements that includes the best of both worlds we get to do it looks simple to the user and doesn't seem that way but it is we get accurate stresses we get deformations we account for the real stiffness of structure so elastic modulus is part of it we can put very complex geometries into a finite element model and it works very well okay so I'm just going to call this best of all worlds plus more you can view things with finite element analysis couldn't begin to do with either one of those other tools now in the old days even almost when I was still in school I graduated in 1985 so the dinosaurs were still crawling out of the oceans that I'm sure people still did something else in between here there was still a lot of analytical work going on solving big gnarly differential equations it was kind of the tail end of that and I don't know people still do that anymore or not but certainly finite element analysis accounts for almost all the structural analysis that goes on now I've been talking for about nine and a half minutes here give me about three more minutes and I'm going to give you an example of why finite elements is useful and then I'm going to stop okay so let's I was trained as an aerospace engineer I actually learned to design airplanes rather than bridges it's pretty cool let's take an aerospace example there's the centerline of an airplane and there's the fuselage maybe it's an airliner and so I've got a wing all right big long way and they act kind of like beams they get analyzed like beams so the wing is swept all right and it's a taper so it's a pretty complex being and of course maybe there's there's a big engine down there all right the engine weighs a lot and it's got a force going this way and the other part about this is that the load across the long they've been winged is worse distributed and it's an ellipse well except for maybe let's say that there's a control surface the aileron is drooped a little bit so that the planes going to roll that way that's a very very routine thing well this doesn't look like that anymore it probably looks more like that so I got to take that out okay this is a very routine problem there's nothing unusual about this this is something in airplane design I'm sorry got that going on wrong way don't I this is something an airplane designer would see all the time okay okay so there we go there's the additional force from that aileron going down I could model that as a beam in fact people do all the time and here's the equation I gotta solve okay I'm gonna write this down but I'm not going to solve it cuz it's awful [Music] okay this is the Euler beam equation and this is at the root of all the beam analysis that we do so this is the second derivative with respect to X where X goes this way okay of E and I now he is the cessation all made out of aluminum well he's the same all the way down here I isn't it tapers so I is now a function of X so you have to take a derivative of that and that W there is the deflection so W if if the Ling deforms that way okay that's that that function there is W of X and we'll just solve this equation you're trying to find a w of X that makes this true right Q is the shear well there's the load you can figure out shear from that you want to try to solve that analytically I don't I'm not sure I could well nobody else can either so this is where finite element analysis comes in to solve this analytically would be a nightmare to solve it using finite elements it's actually pretty simple and all I'm gonna do is I'm going to say well I can't analyze that whole structure it's just too complicated what I can do is I can start breaking it down into little pieces like that okay I'll break it into the little pieces and I can analyze any one of those little pieces that's easy if I can analyze all the little pieces and add them together in the right way so they're all compatible with each other and the effect on each other is is accounted for in the math well it's like Legos you know the little blocks you build things out I can build an entire castle on a Lego block so the Lego blocks are just these little rectangular things well I can build an entire wing of an airplane out a little sort of mathematical Lego blocks I can analyze the little blocks and I can assemble them into something as complex as I want that's finite element analysis that allows you to do very complicated problems if I don't know loads I can calculate the deformations and the stresses using finite element analysis for problems that are way too complex to do any other way that's the big idea okay

Channel: purdueMET

Views: 39,828

Keywords: FEA, FE, finite elements, finite, element, analysis, math, engineering, computer, strength of materials, statics, structures, structural analysis, engineering technology, technology, educational physics

Id: WQJS7Z-uebw

Length: 14min 11sec (851 seconds)

Published: Tue Jul 26 2011