#### The role of software and math in FEA

I used to think about the role of math and software in FEA as about two different phenomenons. But recently…

21 November 202226 minutes read

It must have been my first real interview. The guy doing it was super friendly, so he wanted to start easy on me. It must have been obvious to him, that “what is FEA?” must be the easiest question he can start with! And he completely killed me with it! I gave the subject a lot of thinking. Finally, I feel it’s finally the time to write the post I should have written so long ago…

**FEA (Finite Element Analysis) is a very fancy “engineering calculator”. It allows you to ask a question, and it will compute the answer for you. What is great is, that FEA seems to know all the answers**! **But like in any good fantasy story, you really need to pay attention to the questions you are asking!**

If you will talk with enough engineers, you are sure to find FEA enthusiasts (like yours truly). You will also find folks who just don’t care! And of course, the people who see a lot of evil (in its pure form!) in FEA. And to be honest… I think that all of them are right to some degree!

And in today’s post, I will try not only to explain to you what FEA is. We will also discuss a bit why there is so wide a range of reactions to FEA in general!

There is a reason it’s difficult to answer this question easily. FEA in some sense is a lot of things at the same time.

I can be super factual about this thing. It’s enough to say, that FEA is a fancy calculator. It can accurately estimate the solution to equations you wouldn’t be able to solve otherwise. So let’s stop here, and wonder a bit about what this means.

I’m first to admit, that mathematics is not my thing (it will become apparent pretty quickly). It’s clear to me that you can most likely describe everything with differential equations if you are good enough. The problem is, that later… you have to solve those! And while I admit that I really respect folks who solve those equations… I’m just not one of them. So I use FEA to do the equation stuff for me!

In engineering, we often use equations that others before us solved and simplified. Thanks to this, I can do some basic engineering calculations to get stresses in my model. I don’t think the below will surprise you:

Those are the equations that you simply know as an engineer. While they sometimes are more complex, those are “easily solvable” most of the time. Thanks to the above, I can instantly tell you how the stress state looks in that entire element. This is true, as long as you can assume some things about support here. We want the specimen to be able to freely deform in a perpendicular direction. Otherwise, we would have a mess related to Hooke’s Law.

Now imagine a set of equations that would allow me to calculate accurately stress state in the connection below:

Yea… I don’t know about you… but I see a lot of weird math symbols in my head when I think about it. And I don’t like that!

Still… we need those accurate outcomes more and more since everything is optimized nowadays. And there are good reasons to optimize stuff, of course! Not all of them are economical too. Still, an engineer is left there with a nice challenge: “calculate it as precisely as you can and optimize it”!

And if you, like me, don’t cherish hours spent solving some weird equations… FEA can do this for you!

When I first realized how useful FEA can be in engineering design I was shocked! It took me quite some time to deepen my knowledge and realize that nothing is “just simple” in life. And I actually think it’s a good thing. Nobody values the things that are easy and quick to obtain by everybody.

What I realized however is, that FEA is a “fortune teller” that knows the CORRECT answer to every question! And if you ever read any fantasy novel you instantly should know a very important thing! It’s not the “correctness of the answer” that is the problem (since those are always correct). **It’s the question that counts!**

Simply put, if you ask a stupid question, by modeling your problem in some weird way, **you will get a correct answer to a stupid question**. And that answer may actually damage your design. Not only because you asked the wrong question, but mostly because you know that FEA always gives the right answer! So you will be super inclined to believe, that whatever FEA gave you… is the solution you need. While more often than not, it’s just smart looking correct answer to a stupid question that solves nothing!

And this is the real “trick” here. You simply need to learn to ask the proper questions. Of course, you also have to be ready to correctly interpret the answers you receive back. Let’s take a look, at what that process involves.

OK, so you already know that FEA is a smart tool. It can calculate a lot of engineering parameters of the model you wish to “solve”. Above I showed you that you can easily calculate stress in your model. I would guess that is the most common thing you use FEA for. But of course, there are other things that may interest you (like strains, deformations, reaction forces, and many others).

To get those answers, you will first have to “ask the question”. This means, that you need to show your FEA software, and what problem you wish to solve. This way, the solver will know what answer it has to give you back.

The process of “asking the question” consists of several steps:

**Making the model geometry.**This is usually where you will start. Sometimes you will receive a .stp file from your Customer (with their model from CAD), sometimes you will start from scratch. Just remember that the FEA model is not a “manufacturing model”. You are using it to analyze things. Many small details that some CAD models have, will just get in the way of your analysis! This means that you should “clean” your model and remove those unnecessary features! You also have to assign material models, thicknesses of plates (if you use 2D mesh), etc. Geometry usually looks like this when finished:

**Meshing your model.**FEA doesn’t really solve “your problem”. You already know from the connection example above that things are complicated. There are no defined equations you could solve for most of the problems out there. What FEA does instead is pretty smart. It “divides” your problem into super small “chunks” (called elements) and solve the “simple problem” of each element separately. And then simply “combines” those small solutions into one single big answer. The problem is, that it is you as the user who divides your problem into those smaller chunks. So dividing your model into elements is your work! We call this phase of work “meshing”. And this is the model we discuss after you would nicely meshed it:

Meshing is a rather complex thing when you are starting…But no worries, you are not alone in this! You may learn more about meshing by reading some of my previous articles:

What are nodes and elements in FEA?

What are the types of elements used in FEA?

**Loads and Boundary Conditions.**The above gives you the “base”. Now you need to explain to your solver, what you want to do to your model. How it is supported, where the load will be etc. This is often a tricky part! I would be willing to say, that properly supporting your model is one of the most difficult things in FEA. In our case, the model would look almost the same with and without supports. Support symbols are small, and would be barely visible. So I added red lines to indicate applied load and pinned boundary conditions):

Something about boundary conditions and loadsIf you are interested in boundary conditions and loads in your model, you can read those:

**It’s time to ask the question!**You do this by defining an analysis. In simple cases that is by pressing the “analyze button”. But in more advanced nonlinear calculations there are things you can control to “aid” the FEA solver in solving the problem quickly for you. For now, let’s just say that this is a simple linear analysis, so pressing “calculate” is enough!

This may seem pretty straightforward, especially since nowadays FEA software is super simple to use and quite user-friendly. However, in reality, there are many questions you need to answer at this stage like: Is my mesh good enough? Did I support my model in a reasonable way? What about loads – did I think them through and applied well? And so on.

I’m not trying to discourage you AT ALL. I just want to show you that things are complex, so you can avoid doing some beginner mistakes!

I feel that this is especially important nowadays. The simplicity in which you can use the software may lead to the conclusion that this is all simple. And this is a whole other problem…

Software simplicity may be a problem in its own right!Nowadays, a lot of programs allow you to use FEA, and those programs are also pretty easy to use. This means, that it’s easy to ask “any question”, but not necessarily the “right one”!

Remember, that answers from FEA always look smart – this makes them easy to believe in! If you ask a stupid question, the answer will be correct, but still won’t lead to a good design.

You need to ask the right question, and the fact that asking questions “comes easy” nowadays, doesn’t mean that the questions themselves are easy. Usually, that is not the case, and I feel this will have some serious consequences in the future!

I wrote more about simple to use software and how I think it impacts engineering in this post.

At this point, you managed to ask a question. FEA solver will work to produce the answer. When this happens, you enter the “second stage” of FEA work.

**The second part is understanding the answer.** I’m not sure if this is simpler or more difficult than asking the right question. But it is definitely not easy peasy!

Let’s assume for now, that you answered the correct question. By this, I mean that you did a decent model. You know, the mesh was good, loads were reasonable, with decent supports. In short, your model nicely represents the problem you want to solve. This is definitely a big part of the success!

So now, you obtained a correct answer to your good question, and the answer looks like this:

Awesome, but… what now?

And that is a really great question. You can see all the stresses, strains, deformations, and literally thousands upon thousands of other numbers. You can display all of those easily on your screen. But the final question remains: is my design ok?

And the funny thing is, this is not a question you can ask your Solver. This is something you have to decide for yourself. You do this based on all the information you’ve gathered from the “FEA answer”. Your job is to form a conclusion about whether this will be ok, or we need to make changes.

This doesn’t have to be a simple call to make, and there are no “easy guides” here. There is a learning curve you will have to beat in order to “get there”. But don’t lose heart – it’s all doable.

Some more FEA resources for you!If you wish to learn more about understanding the answer, you can read more about analyzing outcomes in this post!

But I have a feeling you may also want to check my complete FEA beginners guide, here!

To me, what happens between me pressing the “analyze button” and me obtaining the “FEA outcomes” is pure magic! I was never a big fan of learning the internal works of FEA solvers. Just as I don’t really care how precisely my laptop works (and still I use it all the time). We live in a complex world, and it’s simply impossible to learn about everything… and I let it go.

But I took some time a while ago, to write a simple guide on how FEA solver works. If you are interested, you can read it here!

And this small add-on nicely brings us to the topic I feel I really should cover here. And that is… what FEA is NOT!

If you would read some about the subject, you will quickly realize something. There are two acronyms thrown around (often interchangeably). That is FEA (Finite Element Analysis) and FEM (Finite Element Method). I think that we should clear this division before we will move forward.

**The Finite Element Method (FEM) is a pretty scientific thing.** In short, it teaches folks how FEA knows the correct answer to all questions. It’s the thing that your computer does between you ask a question, and you obtain the answer. Note, that FEM has nothing to do with the way in which you ask the question. It also doesn’t help you to analyze the answer. But it teaches you how the questions are being answered by the computer (like all internal mathematics of it, etc.).

It is often said that FEM is extremely theoretical, and I don’t think that is the case. I mean, what they teach you about FEM at university definitely is. But I know folks who work in the field. They are extremely skilled professionals that understand stuff I could not even name! Sitting in their offices they write solver algorithms. They figure out how to make analysis converge quicker. They even implement new calculation possibilities to the existing software solutions (or create new ones, of course!). If you are the best in the field, this can be an extremely well-paid job. Just don’t expect those folks to design much – this is not what they do! I think of it more as the IT/Complex Math field in software dev. A great thing to do, just not something that interests me.

Funny enough, FEM is way easier to teach at University! At the “beginner level” it is a very “closed form”. This means that there is a set of things and equations you have to follow, and it always works! A perfect thing if you want to quickly assess if all of the 100 folks in your lecture “understood this”! This means, that if you had FEA classes at University, you were most likely taught very basics of FEM. This means I have some bad news for you!

**Finite Element Analysis (FEA) is the practical stuff!** You could say that FEA is simply the practical use of FEM in solving real problems. It’s the “art” of asking the right question and analyzing the answer you get back from the software.

Some engineers would say, that you need to understand a lot from FEM to do FEA. That understanding FEM is needed to be able to ask the right question and understand the answer. And I’m not downplaying that argument, although I do not agree. Mostly because I don’t know a thing about FEM, and yet I can use FEA on a very good level.

But without a doubt, there is a certain understanding of “how things work” that is needed to effectively use FEA. You can gain this understanding in several ways. One of them is definitely learning all about FEM. But this seems to be a very time-consuming way (and success is not obvious either!).

You can for instance do a trial and error instead (this was my choice). What you need then are some time (a few years in my case!) and analytical thinking. With some effort, you can actually figure out a lot of this stuff yourself.

Of course, you can also learn from other practitioners (like myself i.e. from this blog). I admit this is also what I’m doing now myself by asking around my “FEA Friends”!

What I’m trying to say here is, that you don’t have to know FEM to use FEA effectively. I don’t know it at all!

But you definitely need to know the “wisdom” that comes from FEM. There is an analogy I often use:

You don’t have to understand how the clutch works in your car. All you need to know is that you need to press it before you change gears! Sure… understanding how it works would help. If you knew that you would most likely conclude that this has to be done to safely change gears.

However, there is a way more efficient way to learn this. All you need is to learn from someone a simple truth: “in order to change a gear, press the clutch”! It works whether you understand how the clutch work or not. It’s as profound as that! Sure, FEM provides the wisdom that is easily applicable. The problem is that it can be wrapped in a LOT of complex stuff you don’t need! Just like you don’t need the understanding of the inner workings of the clutch to press it!

**Faking FEA!** At this point, it’s quite clear that for a practicing engineer FEA is way more appealing than FEM. Unless, of course, you want to work more in the IT sector, which is awesome in its own right! This is why a lot of “Faking FEA” has happened over the last few decades!

If you follow my blog for a while, you most likely know that I don’t like FEA books at all. Most of them are glorified (and boring) FEM manuals that I’m just not interested in! Heck, I even saw a few “Practical use of FEA in engineering” books, where the practical aspect was that they used “numbers” instead of “symbols” in solving all of the FEM equations given in the book!

To someone who does FEA design for a living (and doesn’t use those equations at all), this is infuriating! Not to mention that if I ever write an FEA book… I don’t even know how to tile it, since nobody will believe that it is useful at all…

So to wrap this part up, FEA isn’t about solving the FEM equations. Heck, I wouldn’t even recognize FEM equations if you would write some down and show me! Not to mention writing them myself (which is impossible, since I cannot recollect stuff I never knew!).

I’m afraid that there is a huge “scientific industry” that would like you to think otherwise! I have “discussions” with folks about this on Linkedin. So far nobody managed to convince me of anything. But I have to mention Antti. He wrote his own solver and now uses it in industrial applications in his own company. But this is not an argument here – Antti simply has to be an alien!

Funny enough, all of the “FEM apostles” that I’ve met, refuse to have an online public discussion about this with me. No idea why I’m a super relaxed guy! A few were “initially interested”, but after I told them my stance (that I described here) they quickly backed off…

**FEM vs FEA, and your road ahead! **You may be surprised why I spend so much of your time explaining the difference between FEM and FEA. But there is a very practical reason for this (as to almost all things on my blog).

I’ve met a LOT of people who spend years learning about FEM. They hoped that this way they will be “great practical FEA designers”. Usually, what waits at the end of that road is the feeling of disappointment!

Because you need to learn/know/understand completely different things to be good at FEA. Sadly, “how FEM works” is super low on that list! It is on the list, don’t get me wrong. But there are so many more important things, that starting from learning FEM makes absolutely no sense.

The problem is, that the practical things you have to learn are “different”. They are not “closed formed” as the basics of FEM. This is why they are rarely taught at Universities I think. After all, no matter what the problem looks like, solving a task with FEM follows a strictly defined procedure.

On another hand, supporting a complex model isn’t obvious. It always depends on the model. You can do it in several ways that “aren’t perfect but are good enough”. This makes learning those things a bit more tricky. Especially in a University setting. But trust me those are the skills you will need the most!

So if you want to start learning FEA, instead of spending months over some FEM manuals, read the list of skills I think are the most needed to successfully start in the FEA field. Perhaps I manage to convince you, that learning those will be way better for you. I can honestly tell you that it was way better for me for sure!

All right, now you know I hope what FEA is, and why there are so many misconceptions about it.

So now, let’s take a look at what people think about it… and why!

I won’t lie, I’m in this group for sure!

But this doesn’t mean of course, that I’m blind to the problems I will mention later. Truth be told, the good things about FEA only apply if you do FEA correctly. And this can be treated as a critique – and rightfully so!

We will get to the bad parts later, for now, let’s assume we know what we are doing. So if you have a sufficient skillset, the main positives are:

**Outcomes from FEA are great!**In complex cases, engineers for years were simply estimating, or even guessing outcomes. Using experience and engineering judgment, they tried to asses how something will behave. And while you could not be certain, you could roughly guess the stress distribution in a component. Now, this uncertainty is completely gone. Correctly done FEA simply gives you the correct answer. No need to guess, estimate or judge anything!**Limitless possibilities!**At this stage, I feel comfortable saying to my Customer, that if the thing is made from metal… I can design it in FEA. If you master this craft, there aren’t many limitations, apart from your knowledge. You can do in FEA whatever you like, and be reasonably certain about the obtained outcomes!**Solve unsolvable problems!**Yup… just that! I’ve made a Ph.D. in shell stability. To this day, many things are simply unsolvable without FEA. Shell stability is just too complex, and this means that it’s not “described” with closed-form simple equations. And while each shell problem is different, all of them can be solved in FEA. Regardless if there are codes for them or not!**This is a highly sought-after skill!**My company only does nonlinear FEA. We do not draw things we calculate, we don’t even check drawings made by others. We just calculate stuff! And trust me when I say, that there are companies out there really searching for such services. Because a lot of folks can do “some calculations”, on a basic level. But finding someone who can do a really good and reliable nonlinear FEA design is absolutely not easy. I will say that going this route was a great career choice that I’ve made those years ago. FEA is just worth it!

In summary, FEA is the most powerful tool in my engineering arsenal. But of course, you can’t just use this lightly.

I believe in everything I wrote above, but I have to point out something. Those benefits work for you when you really know how to do FEA correctly. When you understand what question you want to ask, how to ask it, and how to interpret outcomes.

It seems obvious, but in reality, it’s not that simple. And I would say that the main FEA critique comes from the fact that people do not understand that!

As I mentioned, I’m well aware that FEA is not only sunshine and rainbows. There are some drawbacks to it as well! Let’s unpack them.

**FEA is difficult!**It takes much effort and time to learn how to use FEA properly. This is of course a drawback on its own. But it gets worse. Many folks “give up” along the way, and while still not knowing enough they start to provide FEA services. This means, that there are many folks who use FEA but not necessarily in the best way. And while we all learn and develop as we go (and it’s good!) I really worry about folks who do stuff as they always did!**FEA outcomes always look smart!**You already know this from this article! You will always get “some” outcomes. They will always look smart. But if you ask a stupid question… those answers can be harmful, not helpful for your design! The amount of complex analysis of wrongly supported models I’ve seen is terrifying. Outcomes from those are literally worthless… but they still look smart!**It’s not only about FEA!**This is very often omitted I think. FEA is like a calculator. It’s good that you can use it, but unless you know what you want to calculate, it won’t help you much! This is somewhat tied to “asking the right question” I would say. You simply need to have good engineering skills and understand a lot of things to use FEA. And those things are more “engineering” than “FEA”. This means that it’s not immediately obvious that you need those skills. But you really do!**Computing can take ages!**If you want to accurately analyze a complex model, computing of the outcome can take hours or even days. While you don’t “work” during this time (it’s the computer’s work) – it still takes time. Hand calculations (especially automated in spreadsheets etc.) would only take a fraction of that time. So effectively, in order to get a very accurate answer, you have to use “more time”. Sometimes, this is a time you may not have.

Let’s start from the end. It’s true. Advanced FEA is time-consuming. This is a drawback, but perhaps not as big as you would think. You get used to running models during the night and that sort of thing. But the “recalculating” model in 10min on a meeting is not a thing. And clearly, in some situations, it’s a drawback. All I can say is that the possibilities and accuracy of outcomes make it worth it to wait. At least in my eyes!

You can boil down the rest of the drawbacks to a single thing:

If you want to use FEA in design, you have to be good at it!You not only have to understand very well how to use FEA in design. You will also need other engineering skills, not necesairly connected with FEA. Skills that will make you a good designer (FEA or not) in the first place!

And the scarry part is, that whitout those skills, FEA may be dangerous for you – so be very careful when you start! Always double check your outcomes with some other methods. Just to be sure you know that what you received is correct!

This is, of course, a huge drawback. Especially since FEA seems so easy to use nowadays. It’s almost as if any CAD user can do FEA now, and many unprepared engineers do!

Effectively, this leads to a situation where many FEA users, are not trained enough. And we all have seen outcomes from “stupid analysis” I’m sure.

This kind of gives FEA a “bad rep”, as many people were burned before.

But is this an FEA drawback, or just our carelessness as engineers? I don’t think I can answer it, as it is definitely both.

All I know is, that if they would take all school teachers, and ask them to be jet pilots after a brief training… we would have a lot of jet crashes for sure. Does this make jets any more dangerous? Yes, and No I guess. Jets would be just as safe… in the hands of an actually trained pilot. I really feel FEA (and engineering in general!) is just like that.

And here we are, at the end of this ultra-long post. I really hope that you don’t mind the length and that you actually learned something useful here!

We’ve covered a lot of things in this article, but I want you to first and foremost remember this:

Practical use of FEA is the art of asking a question, and understanding an answer.To ask a question you have to be properly trained. You need to understand how to use FEA, but also to have some engineering knowledge needed in design.

Knowing FEM (the math behing how solver computes the outcome) may help a bit. But this is a very small, and even unnecessary portion of the thing.

What is the most important part, are the practicalities of using FEA: How to properly support and mesh and load your model!The answers from FEA are always true… but

if you ask a stupid question, the answer you get may damage your design, not help it!It will be super easy to believe in FEA outcome – so always be critical about the question you asked!But in the end,

when you finally master this skill, FEA is just unpararell. It opens so many doors, goving you incredible opportunities. It’s definitely worth all the effor needed to learn it!

##### Categories:

- FEA Fundamentals

10 Lessons I’ve Learned in 10 Years!

10 Lessons I’ve learned in 10 Years!

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