What are the Applications of Finite Element Analysis

I think that I have a tendency to overuse FEA. Since I know how to do it, it feels natural for me to do so! I guess it’s true that when you have the hammer, everything looks like a nail to you! Thinking about this, in this post I want to discuss what are the applications for Finite Element Analysis!

Finite Element Analysis allows you to solve any engineering problem that is “unsolvable” otherwise. It also greatly increases the accuracy of your solutions. However, it takes time to perform FEA correctly, so using it for problems that can be solved otherwise may not be the best approach.

Let’s dive deeper and see, where FEA is most useful and where to avoid it!

You need to simplify things to calculate them!

I think that in order to design something, you need to be able to describe it in a simplified model first. Let’s face it, whatever you are trying to do, it’s most likely far more complex than anyone can imagine. Trying to take “everything” into account would drive you mad for the simplest of tasks, not to mention the complex problems.

I think it’s easy to prove! Imagine a wooden board that you try to use as a footbridge over a stream. A pretty straightforward task eh?

Let’s run our imagination wild and wonder what could go wrong! My list would be something like this:

• I’m too heavy – the board will break under me
• The board can deflect too much… I won’t feel comfortable walking on it
• There is a gnarl in the board… maybe this place will break unexpectedly?
• What if the riverbank is too soft and the board will slide to the water at any end?
• Maybe I should also consider someone heavier going over my footbridge later?
• What if that guy will take a barrow of sand with him!?
• Will this board withstand years of usage, or should I replace it every now and then?
• Bugs can eat my board – if I fail to notice it I might get wet…
• If I run too fast, the board can “jump” with me and fall into the water
• If I accidentally kick it to the side it might be too light (friction won’t help in such a case) and it will fall into the water

I’m pretty sure you get the point – there is A LOT of things that can go wrong even in such a simplistic problem! But we can’t analyze all of them. Some are not that probable, others we will decide are out of the scope of what we want to worry about. Regardless of why we won’t analyze all of the above, we will analyze only some of the problems. And even then, we will simplify the problems even more, before we even attempt to solve the task.

I think that it’s pretty obvious to see, that the problem I’ve chosen leads to the simplest possible schematic:

In the above, a lot of the problems just disappeared. I won’t analyze the gnarl, I will use the “average” wood strength instead. There are no bugs, and somehow I limited the possible loads to only one “worst acceptable case” and so on…

This is called idealization. It’s a process of simplifying your model enough, that you can actually solve it!

Very important point:

I’m sure you’ve heard the term idealization somewhere. Authors usually assosiate it with FEA. This makes some sense, as you have to simplify “reality” into a rather simplistic model to solve it in FEA.

However, all other approaches to solving the problem requires just as much (if not more!) simplifications! So idealization happens regardless if you are using FEA or not. It’s a part of the engineering approach to solving problems regardless of what solution method is used!

I’ve written the above example just to point out that regardless of the approach to solving the problem idealization will happen! This just means that idealization is not a disadvantage of FEA! It’s rather a disadvantage of engineering itself (assuming that idealization is a disadvantage at all)!

All the tools at our disposal

Knowing all this, let’s wonder what approaches we can have to solve engineering problems in general. This will really help us to decide what are the applications of Finite Element Analysis!

I would divide the possible approaches into 3 categories:

Tests

Testing is the backbone of engineering. After all, at the “beginning” there were no other options! If you are not sure if something will work… do it and see what will happen!

Of course, not everything can be done “just for a test”. Some things are simply too big/costly/problematic to build to verify the solution. This is why scale-down or simplified models are used for testing most of the time. I mean, I did a Ph.D. on shell stability, and my lab models were 1m in diameter (while a “typical silos” has more like 6-10m diameter). This was necessary, as I was able to order such small models and I actually had access to gear that could reliably destroy my models. Building an 8m in diameter silos just to destroy it (and see what will happen) was kind of out of the budget for my Ph.D. research. And even if I would have money for that (yea…) I would need to build at least several silos for statistical reasons!

Typically testing in engineering works like this:

• Think what you want to test. Try to single out the most important thing you wish to verify!
• Design a model that will work like a “real thing” (or as close to that as possible). You need to think about the testing rig you have, how to measure stuff and all that.
• Create the model. Most likely you will have to measure it accurately, check for defects and all that.
• Perform the test – see if your assumptions about the model are correct, if nothing unexpected happened, etc.
• Create more models and test them as well.
• Draw conclusions and make the statistics

Does this look like a very expensive and time-consuming thing? Well… it should! Tests are an awesome way to learn things, but they also cost a lot, and many companies can’t afford any real-life testing. This is why other approaches were developed. Next in line is math!

Math

If everything would be doable with the math approach easily, FEA wouldn’t be necessary! It seems that “the math approach” has not so many drawbacks. Well… at least if you happen to be solving a problem that was already solved previously! If you face something new… you may have to fight with a swarm of differential equations and other monsters from the math realm. Not all emerge victorious from those fights I can tell you!

And this is the only drawback of the math approach I think – stuff is complicated. It’s complicated so much, that it may actually be unsolvable! And I’m not talking about anyone’s math skill level… the problem might be unsolvable “in general”! We have a lot of really cool equations we use, and take for granted nowadays. Every time you calculate normal stress in bending by dividing a bending moment by section modulus you are using solutions that were derived by someone in the past. When you have such solutions… math is simply the best approach!

How mathematics is used in solving engineering problems:

• If you have a “closed” math solution of a given problem, all you have to do is to input numbers into the equation and your set! You will simply get a proper solution with 100% accuracy. How cool is that?!?
• Sadly, only the most basic problems have a closed mathematical solution. This means that while this approach is super great, its use is very limited. You can solve only problems that can be solved this way!
• If you are attempting something new… you will have to figure out the closed-form solution yourself by solving a lot of differential equations. While this is doable, it’s definitely time-consuming. And… sometimes you will end up with the equation that is cumbersome and difficult to use.

Before we move on, let me demonstrate something. Imagine that you want to know the stress distribution in a complex connection like the one below. How would you imagine an equation that allows you to calculate such a stress distribution by hand?

Yup – this is a tricky question – this is why we use FEA most of the time (or do a test and measure strain with strain gauges on real models of course!).

Finite Element Analysis (FEA)

We’ve made it! Now it’s time to wonder where FEA kicks in in all of this.

You already learned that not everything has a mathematical solution. Most engineering problems are so complex, that they are more or less unsolvable with the differential equations approach. On another hand, tests are expensive and time-consuming (and not always possible, to be honest). This means that there is a “gap” between the two approaches we described before. A gap that is nicely filled with FEA!

In essence, FEA helps you with solving problems that are unsolvable otherwise. You know everything is too difficult to solve with a “direct” math approach, while too expensive or problematic to solve with tests. I think this is the *power* behind FEA, and why it’s getting more and more popular among engineers.

How FEA works in engineering problems:

• You need to define your model correctly. It’s actually difficult, just like in case of laboratory tests. You need to precisely understand how your model will be supported and loaded etc. There are also FEA specific problems you have to deal with like meshing.
• When you have the model, you need to decide what sort of analysis do you wish to perform, and be sure if you can analyze the outcomes correctly.
• Finally, you do the analysis and get all those awesome solutions. I strongly believe that you can analyze anything in FEA. But of course, some of the problems would take quite some time to solve!

It’s true that FEA delivers “estimations” and is not “precisely accurate” like differential equations. But it also is true, that the “math errors” in FEA are negligible if you know what you are doing!

I think that the biggest mistakes come from not understanding the problem itself. It’s just like planing an experiment. If you don’t fully understand what you want to solve and why… you won’t get correct answers. In that regard, FEA is just as difficult as math or laboratory tests. The problem is, that if the test fails it’s usually apparent to the experimenter. Sadly, FEA displays stupid and correct outcomes all the same…

How engineers solve stuff!

I don’t have to explain to you, that all of the 3 approaches I just described are needed. After all, if any one of those wouldn’t be needed, we wouldn’t use it!

The really skilled engineer knows when each approach is the best.

But experts can also combine the approaches in various ways to solve really difficult challenges accurately. And this is the true mastery I think!

What I really like is how nicely FEA “fits” with the other two approaches. To be honest, in the beginning, you cannot be sure if the outcome you got from your analysis is correct. It’s definitely true that you can obtain wrong outcomes and draw false conclusions with FEA (just like in the case of math or tests for sure!). This is why it’s great to solve problems that have a math solution (or previously obtained and tested solution of another kind). You do so simply to compare your FEA outcomes with the know ones. This way you learn if you can actually deliver proper FEA results! Such actions are often referred to as *benchmarking*.

Also, when you do testing on smaller (or simplified models) you may want to solve the same problem with FEA and see if you get the correct outcomes. If that is the case, you know how to model something in FEA! This allows you to “scale” the test outcomes to more complex or bigger models without suffering the costs and efforts of additional lab tests. I would call this *calibration*, which is also important.

Finally, you get better with time. After a few benchmarks and few solved problems, your confidence in solving a particular type of problem in FEA grows. This allows you to solve problems similar to those you did before without benchmarking and testing – which is a huge benefit that comes with experience. I admit that getting there takes time, but all the possibilities… I never regret that I’ve sacrificed a few years to learn what I know! It was definitely worth it, and I’m still learning new things! FEA is super fun – trust me!

When to use FEA?

Ok, you know the background now, so let’s wonder where Finite Element Analysis is best used.

Of course, there are myriads of ways you can use FEA! Instead of making an unending list, I will first write a short list of conditions, and then show you how I developed my skills in FEA, and how I progressed from various problems to solve more and more complex things.

Thoughts on using FEA in engineering:

• If you can’t test something, and you don’t know the math solution to the problem – FEA is your best friend!
• It’s always good to be able to predict the outcomes for a problem. Even as an unaccurate estimate. Alwyas bear in mind, that you can do something wrongly (in testing, FEA or math) and if you can’t estimate the outcome you may miss your mistake!
• In the case when you can’t estimate the outcome it is best to use at least 2 methods simultaniously. I.e. you can use FEA, but also do a simplified test or try to estimate the outcome mathematically. This way you greatly increase a chance that you will find your potential mistake!
• If you have a closed math solution of a problem, doing FEA is a waste of time. Unless of course using the math equations requires ungodly amount of effort, or you want to verify if you can get a correct answer using FEA.
• If you directly tested something most likely there is no need to do FEA, but I would strongly encourage it simply so you can see if you get the proper answer from FEA! This way next time you will know how to make FEA for such a problem, and maybe tests won’t be necessary anymore?

When thinking about FEA, I would advise you to start small. This is the road I took (well… almost :P), and thanks to this approach I haven’t given up along the way. If you will start by approaching a really difficult problem first, you will need to have a very strong drive to finish the task. Starting small, and having some successes along the way is so much better 🙂

So below, there is a list of things you can do in FEA if you are interested in steel structures and stability (like I am). I’m absolutely certain that other industries have similar lists, but I would like to focus on what is close to my heart here. It’s not even to answer the question “what FEA is for?”. I think you already have a sense of that after reading so much of this article. Instead, I want to show you the natural progression of things – something you should search for in whatever field you are in!

My FEA step #0: Simple linear analysis of beam models

Well, this is where I started. To be honest, I’m not sure if I even understood that what I did was FEA. To this day I meet people who tell me they don’t do FEA but only “the simple beam static”. I mention it here only to point out one thing:

It’s really good to have an understanding no how things you wish to calculate work!

Since I was designing steel beam structures I understood how forces, moments and stresses worked. I was also able to calculate connections (welds and bolts) by hand. This is the skill I use till today, as it provided me the tools to use when I want to estimate something. This is why I’m a big fan of hand calculations (as long as the math is simple!).

Perhaps you work in the industry where beam models aren’t used at all. No worries – as long as you understand how stuff works you’re fine. Perhaps even you had a better start than I did!

My FEA step #1: Useful details and additional small models

This is where FEA is super useful for people who actually design beam steel structures. Every now and then, there is this stupid joint you can’t just calculate by hand. Or you are sick and tired of calculating end plates for anchoring with simplified by-hand schematics.

This is where it started for me. Instead of calculating something by hand, I started to make small FEA models to quicken and simplify the solutions. It’s so useful to do such things, and yet so few people I met actually perform such calculations. I would say, that those “simplified” small models were the reason why I fell in love with FEA.

My FEA step #2: Solving small problems with FEA

I must humbly admit that at that stage I felt like a real expert. You know the Dunning-Kruger curve and all that… This is where I started solving problems with FEA. I didn’t use any “advanced” stuff yet, but I could solve a problem or two. This is definitely a stage in FEA development and a pretty fun thing to do!

You can solve a lot of problems like those. You know, the capacity curve for a “weird connection”, some stress verifications or maybe a simple plate model and things like that. It’s a really rewarding stage, as you can feel that you are earning your living with FEA. I was so happy when I finally got there (even though at that time I was still doing workshop drawings and all that!).

What I did learn here is universal I think to all FEA “fields”. You know the critically important things like how to support your models, how to load them, and how other assumptions impact the outcomes. This is a really important lesson! This is why I’m so strong on those points in my Breakthrough FEA online course!

My FEA step #3: LBA – selecting your expertise field

And yet again I felt like an expert, and now it only brings an uncomfortable smile on my face at that memory. This is when I started to “specialize” in something. I think that I was finishing my Ph.D. at this stage. I realized that stability is something I considered “fun” and I started to aim in that direction.

By all means, you can specialize in something else, but it’s obvious that every expertise starts with something. What is important here is to deepen the general knowledge in the field that interests you. You will also learn about other assumptions you were making (unaware of) in your analysis! Of course, you will deepen your understanding of the “basic” concepts here as well.

For me, this step was where I understood LBA, and I started using it to calculate critical moments for complex beams or checking buckling lengths in weird frame systems. Not to mention a simplified verification of stability in various models! Solid skills to have, and useful in many situations

My FEA step #4: Nonlinear stuff – becoming familiar with your field

And yet again I was thinking I was an expert (start to see a trend?). I finished my Ph.D. and I thought that just because I know how to set up a nonlinear analysis I know what I’m doing 😛

I admit that using nonlinear FEA is a powerful thing, and it is useful in a lot of fields (not only in stability obviously). Of course, in various problems, you will focus on something slightly different, but the principles remain the same.

Learning nonlinear FEA took me years, and some additional years to deeper understand the subject. Again I started from small and simple problems to develop my skills more and more. And at some point, I reached a level in my field that I’m happy with. Of course, I still try to learn more, but I think that at some level it’s a game of diminishing returns.

With proper use of nonlinear FEA, you can do pretty fun and “magic” things. I managed to verify very weird connections and details, calculated capacity, and stability of really weird stuff, as well as did explosion calculations and other “more fun” things. All in all, this is all doable in FEA, and it gives me so much joy to do those things. BUT (there is always a “but” right?)… If someone would ask me to do such things at the beginning of my road… it would only cause a lot of frustrations. I simply knew too little back then to be ready to take a swing at some of those problems. It just comes to you in time I think!

My FEA step #5: Expand your field of expertise

This is a lovely place. And I admit that I still consider myself a specialist, but I’m way more humble now! I’ve noticed that at some point you know a lot about one thing… and that you can “expand” what you know to other fields.

Since I had to learn about meshing along my way (surprisingly late I must add), I was ready to learn how to do fatigue design in FEA. Having done that, I switched to pressure vessels design (quite fun I must add) and since I have several projects behind me I’m already thinking about something new (maybe finally I will have some time to take a serious look at composites?).

What I’m trying to do here is, that there is A LOT you can do in FEA. And when you reach a good level in “any one thing” it will be much easier for you to learn new things. It’s like hiking. Climbing the first mountain is tough… but then at the top, you can relatively easily go from peak to peak while enjoying awesome views.

I want to end here, as I have no idea what is further down the road. I really hope that one day I will add another step to the list, starting with “amazingly I had the audacity to call myself a specialist back then, which now causes an uncomfortable smile”… we will see.

Just rest assured, that there is SO MUCH you can do with FEA that is unbelievable – and this is the message I really want to leave you with! Sure, at the beginning nothing works and everything is frustrating. I’ve been there – I know how this feels. But if you stick to your guns, you will get to this wonderful first peak, where you will feel that you have a handle on something. And it will be so close to the next peak, and the next one. And before you know it, you will be able to do in FEA whatever you wanted to do. Just practice a lot, never run away from challenges and endure. The rest is a matter of time!

Solid learning at the end!

Thank you for reading! I really hope you liked the article. It would be super cool if you could tell me what you think in the comments below.

Also, if you want to learn the most important things about FEA that I learned during my 10 years in the industry, definitely sign up for the free online course I just finished. Just sing up below – I’m pretty sure you will enjoy it! See you around!