Do you need to know math behind FEA?

Recently I asked a lot of my subscribers what they think is the most difficult thing in FEA.

While “interpreting results” or “too much theory in materials” appeared quite often, I also got several answers like:

My biggest obstacle is actually understanding the mathematical concept behind it. Although I am really interested in the application but I believe understanding the maths behind it will be extremely useful.

As I wrote few emails about it, I figured it will be more efficient to collect the thoughts into a post – so I can simply link to it in future : )

Is understanding “math” behind FEA important?

This is a very important question I think. Whatever you think about it at least a LOT of your time is at stake!

It doesn’t really matter if you are just starting with FEA or you want to go into nonlinear or explicit analysis. If there is something new you want to learn there is a choice you need to make:

Do I want to learn math and theory or not?

Whatever is your answer, learning that theory, understanding match etc. is a very time-consuming task. Which most likely mean it makes sense to consider if it is even needed : )

Below I want to show you how I think about it, and put some arguments forward. Bear in mind that this is not an “ultimate” answer but rather my approach to things. Most likely it comes from my past experiences, philosophy and who I am.

I write this with a bit of courage though, as a few months ago I asked several of very good FEA experts about this. I asked them without showing my position on it (not to suggest anything) and it seems most of them agreed with my opinion.

However, I don’t want to convince you about this – much rather I would love to know your opinion! It would be great if you could share your thoughts on the matter in the comments below!

Cars, calculators, computers and other tools

To start with the topic I think it is best to say that FEA is a tool. A very complex one, but still it serves a purpose and you use it.

What you want from FEA is to model something correctly, and obtain results that interest you. This can be anything from stresses to vibration frequencies. I don’t want to go into specifics here. What is important is the “process”:

FEA works like this:

  • You ask a question by defining a problem, meshing it and supporting it
  • FEA solves your problem and give you an answer
  • You interprete the answer

To this end, it is exactly like using a calculator!

You define the problem by punching it in, calculator solves the problem and then gives you an outcome. It’s up to you what you will do with the outcome.

How does calculator work?

Ach, this is one of my favorite questions… I don’t know!

I’m using one each day, but I would not be able to build it, fix it or even explain to my kids how it operates! I understand that this has something to do with a lot of “zeros” and “ones” but that is about it. I’m a civil engineer and I wouldn’t be able to build a single logic gate if my life depended on it!

The same goes for my car, or the computer I’m using right now… things just work (i hope!).

So the important question arises – is the knowledge of how things work important?

The answer is obvious: of course, it is!

But there should be a second question here which is: to whom?

And this is a bit more difficult : )

Do you want to manufacture calculators?

I think that how things work is a very important knowledge… to people who want to make those things.

To drag the example a bit more, if you like to manufacture calculators it is critical to understand how they work! But is it that important in using them? I dare to disagree… after all, I do use mine and so far nothing bad happened 😛

The same goes for cars (nope, I’m not this kind of guy who can build their own car from few screws and board), computers and the rest of what surrounds us.

I’ve read somewhere, that there is not a single person on the planet who knows how to make a computer mouse. Ranging from plastic injections to optics and electronics the scope of knowledge to gain is simply too big!

And yet… we all use one, don’t we?

Let’s get back to FEA shall we : )

The understanding math behind FEA, all those algorithms and equations is critical… if you want to write your own solver. This is an incredibly difficult field (for complex nonlinear problems at least), but definitely a path to consider. Is there a business there to be made? I have no idea – this is not my path!

If like me you want to use FEA as a tool in design things are a bit different. I think in such case it makes no sense to learn how FEA works with great details. Just as with calculator it is far more important to know what questions to ask and how to interpret outcomes!

Sure I will make few benchmark tests to see if the FEA soft I’m using “actually works” – but this is a completely different thing that checking equations manually…

Just be aware that “not learning how math works” does not mean you can simply ignore the method completely. There are things like “stress averaging” or “convergence” that you need to be aware of to correctly interpret results. You don’t have to solve the math, but being aware of the potential traps is very important!

Why things are as they are?

I think this “quest” to learn theory comes from universities. After all, the theory is something that is easiest to teach. And since no one likes to look bad it is better to say that this is the most important thing there is! (let me just once more say that it really is the most important thing… if you want to create your own solver!). You know organizing laboratories for all students taught by experience designers sounds nice! But since each design takes weeks to do (not to mention teaching in the process!) it is more or less impossible to organize. Even if there would be a will to do so…

I think that “understanding math” and “designing with FEA” are two completely different paths. While creating your own solver must be fun (och, I would love to know that all!) there is also a lot you need to know about design.

The design is neither easier or more difficult than “math” in FEA… it’s just a different skill set!

You don’t solve equations but instead, you will have other problems. The things like “how to support my model so it makes sense” or “how to interpret outcomes”. Those things don’t get any easier with understanding math I’m afraid. Not to mention all the additional things you need to know to design something with FEA from “what failure modes should I check” to “what are the code requirements”.

Sure that there is an overlap here, but if you want to practically use FEA I would focus far more on practical aspects of it! Sadly there are not a lot of materials and courses teaching that… which is an additional problem (and hopefully a chance for me and my blog!).

I hope this gave you something to think about! As I wrote at the beginning I don’t aim to convince you, but simply to provoke some considerations. I would love to know what you think about it. Share your ideas in the comments below, so we can further discuss this!

Want to learn something practical about FEA?

This is great! I have 2 different free courses on FEA. You can get them below (two at once might be an overkill, so maybe pick the one that interests you more or do them one by one : P)

Free FEA essentials course!

Free nonlinear FEA course!


  1. Gaurav December 5, 2017 at 1:52 am - Reply

    As usual Lukasz, you took a problem we face and solved it at grass-roots level. Do you solve engineering problems the same way?

    • Łukasz Skotny December 5, 2017 at 8:16 am - Reply


      Well, I always try to look at things from the basic point first, but since I really enjoy FEA I tend to sometimes overcomplicate what I do simply for the “fun” I guess 😛

      Thanks for writing, I really appreciate that 🙂

      All the best

  2. John K. Shebuski December 6, 2017 at 5:13 am - Reply

    I think learning how to perform a basic 3 or 4 element solution from scratch is important, especially if you want to advance and add to your engineering analysis toolbox. It also helps you learn to choose the best elements.

    • Łukasz Skotny December 6, 2017 at 7:33 am - Reply

      Hey John!

      Thanks for the reply!

      I can see where you are coming from – definitely a good point.

      I admit that when it comes to element selection I try to do benchmarks on bigger problems instead… what do you think about such approach?

      All the best!

  3. Pavel Manolev December 7, 2017 at 7:30 am - Reply

    Recently we had one particular case, where we needed to go deeply into math behind the software (and to understand it), to find out what input and how it need to be inserted. The main problem was what theory in this area is still not well developed ans, let say, standartised. However it is one special case that, and
    I will agree that ussually we do not need to know how the solver works.

    • Łukasz Skotny December 7, 2017 at 7:48 am - Reply

      Hey Pavel!

      This is a great example! Indeed when something is “new” such approach makes so much sense! I have never been in a situation like this before, but I can totally see the merits!

      Awesome point Mate!

      All the best

  4. Peter Bartholomew December 27, 2017 at 10:03 pm - Reply

    Do you need to know the math behind FE? It is possible to work on the basis of a more empirical understanding and there are limits to how much knowledge might be expected of any individual. It may be more important to understand the practical limitations of the manufacturing processes available to you, for example.

    That said, an understanding of the mathematics underpinning FE makes the method far more logical and predicable. There is no harm in understanding convergence rates, variational principles etc. The math merely provide concise descriptions of phenomena you will have to come to terms with anyway.

    • Łukasz Skotny December 27, 2017 at 10:10 pm - Reply

      Hey Peter!

      Thank you for the comment! I think you really neatly wrote something important here!
      It is true that there is a practical limit to what you can learn in a year or 10, and at some point, choices have to be made.

      I agree that knowing “all the math” helps – there should be no doubt about that. But as you pointed out there are other things that may help you even more.

      Thank you for taking the time to write this : )

      All the best

  5. Satya January 8, 2018 at 8:13 am - Reply

    Hi there!

    I find it an interesting conversation on FEA. But often when you see FEA analysts with a passion for solving complex FEA problems sometimes fail to understand simple cantilever beam or simply supported beam.

    I support your statement on knowing the math behind the FEA is always helpful. Although learning complex math is difficult, at least its better to have a basic understanding of it.

    • Łukasz Skotny January 8, 2018 at 8:45 am - Reply


      I agree that math helps. But as you pointed out complex match is well… complex : )

      I think that as you pointed out it is better to spend this time understanding and learning how things work – in the long run it should help you more : )

      All the best!

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