There is a lot of talk about Finite Element Analysis in engineering. Whatever you try to learn or whichever engineering field you have chosen – FEA is waiting there for you! For me, Finite Element Analysis was the tool that literally transformed my career. I’m pretty sure it can be just as important for you. So let’s talk today about what is FEA for.

At this point, I would like to express gratitude to my friend Piotr, who had a great discussion about FEA with me. His point of view on this matter is incredible, as you will soon learn ðŸ™‚

#### Finite Element Analysis (FEA) is a tool

FEA is used mostly by engineers to solve engineering problems. As a tool, it helps us to solve problems faster and with less effort.

To discuss these further let’s take a look at what are engineering problems and how we can solve them.

#### How you can solve an engineering problem

Most if not all engineering problems require a model in order to solve them. You simply “model” the reality to see how the object of your interest behaves in certain conditions.

Let’s assume that we want to cross a river. Building a bridge seems reasonable, but it is simpler to cut a tree and simply walk across the river on its trunk. To me, that would be a nice engineering approach. However, that is not all – as an engineer, you will also have to decide how thick tree to cut. Cutting down a smaller tree requires less work, but there is a risk: if a tree will break you will be wet!

And this brings us to how you can solve problems in engineering.

Apart from simply trying (risky, requires all work up front, may fail), you can make a model of our “bridge” check what will happen. In general, there are 3 models for a problem:

• Physical
• Mathematical
• Numerical

#### Physical models

In the physical model we try to do a test to see what the outcomes would be. Trying our “bridge” over the river would be tricky. Of course, we could make a test on a similar tree. All we have to do is putting a “test tree” on two stones slightly above the ground. This way be can see if a similar tree will hold our weight, and if not we won’t get wet.

This is a nice approach, but it is not perfect. Tests are costly! You had to cut down the second tree after all. Usually, one test is much too little… some testing setups go in thousands of samples tested! It also requires a lab to do a test in (nowadays) – a tricky thing to pull off sometimes.

There are good sides to tests as well. I.e. you don’t have to understand something to test it. It’s irrelevant if you know the wood properties, understand the nuance of wood structure and have basic knowledge of static. Just cut the tree and stand on it!

Note that this absolutely doesn’t mean you don’t have to have specific skills to run tests. Far from it – tests are tricky to do correctly with more advanced problems. This is, however, a completely different topic…

#### Mathematical models

This is a second type of the models for engineering problems. Since tests are expensive and time-consuming we needed another way of solving problems. That way was in mathematics. By observing the world we can see the rules that govern it. With repeating tests of similar problems we can observe relations between various inputs and the final outcome. This means that we can describe reality in a mathematical way.

Thanks to this model we did not have to build a “test house” first to check if it will fail and then build a “real” house. All we had to do is to learn some design rules and follow them. Mostly this is what codes are for. We saw the relation between various phenomenon and we have described them. Now if you want to design an element you take the code (like Eurocode) and you simply search for mathematic rules that govern this case.

The thing is… those tend to be more and more complicated. We want our outcomes to be more specific, touch the problem with several different disciplines in mind. We want to take into account new factors that we learn about etc.

The mathematical model can always be solved with pencil and paper. But nowadays engineering problems are so complex that often there is not enough paper in the office to solve a problem (not to mention the workload). We analyze more and more complicated problems, and we want the outcomes as fast as possible.

This is why we created the third kind of the model:

#### Numerical models

With the complexity of math problems calculating everything by hand required enormous effort. But computers came around and they do math operations at a speed that is currently unmatched. There was a problem, however – we must describe to the computer what problem we wish to solve. We have to tell what is the issue, and what outcomes interest us.

This is how engineers have developed several approaches to implementing problems. Simply out of the need to show computer what to calculate. Finite Element Method is one of those approaches – currently the most popular one. It allows us to implement the problem as a numerical model, so we don’t have to solve it by ourselves.

Of course such implementing (as any programming in general) is governed by a lot of rules. You need to know what to model and how. Which parts are important, what can be done and what cannot etc. This makes FEA somewhat hard to learn at the beginning – simply because it can be overwhelming at the start. However, if you dig deep enough there is literally no limit to what you can solve with this method ðŸ™‚

#### To sum it up

Knowing that there are 3 models for each problem the reason for FEA becomes quite clear. You don’t have to run tests a lot of the times. There is no need for complex mathematics and time-consuming hand calculations. When you implement an engineering problem with Finite Elements computer will solve it for you.

Note however that FEA is not the “ultimate” answer. Each of the models has its uses:

Respect the math!

There is no point in solving something in FEA when you have a simple math rule that gives specific, correct outcome.In such cases, modeling is a pure waste of time. Be aware, as this is a very tempting possibility. I suspect that a lot of analysis performed now are completely unnecessary. You can obtain outcomes for those problems from simple math rules at a fraction of cost and effort. FEA makes some people lazy. Since it can answer almost any engineering question people tend to forget about other models that are available… and often waste time and resources!

Physical tests are needed.

It is really easy to say, that with FEA you don’t need them at all. This is not the case, however. Sure, if you want to optimize a structure, then doing a lot of physical tests rarely makes sense. Also if you are doing a model with well-known materials and uses, FEA is your friend. Be aware however that most of the information you include in FEA (material models/parameters values etc.) is strongly based on physical tests.

You can’t “discover” Young Modulus with FEA. Such parameters have to be tested and then implemented. Also if there is a new phenomenon to be discovered (like bizarre material property in high temperature), FEA is almost defenseless! First, you should discover the phenomenon, and then create the model or set of parameters that will make it possible to take that into account in FEA. This means that if you are doing something “new” with new materials or conditions, physical tests most likely will be needed!

Tying it all together makes it perfect!

This is why I think it is worth understanding this. FEA is tricky to use and requires enormous experience. In many cases, you will use physical tests to “calibrate” the model. You make a limited amount of testing and reproduce the tests outcomes with FEA. When everything matches between numerical and physical tests you know that the method you are using works and that the assumptions you made in FEA work properly.

Now instead of making enormous amounts of lab tests you can make additional numerical calculations. Usually, numerical models are faster and cheaper than laboratory tests. At that stage (with all the numerical models done) you have so much information, that you can build a mathematical model. This way in future for similar problems you won’t have to do FEA! A simple math will do (assuming that simple math model is possible in your case). Such use is the power of understanding what each of the models is for!

Without a doubt, FEA is a great tool and it is very often used nowadays. I’m very fond of this method because the knowledge about it literally changed my career! I foresee that FEA will be even more popular in the future until we figure out a different way to model our problems or a completely different approach.