Found another cool website&company called Enterfea

Hi guys, and gals! You may remember one of my posts a few weeks ago…You keep tabs on my work, don’t you? If you don’t, please do so by typing your email address into one of those nice little pop-ups about me newsletter, or simply by clicking here.

…where were we? Oh yeah, the post!

This one here. My review about FEAforAll, a blog-like resource site on finite element analysis (FEA). Since writing that piece there, I have found several cool new sites. All somehow related to numerical analysis, and all approaching it from their own interesting angles.

And now, I’m sharing my findings with you.


The first on my list is Enterfea.

Enterfea logo. Taken from their website - I believe I'm using it constitutes fair use.
Enterfea logo. Taken from their website – I believe me using it constitutes fair use.

Enterfea is a company and a website, owned and maintained by one Łukasz Skotny. I’ve had the pleasure of making Łukasz’s acquaintance on LinkedIn, and he seems like a really nice fellow and all-around good guy. He has a passion for education and learning both.

The only complaint I have about him is the fact that I have to copy-paste his first name everywhere – I have no idea that barred L-thingie. The closest I can manage is a stricken-through L. But then, my surname demonstrably also gives people headache, so maybe we’re even. And I digress a lot.

Back on track. Enterfea has a quite a strong focus on steel structures, especially those of the nonlinear kind.

Same but Different

Talking about nonlinear analyses – those are whole different beasts for mechanical engineers compared to us electrical people. Nonlinearity in electromechanics is fairly standard – iron parts saturate with high magnetic flux densities. This is often modelled by a single-valued BH-curve like the one below.

The familiar kind of the Pareto principle for us electrical engineers.

In reality, the situation is slightly more complicated than this due to the hysteresis phenomenon. So, instead of a single curve we have a hysteresis loop like this at least with sinusoidal supply. Kinda like two single-valued saturation curves placed near each other. That’s in steady-state by the way, it usually takes a few periods to reach something like this.

I no longer need Matlab for plotting. Paint for the WIN!
I no longer need Matlab for plotting. Paint for the WIN!

There might be some minor loops, too, but my point still remains: we stay around the same region.

Not so much in mechanical engineering. There, nonlinearity is quite often related to plastic deformation – meaning it’s nonlinear. In curve form, it looks like this:

Edited after Moondoggy; original and license here.
Edited after Moondoggy; original and license here.

The blue part is linear and reversible. But, once we enter the green nonlinear region, we lose the reversibility: we are causing permanent damage to the material. Go far beyond that, and it fractures.

Also, you can notice that the curve evens out long before the fracture. In other words, it sort of gives up, stops trying, and ceases to resist the deforming force.

Bearing all this mind it’s easy to draw the logical conclusion: nonlinear analysis is difficult in mechanics.

But Enterfea is doing a great job at making it more accessible. Check for instance this post here for some common errors.

Note: the closest equivalent we have in electromagnetics are permanent magnets. Those can get demagnetized, but even then the behaviour is closes to the hysteresis loop I made for you, rather than the mechanical yielding curve below it. Additionally, modern permanent magnets pretty much have to be nuked for any demagnetization to occur. Except for Alnico magnets – those get damaged from the luxury of simply existing.

It gets worse

Additionally, nonlinearity in structural FEA is not limited to material characteristics. Also the geometry itself can behave in a nonlinear fashion.  In some way.

Since this quite a new thing for me too, I’ll let Enterfea do the explaining in their own words. So, apparently geometric nonlinearity is about how “deformations of the model can have big influence on force distribution and further deformations”.

A string tied from its ends is used as an example, also illustrated below. The left subfigure is from linear analysis. As you can see it’s fully unrealistic: the string behaves like a loose spring. By contrast, the right one is from geometrically nonlinear setup.

But, for better understanding I recommend you read the post (simply click the figure above and it’ll open). They’ll do a much better job at explaining than I can right now.

Indeed, geometric nonlinearity is something we don’t really have in electromechanics. Well, we do have magnetostriction – magnetic field causing strain in the material, but the displacements are usually so small that the coupling back to magnetics is close to negligible. An exception might be giant magnetostrictive materials, but those are pretty much in their infancy. And the striction is by no means giant, it’s just bigger than in other materials. But, other kind of magneto-mechanically coupled phenomena can be quite significant indeed – something our group is currently researching with good progress. Just saying.

The closest equivalent to geometric nonlinearity would probably be an electrical machine under variable speed. Like starting the machine, or analysing some speed-controlled application. In those cases there’s obviously a strong coupling from the magnetic characteristics to the geometry. This is of course via the torque determining the position of the rotor in the future, and hence contributing to changes in the geometry.


Feel like you know nothing about mechanical stuff no?

I certainly do.

But fear not! We, my dear readers, are in luck!

Enterfea also does courses and consulting.

Which is all kinds of awesome.

Firstly, there’s that learning aspect I mentioned. Secondly, I’m also considering doing the same thing. Meaning courses or consulting, or maybe both. So, if you have any good ideas or topics, let me know!

Also, if you have any course topics for Enterfea, let them know by clicking the link above and using their contact form there. They are offering both dedicated and open courses, as well as possibly online ones.


The other website I mentioned is by one Peter Lyu. I found it after a recommendation from a colleague of mine, and it seems impressive indeed.

The site focuses on aerodynamics, which is by no mean s an expertise of mine. Thus, I won’t even attempt to do any kind of deep analysis.

Instead, I took a liberty of stealing one of Mr. Luy’s figures here:

Copyright belongs to Peter Lyu, but I believe me using the figure here for promoting him constitutes fair use.
Copyright belongs to Peter Lyu, but I believe me using the figure here for promoting him constitutes fair use.

Also he has a blog and a list of publications I’m really envious about.

That’s all for today. Have an idea about what I should cover next?

Hit me a comment!


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Don’t Miss out on These Resources: Enterfea and Peterlyu

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