“FEA world” should be divided into two parts when considering this problem: you are either an FEA mechanic or an FEA driver
If you intend to code your own solver (aka “the FEA mechanic”) then, by all means, you need to know all of the math. If you succeed let me know, so I will envy you your skill set a bit ; )
If you want to design stuff with FEA (aka “the FEA driver”) you don’t really need all the maths – you just need the basic understanding of how things work. Far more important in this case is the “engineering judgment” and skills related to outcome estimation. Those are usually difficult from the engineering standpoint, but no complex math is usually involved.
Both Tony and I believe that you can be good at practical FEA design without knowing how most of the algorithms work : )
Oh, and BTW… as far as I managed to check the “typical” breaking distance at 50mph is around 5 London buses (including “thinking distance”). You can read more here, but the typical length of the London bus must be verified separately (it’s around 10m as Google suggests).
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I have over 10 years of practical FEA experience (I'm running my own Engineering Consultancy), and I've been an academic teacher for a decade. Here, I gladly share my engineering knowledge through courses, and on the blog!