Part of the question is whether you intend to describe form or function, and I think few would argue that form is really what you're interested in: that is, the actual shape of a part, rather than how it's used, because the latter is endlessly variable.
The problem is that many of the proposed terms have intrinsic meanings of function. For example, an arch has a particular structural purpose, which is derived from and relative to its shape, but there are certainly parts that have arch-like shapes that are coincidental to their possible function as arches. Some of these might be currently classified as "bow" or "mudguard" or similar terms.
"Corner" is another example: the original corner piece was the 700H corner brick, basically two 2x4 bricks fused at a right angle. Over the years, this gave rise to a number of other parts whose use may have been originally "intended" as corners, but also any number of other parts whose use as such may be incidental.
I guess what I'm getting at is that, since you're describing form, you'd want to avoid terms the connote function. However, this is hard to do because almost every new element does have some kind of original, intended function; furthermore, the element's form can often be described far more intuitively using a functional label, but this doesn't always apply to every element that fits into the same category with respect to its form. To really have a comprehensive system of nomenclature, you have to have a non-trivial consideration of the history of the system as a whole; otherwise you end up with terminology so dry and empirical that it isn't really any more descriptive than pure element numbers.
The problem is that many of the proposed terms have intrinsic meanings of function. For example, an arch has a particular structural purpose, which is derived from and relative to its shape, but there are certainly parts that have arch-like shapes that are coincidental to their possible function as arches. Some of these might be currently classified as "bow" or "mudguard" or similar terms.
"Corner" is another example: the original corner piece was the 700H corner brick, basically two 2x4 bricks fused at a right angle. Over the years, this gave rise to a number of other parts whose use may have been originally "intended" as corners, but also any number of other parts whose use as such may be incidental.
I guess what I'm getting at is that, since you're describing form, you'd want to avoid terms the connote function. However, this is hard to do because almost every new element does have some kind of original, intended function; furthermore, the element's form can often be described far more intuitively using a functional label, but this doesn't always apply to every element that fits into the same category with respect to its form. To really have a comprehensive system of nomenclature, you have to have a non-trivial consideration of the history of the system as a whole; otherwise you end up with terminology so dry and empirical that it isn't really any more descriptive than pure element numbers.