I found in this magazine the statement "[...] ruled surfaces are statically efficient, especially in the case of skewed ruled surfaces, which are very stable due to a generally negative Gaussian curvature".
Why would a negative Gaussian curvature imply (or help with) the stability of a surface? I did not find a mathematical argument for the claim in the magazine, nor any mention of the same fact elsewhere. Is it really true?
I'm interested in this question because I'm studying ruled surfaces (which have non-positive Gaussian curvature) and their applications in architecture and product design in general, and if such surfaces have strength or stability advantages, I'd be very interested to know.
Imagine a sphere. It's easy to see how one can make a dent by pushing it inside. However, it's harder to make a dent by pushing the sphere from inside. You would need to stretch the material, instead of bending it. And bending modulus is way smaller than expansion modulus (meaning, you can bend metal wire, but good luck stretching it).
The surfaces with negative curvature are stable, because no matter where you push, there is always a direction, for which this push is from inside, requiring stretching. You cannot easily dent such surface.