how to unfold a spherical metal sheet by segment
In Solidworks 2015 and greater complex surfaces can be flattened. There are some youtube videos demonstrating the functionality, unfortunately I'm still running 2014 so I can't be much more specific. It's in the 'surface' feature set.
If you already have a solid model of a segment, you can probably 'knit surface' on the segment to generate the surface feature you intend to flatten, 'flatten' it, and then 'thicken' it to get a 3d flat pattern.