Shell arches are somewhat in the same category as short shells in that the shell action is subservient to the arch action. All the thicknesses can be made quite small of an arch is used because the stresses will be principally compression. The curve of the arch has to be generally a funicular form, that is, it should fit the thrust line of the applied loads. Shells are not very efficient structures if the bending moments are high, as in the folded plate rigid frame.
There are types of shells that fit in several categories. The hyperbolic paraboloidal dome is really a shell arch.