To the problem of 2D calculations: I have every time a thickness. In the case of a uniform thickness You could eliminate it by 1 and transform the loads etc. The practical sense for the thickness is a simulated Z-coordinate in stress calculations. In the book of Zienkiewicz, 3th edition, page 110, You could find an example of a buttress dam, where the foundation is plane strain and the dam is plane stress of variable thickness, quasi defined as Z-coordinate. But You could also use it in the case of acoustic or dynamic calculations as example for a violin bridge, which is smaller on top and thicker on the base. So You don't need a 3D calculation. The book of Zienkiewicz is quasi a standard for FEM. In ABAQUS, CALCULIX, ANSYS, TOPAS etc. its also seen in this context. I hope I could give You an idea for the sense of the thickness !
