How to make this deceptively simple 3D shape?

If you want to stick with After Effects try creating a shape layer with the side view of your gondola. The one in the center of drawing 1. Just do the outline. Next, create your animation with a camera move but don't worry about only having one surface. When you are done, save the AEP file, select the Comp and choose File/Export/Maxon C4D file.

This will give you the AE camera and the shape that you can extrude and texture, and even make windows in C4D lite. I don't have time to show you screenshots and a true step-by-step. On one of these days, I should do a tutorial. I export 3D shape layers and 3D text layers all the time to C4D files. 

The other option, and one that is free, would be to go to http://blender.org and download Blender. It is an incredibly powerful open source (means free) 3D program used by many professionals and it integrated amazingly well with After Effects. You can get some truly amazing results if you spend a few hours using their free training tutorials. I use Blender all the time. 

AE is not a 3d software so there is not way to make this elegant.

You can fake the perspective using shape layers (or disort effects, puppet pins, whatever) and animating the paralax. Or you can create the funicular as acutal 3d model and insert it as 3d object using cinema4d.

*Martin

The built in 3D modelling capabilities in AE are not very powerful, and really just designed to build and distort primitive 3D objects like planes, spheres and cylinders.  I'm not saying it won't work for you, but it may be a bit tedious and frustrating, compared to a genuine 3D modelling tool like Cinema 4D or Blender.

The key will all be in the mathematics.  The curvature of your side panel has to be uniform, ie it can't curve more steeply at the base than the top, which it appears to in your sketch.  For example, if your side panel's curvature is 70 degrees, then you'll need to draw the front panel's rounded edge with exactly that curvature along the edge in order to marry the two objects - or manually mask it once the side panel is in place, I suppose.

I tried to roughly mock up what you're doing - see the GIF below - and you'll see already there are some visible errors along edges where the mathematcs is not perfect.   Stick to the maths religously and you might get what you're after, but otherwise consider using a real 3D tool to build your model.